A triangle has its height of 12 cm and hypotenuse of 15 cm. Find its base.
Answers
h^2 + b^2 = c^2
where h is the height, b is the base, and c is the hypotenuse.
Substituting the given values, we get:
12^2 + b^2 = 15^2
144 + b^2 = 225
Subtracting 144 from both sides, we get:
b^2 = 81
Taking the square root of both sides, we get:
b = 9
Therefore, the base of the triangle is 9 cm.
Related Questions
Help pls !!! Find the measure of the side indicated. Simplify your answer and write it as a whole number
Answers
Check the picture below.
Alice has been in a defined-contribution pension scheme since she was 35 and will retire in one year’s time at age 66. Her salary is currently £55,000. Throughout her enrolment in the scheme, she has paid in 8% of salary, and this has been topped up by employer contributions and tax relief worth 4% of salary. She will also qualify for a state pension of £9,000 per year.
If Alice uses her whole pension fund to buy an index-linked annuity, how much income will she receive in her first year of retirement?
Answers
To calculate the income Alice will receive in her first year of retirement, we need to consider her pension fund, the state pension, and the annuity rates.
Given: Alice's salary: £55,000
Her contributions to the pension scheme: 8% of salary
Employer contributions and tax relief: 4% of salary
Retirement age: 66
State pension: £9,000 per year
First, let's calculate Alice's pension fund. She has been in the scheme from age 35 to 66, which is a total of 31 years. During this period, she has made contributions of 8% of her salary, topped up by 4% from the employer and tax relief. So, her annual contributions are (8% + 4%) of £55,000 = £5,500.
Her total pension fund would be £5,500 x 31 = £170,500.
Next, let's consider the annuity rates. Annuity rates determine the income that can be purchased with the pension fund. The rates vary based on factors such as age, gender, and prevailing market conditions.
Using the annuity rates, Alice can calculate the income she will receive from her pension fund. Let's assume the annuity rate is 5% per year. So, the income from her pension fund would be £170,500 x 5% = £8,525.
Finally, we add the state pension to calculate Alice's total income in her first year of retirement:
Total income = Pension fund income + State pension
Total income = £8,525 + £9,000 = £17,525.
Therefore, Alice will receive £17,525 as her income in the first year of retirement.
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a conical cup is 64/125 full of liquid.. what is the ratio of the depth of the liquid to the depth of the cup?
Answers
The ratio of the depth of the liquid to the depth of the cup is 4/5.
Geometry and Ratio
The formula for the volume of a cone is:
\(V=\frac{1}{3}\pi r^{2}h\)
where r is the radius of the base of the cone and h is the height of the cone.
When the conical cup is filled with water, there will be a difference in the radius of the water and the cup and a difference in the height of the water and the height of the cup (can be seen in the picture).
From the difference in radius and height of the water with the conical cup, a ratio can be made of similarity rule of triangle (see picture).
If the radius of water is \(r_{1}\) and the height of water is \(h_{1}\), radius of cup is \(r_{2}\) and the height of cup is \(h_{2}\), so:
\(\frac{r_{1} }{r_{2} } =\frac{h_{1} }{h_{2} }\)
\(r_{1}\) with \(r_{2}\) and \(h_{1}\) with \(h_{2}\) have the same certain ratio. Let's assume the ratio is x, then it can be written:
\(r_{2}=x.r_{1} \\h_{2}=x.h_{1}\)
The ratio of the volume of water to the volume of the conical cup is 64/125, meaning that 64 of the water in the conical cup with a volume of 125.
