3 The slope of the tangent line to the curve y at the point (4, 0.75) is: . The equation of this tangent line can be written in the form y = mx + b where m is: and where b is:
Answers
The equation of the tangent line is:
y = 12x - 47.25
where the slope m is 12 and the y-intercept b is -47.25.
To find the slope of the tangent line to the curve y at the point (4, 0.75), we first need to find the derivative of y with respect to x. Let's assume that the equation of the curve y is given by:
y = f(x)
Then, the derivative of y with respect to x is given by:
dy/dx = f'(x)
where f'(x) is the derivative of f(x).
Once we have the derivative, we can evaluate it at x = 4 to find the slope of the tangent line at the point (4, 0.75). So, let's find the derivative of y:
y = f(x) = x^3 - 12x^2 + 36x - 25
Taking the derivative with respect to x, we get:
dy/dx = 3x^2 - 24x + 36
Now, we can evaluate this derivative at x = 4 to get the slope of the tangent line:
dy/dx = 3(4)^2 - 24(4) + 36 = 12
So, the slope of the tangent line at the point (4, 0.75) is 12.
To write the equation of the tangent line in the form y = mx + b, we need to find the y-intercept b. We know that the point (4, 0.75) lies on the tangent line, so we can use this point and the slope we just found to find b:
y = mx + b
0.75 = 12(4) + b
b = -47.25
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Related Questions
Nora is going to invest in an account paying an interest rate of 4.3% compounded continuously. How much would Nora need to invest, to the nearest dollar, for the value of the account to reach $7,600 in 20 years?
Answers
Answer: p≈ 3216
Step-by-step explanation:
Since 1990, when the average monthly price for basic cable TV programming in a particular region was approximately $13, the cost has risen by about $1.10 a year. (a) Write an equation in slope-intercept form to predict cable TV costs in the future. Use t to represent time in years after 1990 and C to represent the average basic monthly cost.
Answers
The equation in slope-intercept form to predict cable TV costs in the future is C = 1.10t + 13
To write an equation in slope-intercept form to predict cable TV costs in the future, we can use the given information:
Since 1990, the average monthly price for basic cable TV programming in a particular region was approximately $13, and the cost has risen by about $1.10 a year.
Let's break down the information:
The initial cost in 1990 is $13.
The cost increases by $1.10 per year.
We can use these values to write the equation in slope-intercept form, which is in the form: y = mx + b, where "y" represents the dependent variable (average basic monthly cost), "x" represents the independent variable (time in years after 1990), "m" represents the slope, and "b" represents the y-intercept.
In this case, we have:
y = mx + b
The initial cost in 1990 (b) is $13, so the y-intercept is 13.
The cost increases by $1.10 per year, so the slope (m) is 1.10.
Therefore, the equation in slope-intercept form to predict cable TV costs in the future is:
C = 1.10t + 13
Where:
C represents the average basic monthly cost,
t represents the time in years after 1990.
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Which document does one need to get permission to use a specific location for a project gmetrix.
Answers
A permit is a legal document that enables a person or a business to utilize a specific area for a project or other activity.
To obtain permission to use a specific location for a project, you may need to submit a request in writing or fill out a permission form. The exact document that you need to obtain permission will depend on the specific location and the requirements of the owner or manager of the location.
You may also need to provide information about your project, including the purpose, duration, and any potential impact on the location. Depending on the location and the nature of your project, you may also need to obtain other approvals or permits, such as building permits or environmental permits.
It is a good idea to research the requirements for using the specific location that you are interested in and to contact the appropriate authorities or individuals to find out what documents you need to obtain permission.
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In meteorology the term virga refers to falling raindrops or ice particles that evaporate before they reach the ground. assume that a typical raindrop is spherical. starting at some time, which we can designate as t = 0, the raindrop of radius r0 falls from rest from a cloud and begins to evaporate.
Answers
A variable, other than the independent variable, that appears to have influenced the dependent variable in a study is referred to as Question 2 options: a covariate. an extraneous variable. a redundant variable. an inverse bias.
Answers
In research studies, an extraneous variable refers to a variable other than the independent variable that seems to have influenced the dependent variable.
These variables are sometimes also called "confounding variables" as they can create confusion or distortion in the relationship between the independent and dependent variables.
Extraneous variables can arise due to various factors such as measurement errors, participant characteristics, or environmental conditions. They have the potential to introduce bias and obscure the true effect of the independent variable on the dependent variable. To ensure accurate and valid results, researchers need to identify and control for these extraneous variables.