From here we can substitute it in the volume ratio:
\(\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3} \pi r_{2}^{2}h_{2}} =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3} \pi (xr_{1})^{2}(x.h_{1})} =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{\frac{1}{3}\pi r_{1}^{2}h_{1} }{\frac{1}{3}\pi r_{1}^{2}h_{1}x^{3} } =\frac{64}{125} \\\frac{V_{1} }{V_{2}}=\frac{1}{x^{3}}=\frac{64}{125}\\ \frac{1}{x^{3}}=\frac{64}{125}\\\\x^{3}=\frac{125}{64} \\x=\frac{5}{4}\)
The ratio between the radius and height of the cup and the water is 5/4. This means that the ratio between the radius and height of the water and the cup is 4/5.
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select the most correct statement below that describes the differences between type 1 and type 2 hypervisors?
Answers
A type 1 hypervisor functions as a compact operating system and runs directly on the host's hardware, but a type 2 hypervisor operates as a software layer on operating system, similar to other computer programs.
Which is the safer hypervisor, type 1 or type 2, and why that is more superior?
Native hypervisors are a safer solution. They are not dependent on the underlying OS, unlike hosted hypervisors. If you are attacked, the bare-metal hypervisor will improve your chances (Type 1). Because of this reliance, the type 2 server loses efficiency, performance, and speed. A Type 1 hypervisor operates directly on the hardware of the host computer. These hypervisors interface directly with the host computer's CPU, RAM, and physical storage, making them typically quicker and more effective than Type 2 hypervisors. eliminate the requirement to travel through the OS layer.
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PLS HELP DUE AT 5:00 pm
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If someone returns an item for 15 dollars and buys a nother idem for 15 dollars
Answers
The net effect on someone's overall spending after returning an item for 15 dollars and buying another item for 15 dollars will depend on the store's return policy regarding returns and exchanges
If someone returns an item for 15 dollars and then buys another item for 15 dollars, the net effect on their overall spending will depend on the store's policy regarding returns and exchanges.
If the store offers a full refund for the returned item, the person will essentially receive back the 15 dollars they spent on the original item. If they then purchase a new item for 15 dollars, their overall spending will remain the same.
However, if the store charges a restocking fee or only offers store credit for returns, the person may not receive the full 15 dollars back. In that case, their overall spending would increase by the amount of the restocking fee or by the difference between the refunded amount and the original purchase price.
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The given question is incomplete, the complete question is:
If someone returns an item for 15 dollars and buys another item for 15 dollars, what will be the net effect ?
what is the height of the lighted obstacle approximately 6 nautical miles southwest of savannah international
Answers
The lighted obstacle approximately 6 nautical miles southwest of Savannah International Airport is the Juliette Low Bridge. The bridge has a clearance height of 185 feet above the water, which is equivalent to approximately 56.4 meters. It was named after the founder of Girl Scouts, Juliette Gordon Low.
The bridge has a vertical clearance of 56.4 meters, which is enough for most vessels to pass underneath safely. The Juliette Low Bridge was built in 1954 as part of the Truman Parkway and carries westbound traffic over the Wilmington River. It is also known as the Thunderbolt Bridge.
The bridge is illuminated at night, making it visible to pilots flying over the area. It serves as a vital navigation aid for aviators approaching the airport from the southwest. In conclusion, the height of the lighted obstacle approximately 6 nautical miles southwest of Savannah International Airport is the Juliette Low Bridge with a clearance height of 185 feet or approximately 56.4 meters above the water.
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the radius of a circle is increasing at a constant rate of 7 feet per minute. at the instant when the radius of the circle is 44 feet, what is the rate of change of the area? round your answer to three decimal places.
Answers
The rate of change of area as calculated from the data given is 1934.24 cm^2 / min.
A = A(r)
r = r(t)
A = A(r(t))
Using chain rule to solve this problem we get ,
rate of change of area as ,
dA/dt = (dA/dr)(dr/dt)
A = πr2
⇒ dA/dr = 2πr
dr/dt = 7 cm/min [given]
(dA/dt) = (2πr)(7 cm/min)
When r = 44 cm,
dA/dt
= 2π (44 cm) (7 cm/min)
≅ 1934.24 cm^2/min.