One common approach is to use statistical techniques such as regression analysis to account for the effects of extraneous variables by including them as covariates in the analysis. By doing so, researchers can isolate the specific impact of the independent variable on the dependent variable, while holding constant the influence of extraneous variables.
Overall, recognizing and managing extraneous variables is crucial in research to establish a clear cause-and-effect relationship between the independent and dependent variables and enhance the internal validity of the study.
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focus groups of 12 people are randomly selected to discuss products of the yummy company. it is determined that the mean number (per group) who recognize the yummy brand name is 9.3, and the standard deviation is 0.99. would it be unusual to randomly select 12 people and find that fewer than 5 recognize the yummy brand name?
Answers
To determine if it would be unusual to randomly select 12 people and find that fewer than 5 recognize the Yummy brand name, we can use the concept of standard deviation and z-scores.
First, we need to calculate the z-score, which measures how many standard deviations an observation is from the mean. The formula for calculating the z-score is:
z = (x - μ) / σ
where
x is the observed value (in this case, 5)μ is the mean (9.3)σ is the standard deviation (0.99)Calculating the z-score:z = (5 - 9.3) / 0.99
z = -4.394
Next, we can consult a standard normal distribution table or use statistical software to find the corresponding percentile associated with the z-score. This percentile represents the probability of randomly selecting a group of 12 people with fewer than 5 recognizing the Yummy brand name.
In this case, the z-score of -4.394 corresponds to an extremely low percentile, close to 0.
The exact probability can be determined using the z-score and the standard normal distribution table.
Since the probability is extremely low, it would be considered unusual to randomly select 12 people and find that fewer than 5 recognize the Yummy brand name.
However, it's important to note that the definition of "unusual" may vary depending on the specific criteria or threshold chosen.
In statistical terms, a common threshold for defining unusual events is a significance level of 5% (or 0.05). If the probability of observing the event is lower than the significance level, it is considered unusual.
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he Skubic family and the Shaw family went on a safari tour in which they drove their own vehicles through the park to view the animals. The cost of the tour was $5.25 per vehicle plus an additional amount for each person in the vehicle. The Skubic family had 7 people in their vehicle and paid $22.75.
If the Shaw family had 3 people in their vehicle, how much did they pay?
$2.50
$7.50
$12.75
$17.25
Answers
Answer:
b
Step-by-step explanation:
Answer:
It’s c 12.25
Step-by-step explanation:
1. Consider the expression R(s) = {Pr(s), V(s)}. Which of the following fundamental risk questions has V(s) as the answer?
A. What can be done about it?
B. What can happen?
C. How bad would it be?
2. Which of the following analytic techniques covered so far in class is an essential part of the weighted ranking method?
A. Pairwise Ranking
B. Eight Elements of Thought
C.Ratio Method
3. Consider two ball caps - one with the New York Yankees logo, and the other with the Philadelphia Phillies. Both cost the same amount of money to make, and both are equally available. Let's suppose it is the 2015 World Series, Game 7, between the Yankees and the Phillies. The Phillies win and as such, there is a rush in Philadelphia to celebrate by donning as much Phillies paraphernalia as possible. What is likely true about change in the value of the Phillies ball cap relative to the Yankees ball cap?
A. The value of Phillie's ball cap increases while the value of the Yankees cap decreases
B. Both ball caps decrease in value
C. The value of the Phillies ball cap decreases while the value of the Yankees cap increases
4. Economics prefer to think of value in the _______ sense, whereas philosopher prefers to think of value in the _______ sense.
A. subjective ... objective
B. economic ... philosophical
C. relative ... absolute
Answers
1. The fundamental risk question that has V(s) as the answer is this:
B. What can happen?
2. The analytic technique that is an essential part of the weighted ranking method is: C.Ratio Method
3. The statement that is likely true about the change in the value of the Phillies ball cap relative to the Yankees ball cap is this: A. The value of Phillie's ball cap increases while the value of the Yankee's cap decreases
4. Economics prefer to think of value in the subjective sense, whereas philosopher prefers to think of value in the objective sense.
How do Economists think of value?Economists tend to think of value in the subjective sense, which means relative to an individual. When thinking of the value of goods and services, economists try to ascertain whether the consumers are satisfied or not.
Also, for philosophers, value is viewed in the objective sense. This means that they try to analyze the inherent value of things as against individual opinions of what is valuable.
Fundamental risk refers to the kind of risks that can impact an entire economy. V in the equation represents what can happen given a particular economic move.
The ratio method is a weighted ranking method where the things that are to be decided upon are first ranked and weights such as 10 are assigned to each of them. To determine a change in value in the Yankees and Phillies, the first value is obtained and then compared with the most current value.
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Solve: – 8( 2x + 4) = 80
Answers
Answer:
x=3
Step-by-step explanation:
Simplifying
8(2x + 4) = 80
Reorder the terms:
8(4 + 2x) = 80
(4 * 8 + 2x * 8) = 80
(32 + 16x) = 80
Solving
32 + 16x = 80
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-32' to each side of the equation.
32 + -32 + 16x = 80 + -32
Combine like terms: 32 + -32 = 0
0 + 16x = 80 + -32
16x = 80 + -32
Combine like terms: 80 + -32 = 48
16x = 48
Divide each side by '16'.
x = 3
Simplifying
x = 3
Answer:
x = -7
Step-by-step explanation:
WORK:
1. 2x + 4= -80/8
2. 2x + 4 = 10
3. 2x = -10 - 4
4. 2x = 14
5. x = -14/2
SIMPLIFY: -14/2 = -7
I hope this helps!
What is the volume of the cylinder to the nearest whole number? a) 942 cm3 b) 3,534 cm3 c)471 cm3 d) 9,420 cm3
Answers
Answer:
V = 3534 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
the radius is 7.5 and the height is 20
V = pi ( 7.5)^2 * 20
V =1125 pi cm^3
Using the pi button for pi
V =3534.291735 cm^3
Rounding to the nearest whole number
V = 3534 cm^3
Answer:
b)3534 cm^3
Step-by-step explanation:
To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.
let g = z4 z4. let h = {(0,0),(2,0),(0,2),(2,2)} is g/h isomorphic to z2 z2 or z4?
Answers
F is a bijective homomorphism, it is an isomorphism. Therefore, g/h is isomorphic to Z2xZ2.
We can start by finding the left cosets of h in g. Let's denote the cosets as g1, g2, g3, and g4. We have:
g1 = h = {(0,0),(2,0),(0,2),(2,2)}
g2 = {(1,0),(3,0),(1,2),(3,2)}
g3 = {(0,1),(2,1),(0,3),(2,3)}
g4 = {(1,1),(3,1),(1,3),(3,3)}
Now, we can define a function f: g/h -> Z2xZ2 as follows:
f(g1) = (0,0)
f(g2) = (1,0)
f(g3) = (0,1)
f(g4) = (1,1)
We can check that f is a homomorphism:
f(g1g1) = f(g1) = (0,0)
f(g2g2) = f(g1) = (0,0)
f(g3g3) = f(g1) = (0,0)
f(g4g4) = f(g1) = (0,0)
f(g1g2) = f(g3g4) = (1,0)
f(g1g3) = f(g2g4) = (0,1)
Since f is a bijective homomorphism, it is an isomorphism. Therefore, g/h is isomorphic to Z2xZ2.
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Please help
Select ALL the true equations.
1. 5 + 0 = 0
2. 15 x 0 = 0
3. 1.4 + 2.7 =4.1
4. 2/3 x 5/9 = 7/12
5. 4 2/3 = 5 - 1/3
Answers
- 15 x 0 = 0
- 1.4 + 2.7 = 4.1
- 4 2/3 = 5 - 1/3
The True equations are
2. 15 x 0 =0
3. 1.4 + 2.7 = 4.1
5. 4 2/3 = 5- 1/3
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
1. 5 + 0 = 0
5 = 0
This is not an equation because LHS ≠ RHS.
2. 15 x 0 =0
0= 0
This is an Equation.
3. 1.4 + 2.7 = 4.1
4.1 = 4.1
This is an Equation.
4. 2/3 x 5/9 = 7/12
10/ 27= 7/12
This is not an Equation.
5. 4 2/3 = 5- 1/3
14/3 = 14/3
This is an Equation
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What is the graph of the function rule? y=|3x|+2
Options below!
Answers
Answer: the 4th/last option
Step-by-step explanation:
Y goes up when x goes down or up. When x = 0, y = 2
Step-by-step explanation: I like to have the 3 on the
outside and we can just write it as y = 3|x| + 2.
Now, we know that this is the form y = a|x - h| + k where
(h, k) represents the vertex of the function.
Notice that there is no value of h so we say that h = 0.
In addition, we know that k = 2 so our vertex is (0, 2).
This eliminates the first graph and the third graph.
Since a is positive, our function opens upward.
So graph 4 matches with our equation.
what is A divided by A% of A? ( A the variable )
Answers
a / (a% of a) = a / (a% * a) = a / (a/100 * a) = a / (a^2/100) = a * (100/a^2) = 100 / a
The correct answer would be 100 / a.