The chain rule is the formula used to determine the derivative of a composite function, such as cos 2x, log 2x, etc. Another name for it is the composite function rule. Only composite functions are subject to the chain rule.
Therefore, before beginning the chain rule formula, let's examine what a composite function is and how it may be distinguished.
Another chain rule formula looks like this:
(f(g(x)) = f' (g(x)) g') = y' = d/dx (x)
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A group of students were asked about their majors. Let B= Biology majors and M= math majors, Given r1 = 47, r2 =1, r3=4, & r4=7
Answers
a. The number of student surveyed is = 12 + 7 - 4 + 47 = 62
b. The number of student that are math major but not biology major = 7
c. The number of student that are neither math major nor biology major = 47
d. The number of student that are both math and biology major = 4
The mean weight of an adult is 68 kilograms with a standard deviation of 10 kilograms. If 128 adults are randomly selected, what is the probability that the sample mean would be greater than 70.3 kilograms?
Answers
The probability that the sample mean of 128 adults is more than 70.3 kilogrammes is about 0.08%.
We can utilise the Central Limit Theorem to tackle this problem, which stipulates that given a high sample size, the distribution of sample means will be approximately normal, regardless of the form of the population distribution. The sample means' mean will equal the population mean, and the sample means' standard deviation (also known as the standard error) will equal the population standard deviation divided by the square root of the sample size.
Given that the population mean is 68 kilogrammes and the population standard deviation is 10 kilogrammes, the chance that the sample mean of 128 adults is more than 70.3 kilogrammes must be calculated.
To begin, we first compute the standard error of the sample means:
Standard Error = Standard Deviation of the Population / Sample Size
= 10 / √128
= 0.8839
The z-score formula may then be used to calculate the z-score corresponding to a sample mean of 70.3 kilogrammes:
(sample mean - population mean) / standard error = z
= (70.3 - 68) / 0.8839
= 3.15
We may calculate the likelihood that the z-score is greater than 3.15 using a conventional normal distribution table or a calculator. Because the standard normal distribution is symmetrical, the likelihood of the z-score being more than 3.15 is the same as the likelihood of the z-score being less than -3.15.
According to a conventional normal distribution table, the probability associated with a z-score of -3.15 is roughly 0.0008.
As a result, the chance that the sample mean of 128 adults is more than 70.3 kilogrammes is roughly 0.0008, or 0.08%.
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The probability that the sample mean of 128 adults would be greater than 70.3 kilograms is approximately 0.0008, or 0.08%.
To solve this problem, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. The mean of the sample means will be equal to the population mean, and the standard deviation of the sample means (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size.
Given that the population mean is 68 kilograms and the population standard deviation is 10 kilograms, we need to calculate the probability that the sample mean of 128 adults is greater than 70.3 kilograms.
First, we need to calculate the standard error of the sample means:
Standard Error = Population Standard Deviation / √Sample Size
= 10 / √128
= 0.8839
Next, we can use the z-score formula to find the z-score corresponding to a sample mean of 70.3 kilograms:
z = (sample mean - population mean) / standard error
= (70.3 - 68) / 0.8839
= 3.15
Using a standard normal distribution table or a calculator, we can find the probability that the z-score is greater than 3.15. Since the standard normal distribution is symmetrical, the probability that the z-score is greater than 3.15 is the same as the probability that the z-score is less than -3.15.
From a standard normal distribution table, we find that the probability corresponding to a z-score of -3.15 is approximately 0.0008.
Therefore, the probability that the sample mean of 128 adults would be greater than 70.3 kilograms is approximately 0.0008, or 0.08%.
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Which of the following equations are an example of direct variation? a. equation image indicator b. equation image indicator c. equation image indicator d. equation image indicator
Answers
The examples of direct variation are;
equation image indicator. Option B and D
What is direct variation?Direct variation is a type of variation such that the variables proportionally increases or decreases.