8.694/0.1267^1/3×0.006974
Answers
Answer:
Hey gd evening
Step-by-step explanation:
Can you please drop me some likes
6. A psychology professor of a large class became curious as to whether the students who turned in tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 students to turn in tests was 78. Using the .05 significance level, was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean?
Answers
Answer: Z is less than Zc ∴ 1.342 < 1.96
Therefore, Null hypothesis is not Rejected.
There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.
Step-by-step explanation:
Given that;
U = 75
X = 78
standard deviation α = 10
sample size n = 20
population is normally distributed
PROBLEM is to test
H₀ : U = 75
H₁ : U ≠ 75
TEST STATISTIC
since we know the standard deviation
Z = (X - U) / ( α /√n)
Z = ( 78 - 75 ) / ( 10 / √20)
Z = 1.3416 ≈ 1.342
Now suppose we need to test at ∝ = 0.05 level of significance,
Then Rejection region for the two tailed test is Zc = 1.96
∴ Reject H₀ if Z > Zc
and we know that Z is less than Zc ∴ 1.342 < 1.96
Therefore, Null hypothesis is not Rejected.
There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.
Testing the hypothesis, it is found that since the p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.
At the null hypothesis, we test if the mean is of 75, that is:
\(H_0: \mu = 75\)
At the alternative hypothesis, we test if the mean is different of 75, that is:
\(H_1: \mu \neq 75\)
The test statistic is:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
In which:
X is the sample mean.\(\mu\) is the value tested at the null hypothesis.\(\sigma\) is the standard deviation.n is the size of the sample.For this problem, we have that:
\(X = 78, \mu = 75, \sigma = 10, n = 20\)
The value of the test statistic is:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z = \frac{78 - 75}{\frac{10}{\sqrt{20}}}\)
\(z = 1.34\)
Since this is a two-tailed test, the p-value of the test is P(|z| < 1.34), which is 2 multiplied by the p-value of z = -1.34.
Looking at the z-table, z = -1.34 has a p-value of 0.0901.
2(0.0901) = 0.1802
The p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.
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Molly is thinking of a number. twice her number take away seven is the same as her number plus five. what is her number?
Answers
Answer:
Number = 12
Step-by-step explanation:
2n-7=n+5 (+7 to both sides)
2n=n+12 (-n to both sides)
n=12
Please help me with this questions please please ASAP ASAP please ASAP help please please ASAP please I'm begging you please please ASAP
Answers
Answer:
32
Step-by-step explanation:
The shapes are the same except for the direction so i think it would be 32
Answer:
32°
Step-by-step explanation:
quadrilateral ABCD is similar to quadrilateral WXYZ
Corresponding angles of similar polygons are congruent. We are told the two quadrilaterals are similar, so the pairs of corresponding angles are congruent.
You know angles are corresponding according to the statement of similarity is written.
quadrilateral ABCD is similar to quadrilateral WXYZ
The vertices are listed in the same order in both polygons showing which angles are corresponding.
<A corresponds to <W
m<W = m<A = 32°
Answer: 32°
Martika says factors and multiples are related. Use the equation 6 x 7 = 42 to describe the relationship between factors and multiples.
Answers
Answer:
x=1.3204690000000001
Step-by-step explanation:
6×7=42
6=6.
x=7
x=(7)
(1_7)
x=1.3204690000000001
Select the correct answer.
After four years of college, Erica has to start paying off all her student loans. Her first payment is due at the end of this month. Her bank told her
that she has 10 years to pay off all of her loans, and that starting this month the loans will be compounded monthly at a fixed annual rate of
9.4%.
Erica currently has a total of $29.158.00 in student loans. Using the formula, what is Erica's approximate monthly payment?
Fpli)
P =
1- (1 + i)-
ОА
OB
Erica's approximate monthly payment will be $370.39.
Erica's approximate monthly payment will be $254.94.
Erica's approximate monthly payment will be $375.70.
Erica's approximate monthly payment will be $2.740.10.
Oc.
D.
Answers
Answer:
its $375.70
Step-by-step explanation:
i guessed and got it right. good luck guys. love u. remeber to eat n drink water and try to spend some time outside if you can! i know its hard rn but we can do it! im proud of u all
The value of Erica's approximate monthly payment is $375.70. The correct option is C .
What is the meaning of Rate of Interest ?Rate of Interest is the rate at which a loan is borrowed or the rate at which an investment gives return .