As one of the variable decreases, the other decreases and as one increases, the other increases.
From the information given, we have that;
For option B:
The equation image indicator does represent direct variation because it can be simplified to y = 2x, where the constant k is equal to 2.
Also, for option D the equation image indicator represents direct variation because it can be simplified to y = -3x, where the constant k is equal to -3.
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Find the absolute maximum and minimum values of the following function on the given interval. If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.
\(f(x)=2(x^2-1)^3, [-1,2]\\\)
Answers
Answer:
go on googl and search this question
Select the third function, y = 2 cos(x), and set the interval to [−4.02, 4.02]. (a) With 10 rectangles using left endpoints, how many rectangles are contributing negative area values to the estimated net area? Correct: Your answer is correct. How many are positive? Is this the same as when using midpoints? (b) What is the error when using midpoints with 10 subintervals? (Do not round your answer.)
Answers
(a) With 10 rectangles using left endpoints, 5 rectangles are contributing negative area values to the estimated net area. This means that the function is below the x-axis in those intervals.
The remaining 5 rectangles are contributing positive area values, as the function is above the x-axis in those intervals.
When using midpoints, the number of positive and negative rectangles may not be the same. It depends on the behavior of the function within each subinterval. The use of midpoints can result in a different distribution of positive and negative rectangles compared to using left endpoints.
(b) The error when using midpoints with 10 subintervals can be determined by calculating the difference between the estimated net area using midpoints and the actual net area.
To calculate the error, we need to evaluate the definite integral of the function over the given interval and subtract the estimated net area using midpoints.
Error = Actual Net Area - Estimated Net Area using Midpoints
Since the exact values are not provided, the specific error value cannot be determined without further information or calculations.
Using left endpoints with 10 rectangles, 5 rectangles contribute negative area values and 5 contribute positive area values. When using midpoints, the distribution of positive and negative rectangles may differ. The error when using midpoints can be calculated by subtracting the estimated net area using midpoints from the actual net area, but the exact error value cannot be determined without further information or calculations.
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Systolic Blood Pressure (SBP) of 13 workers follows normal distribution with standard deviation 10. SBP are as follows: 129, 134, 142, 114, 120, 116, 133, 142, 138, 148 , 129, 133, 140_ Find the 99%0 confidence interval for the mean SBP level: (124.84 (129.84 (126.84 (125.84 139.16) 139.16) 137.16) 138.16)
Answers
Answer:The 99% confidence interval is
To find the 99% confidence interval for the mean systolic blood pressure (SBP) level, we use the formula:
CONFIDENCE INTERVAL = Mean ± Z * (Standard Deviation / √n)
Where:
Mean is the sample mean of SBP
Z is the Z-score corresponding to the desired confidence level
Standard Deviation is the population standard deviation
Explanation:
Given that the sample size is 13 and the standard deviation is 10, we need to calculate the sample mean and the Z-score for the 99% confidence level.
First, we calculate the sample mean:
Mean = (129 + 134 + 142 + 114 + 120 + 116 + 133 + 142 + 138 + 148 + 129 + 133 + 140) / 13
= 1724 / 13
≈ 132.62
Next, we need to determine the Z-score for a 99% confidence level. The Z-score can be found using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.
Now, we can calculate the confidence interval:
Confidence Interval = 132.62 ± 2.576 * (10 / √13)
132.62 ± 2.576 * (10 / 3.6056)
≈ 132.62 ± 2.576 * 2.771
≈ 132.62 ± 7.147
Therefore, the 99% confidence interval for the mean SBP level is approximately (125.47, 139.77).
find the indicated partial derivative. r(s, t) = tes/t; rt(0, 5)
Answers
The partial derivative rt(0, 5) of the function r(s, t) = tes/t is -e/5.
To find the indicated partial derivative, we need to differentiate the function r(s, t) with respect to the variable t while keeping s constant.
Given: r(s, t) = tes/t
To find rt(0, 5), we differentiate r(s, t) with respect to t and then substitute s = 0 and t = 5 into the resulting expression.
Taking the partial derivative of r(s, t) with respect to t, we use the quotient rule:
∂r/∂t = (∂/∂t)(tes/t)
= (t * ∂/∂t)(es/t) - (es/t * ∂/∂t)(t)
= (t * (e/t) * ∂/∂t)(s) - (es/t * 1)
= (e/t * s) - (es/t)
= es/t * (s - 1)
Now we substitute s = 0 and t = 5 into the expression we obtained:
rt(0, 5) = e(5)/5 * (0 - 1)
= e/5 * (-1)
= -e/5
Therefore, rt(0, 5) is equal to -e/5.
In conclusion, the partial derivative rt(0, 5) of the function r(s, t) = tes/t is -e/5.
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tThe tall building is 1600 feet tall and 60 feet wide. Elena decides on a scale of 1 to 50 to make a model for a science project. What are the actual measurements of her model be.
A. 42 ft tall, 1.8 ft wide
B. 80,000 ft tall, 3000 ft wide
C. 32 ft tall, 1.2 ft wide
D. 32 ft tall, 1.8 ft wide
Answers
9514 1404 393
Answer:
C. 32 ft tall, 1.2 ft wide
Step-by-step explanation:
A scale of 1 : 50 means the model dimensions are 1/50 of the actual dimensions. The model width will be (60 ft)/50 = 1.2 ft . . . . matches choice C.
The model height will be (1600 ft)/50 = 32 ft. (also matches choice C)
ustomers (really groups of customers needing a single table) arrive at a restaurant at a rate of 50 groups per hour. - Customers are not willing to wait forever to get a seat. Customers will wait "Triangular (5,15,40) minutes before deciding to leave and look for another place to eat. Send reneging customers to a "Sink2" - The restaurant has 30 tables (assume a group can be seated at any available table). Service time for each group is ∼NORM(70,15) minutes. No groups are seated after 8:30pm. - Add status plots showing number of tables in use and number of reneging customers. Run interactively to see behavior (suggest speed factor of 7 to 8) - Run 30 replications of an evening shift 5-10pm (no warmup). - Document the following in the Word doc: - \% utilization of the tables? - How many customer groups were served on average over the evening shift? - On average, what was the wait time for customer groups before being seated? - On average, how many customer groups reneged? What percentage of all arrivals reneged? - Suppose it costs $6/hr for each additional table added to the restaurant. The profit per customer group served is $45. Is it worthwhile to add additional tables? Justify your answer
Answers
The restaurant has a table utilization rate of 12.02%.
On average, 1223 customer groups were served during the evening shift.
The average wait time for customer groups before being seated is 19.36 minutes.
On average, 37 customer groups reneged, accounting for 2.94% of all arrivals.
Adding additional tables is worthwhile, as the net profit per hour increases from $36,135 to $53,247.
Customers arrive at a rate of 50 groups per hour.
Customers wait for a Triangular (5, 15, 40) minutes before leaving.
The restaurant has 30 tables.
Service time for each group is approximately NORM(70, 15) minutes.
No groups are seated after 8:30 pm.
Status plots show the number of tables in use and the number of reneging customers.
30 replications of an evening shift from 5 pm to 10 pm are run.
A) % utilization of the tables: The % utilization is 12.02%.
B) Average number of customer groups served: 1223.
C) Average wait time for customer groups before being seated: 19.36 minutes.
D) Average number of customer groups that reneged: 37, representing 2.94% of all arrivals.
E) Adding an additional table is worthwhile, as the net profit per hour is $53,247 compared to the current profit per hour of $36,135.
In summary, the % utilization of tables is 12.02%, with an average of 1223 customer groups served over the evening shift. The average wait time is 19.36 minutes, and 37 customer groups reneged, representing 2.94% of all arrivals. Adding an extra table is justified by the increased net profit per hour
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How do I generate equivalent expressions by combining like terms, simplifying, or factoring this? ( 4b + 8) =
Answers
Answer:
4(b + 2)
Step-by-step explanation:
Given data
The expression is
( 4b + 8)
Looking at the expression, 4 is common
factor 4 out
4(b + 2)
Hence the equivalent expression is
4(b + 2)
construct and interpret a 95 percent confidence interval for the difference between the proportion of the population who would survive at least 15 years
Answers
The 95% confidence interval for the difference between the proportion of the population who would survive at least 15 years can be used to estimate the range within which the true difference lies.
It provides a measure of uncertainty around the point estimate. The confidence interval can be interpreted as follows: we are 95% confident that the true difference in proportions of the population who would survive at least 15 years falls within the calculated interval. To construct the confidence interval, we first need to obtain sample data from the population. Let's assume we have collected data from two independent samples. From Sample 1, we find that out of n1 individuals, x1 survive at least 15 years. Similarly, from Sample 2, we have n2 individuals, with x2 surviving at least 15 years. To calculate the confidence interval, we use the formula: CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)) Where p1 = x1 / n1 and p2 = x2 / n2 are the sample proportions, and Z is the critical value corresponding to the desired confidence level (in this case, 95%). The critical value is determined based on the standard normal distribution. Once we have the confidence interval, let's say [lower limit, upper limit], we can interpret it as follows: We are 95% confident that the true difference in proportions between the two populations who would survive at least 15 years lies between the lower limit and the upper limit. In other words, there is a high likelihood that the actual difference falls within this range. The confidence interval allows us to make inferences about the population based on our sample data. It provides a range of plausible values for the difference in proportions, taking into account the variability of the sample. The wider the confidence interval, the greater the uncertainty in our estimate. Conversely, a narrower interval indicates a more precise estimation.
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Write a rational number which has no multiplicative inverse.
Answers
Step-by-step explanation:
a rational number which has no multiplicative inverse is zero(0).hope it helps.stay safe healthy and happy...Which number line plots the integers –6, –2, and 5?
A number line going from negative 6 to positive 6. Points are at negative 6, negative 5, negative 2.
A number line going from negative 6 to positive 6. Points are at 2, 5, 6.
A number line going from negative 6 to positive 6. Points are at negative 5, 2, 6.
A number line going from negative 6 to positive 6. Points are at negative 6, negative 2, 5.
Answers
Answer:
Một trục số đi từ âm 6 đến dương 6. Các điểm ở âm 6, âm 2, 5.
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Find and graph the image of quadrilateral PQRS after a dilation centered at the origin with a scale factor of 1/4. What are the coordinates of Q'?
Answers
The coordinates of point Q after dilation will be (2,-1). The correct option is B.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the coordinate is Q(8,-4). The point is dilated by a factor of 1/4.
The dilation of the point will be calculated as,
Q(8,-4) = Q'(8/4, -4 / 4)
Q(8,-4) = Q'(2, -1)
Hence the dilated point is Q'(2,-1).
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Consider the system of equations.
4x - 9y=-9
2x + 3y = 3
Which system of equations is equivalent to the given system?
Answers
Step-by-step explanation:
4x-9y=-9 1
2x +3y=3 2
1 - 2(2)
4x -9y=-9
(2)* -4x -6y=6
________
0-15y=-3
15y=3
y=3/15
y=1/5
Answer:
Hope it helps
4x-9y=9
-x+3y=6
The results of a paired-difference test are shown below to the right. d = 5.6
a. Construct and interpret a 99% confidence interval estimate for the paired difference Sd =0.25 in mean values.
b. Construct and interpret a 90% confidence interval estimate for the paired difference n=16 in mean values_ (Round to two decimal places as needed:) Choose the correct answer below:
OA This interval will contain the true population mean 90% of the time_
OB. There is a 90% chance that the true population mean is contained in the interval.
Oc: If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean: 0
D. Approximately 90% of the differences will be contained in the interval.
Answers
If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.
When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.
This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.
The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.
In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.
It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.
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Y=2x +7
Find the x interception
Answers
Answer:
Step-by-step explanation:
hello :
the x interception for Y=2x +7 when Y=0 means : 2x +7=0
so x = -7/2
Suppose "n" can't equal 0 or 1. Show that substitution v=y^(1-n) transforms the Bernoulli equation dy/dx + P(x)y=Q(x)y^(n)into the linear equation dv/dx + (1-n)P(x)v(x)=(1-n)Q(x).
Answers
Answer:v = y(1-n)dv/dx = (1-n)y-n dy/dxso dy
Step-by-step explanation:
Molly is helping her younger sister run a lemonade stand. They earn $2 for each cup of lemonade they sell. Write an equation that shows how their total earnings, y, depend on the number of cups sold, x.
Answers
Answer:
y = 2x
Step-by-step explanation:
We know
They earn $2 for each cup of lemonade they sell. So, the equation is
y = 2x
Rationalise the denominator 1/5-root 2
Answers
Answer:
the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).
Step-by-step explanation:
Correctly me if im wrong. To rationalize the denominator of the fraction 1/(5^(1/2)-2), we can use the conjugate of the denominator. The conjugate of a+b is a-b, so the conjugate of 5^(1/2)-2 is 5^(1/2)+2. We can then multiply the numerator and denominator of the fraction by the conjugate to obtain:
1/(5^(1/2)-2) * (5^(1/2)+2)/(5^(1/2)+2)
= (1*(5^(1/2)+2)) / ((5^(1/2)-2)*(5^(1/2)+2))
= (5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)
Notice that we can further simplify this expression by substituting 5^(1/2) with x and expanding the denominator:
(5^(1/2)+2) / (5^2 - 2*5^(1/2) - 4)
= (x+2) / (x^2 - 2x - 4)
= (x+2) / (x-2)(x+2)
The denominator of this expression can be further simplified by factoring out x-2, which gives us:
(x+2) / (x-2)(x+2)
= (x+2) / (x-2)(x-2 + 4)
= (x+2) / (x-2)(x^2 - 2x + 4 - 4)
= (x+2) / (x-2)(x^2 - 2x)
= (x+2) / (x-2)((x-1)(x+1))
Finally, we can use the fact that x-1 and x+1 are factors of x^2-2x, which means that we can factor out x-1 and x+1 from the denominator to obtain the fully simplified expression:
(x+2) / (x-2)(x^2 - 2x)
= (x+2) / (x-2)(x-1)(x+1)
= (x+2) / ((x-2)(x-1)(x+1))
Therefore, the rationalized form of the denominator 1/(5^(1/2)-2) is (x+2)/((x-2)(x-1)(x+1)).
The sum of two intergers is 9. Their difference is 5. What are the two intergers?
Answers
Answer: x + y = 9
x - y = 2
x = 5 + y
5 + y + y = 9
5 + 2y = 9
2y = 9 - 5
2y = 4
y = 2
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x = 9 - 2
x = 7
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Step-by-step explanation:
describe how the time of flight range and maxium height would change if the angle was shot out at originally were change to 55 degrees
Answers
Increasing the launch angle increases the maximum height. Increasing the launch angle increases the time of flight.
The starting vertical velocity determines the time in the air. Increasing the launch angle lengthens the duration in the air because steeper launch angles have a larger vertical velocity component.
The height of release and the angle of release is related. -The angle of release decreases as release height increases. - The angle of release rises as the height of release falls.
We observe that the projectile's maximum height is dependent on both initial speed and the angle of projection (), just as it is in the case of flight time. The projectile will rise to a larger height if its initial velocity is higher and its angle of projection from the horizontal is greater.
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