It is given that
Student Loan Total = $29,158
Rate of Interest = 9.4 %
Time Period = 10 years
The monthly payment is given by
\(\rm \dfrac{F p(i) }{ ( 1 - ( 1 + i )^{-n})}\)
Substituting the values in the equation
\(\rm = \dfrac{29158* (0.094/12) }{ ( 1 - ( 1 + (0.094/12) )^{-12*10})}\)
= $ 375.70
Therefore,The value of Erica's approximate monthly payment is $375.70. The correct option is C.
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Molly is studying two number patterns. Pattern A starts at 0 and has the rule "add 3." Pattern B starts at 0 and has the rule "add 6." What is the relationship between corresponding terms in the two patterns?
The terms in Pattern A are 3 times the corresponding terms in Pattern B.
The terms in Pattern A are 2 times the corresponding terms in Pattern B.
The terms in Pattern A are one half the corresponding terms in Pattern B.
The terms in Pattern A are one third the corresponding terms in Pattern B.
Answers
The relation between the Pattern A is the half of the Pattern B is given below. Then the correct option is C.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Molly is studying two number patterns.
Pattern A starts at 0 and has the rule “add 3”.
Pattern B starts at 0 and has the rule “add 6”.
The relation between the Pattern A and Pattern B is given below.
Pattern A = 1/2 x Pattern B
Then the correct option is C.
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Tim drove at distance of 511 km in 7 h. What was his average driving speed in km/h?
Answers
so, the formula for this would be distance ÷ time. now, 511 ÷ 7 = 73 kilometers per hour
as a result, 73 km/h is tim’s average driving speed!
Tim drove at a distance of 511 km in 7 h. His average driving speed in km/h is 73.
By computing Tim's average driving speed, we have to divide the total distance that he traveled by the time it takes him to complete the whole journey. In this respect, Tim drove a total distance of 511 km in 7 hours.
Average driving speed = Total distance/Total time taken
By putting the values in the equation we get :
Average driving speed =\(\frac{ 511 km}{7 h}\)
Now by computing the average driving speed:
Average driving speed = 73 km
So, Tim's average driving speed was 73 km/h.
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Look at this square. Find the value of
S.
S
Perimeter = 16 miles
S =
miles
Answers
The value of S, which represents the length of each side of the square, is 4 miles.
To find the value of S, we need to determine the length of each side of the square. Given that the perimeter of the square is 16 miles, we can use the formula for the perimeter of a square, which is 4 times the length of a side.
Perimeter = 4 × S
Given that the perimeter is 16 miles, we can substitute this value into the equation:
16 = 4 × S
To solve for S, we divide both sides of the equation by 4:
16 ÷ 4 = S
4 = S
Therefore, S, which stands for the square's side lengths, has a value of 4 miles.
So, S = 4 miles.
This means that each side of the square measures 4 miles, and the square has equal sides and right angles at each corner.
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Helppp!!!!!!!!!!!!!!!!!!!!!
Answers
The value of x is equal to 15°
How to determine the value of x?In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
By substituting the given parameters, we have the following:
3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.
3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.
23x + 15 = 360°.
23x = 360 - 15
23x = 345
x = 345/23
x = 15°.
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If Julian starts a bank account with $10,000 and his bank compounds the interest quarterly at an annual interest rate of 8%, how much money does he have at the year's end?
After 5 years?
Answers
Julian has $10,824.32 at the end of the year and $14,859.47 after 5 years.
What is compound interest?Compound interest is the interest paid by the bank for both of principle amount and the interest the account has already earned.
Julian starts bank with principle amount $10,000.
Bank compounds the interest quarterly at an annual interest rate 8%.
Then, total amount in the end of the year.
\(A = p(1+\frac{r}{n} )^{nt}\)
= \(10,000(1+\frac{0.08}{4} )^{4}\)
= $10,824.32.(at the end of the year)
After 5 years,
\(A=10000(1+\frac{0.08}{4} )^{(4)(5)}\)
= $14,859.47(after 5 years)
Hence, Julian has $10,824.32 at the end of the year and $14,859.47 after 5 years.
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Please help! (Also show work)
Tutorials :D
Answers
The five-number summary is:
Minimum: 9
First Quartile: 16.5
Median: 25.5
Third Quartile: 39
Maximum: 51
3. Range = 42
4. Interquartile range = 22.5
How to Find the Five-number Summary of a Data?Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:
1. The numbers in ordered from the smallest to the largest would be:
9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51
2. The five-number summary for the lengths in minutes would be:
Minimum value: this is the smallest lengths, which is 9First Quartile (Q1): this is the middle of the first half of the data set of the lengths in minutes, which is 16.5.Median: the median is the center of the data distribution which is 25.5.Third Quartile: this is the middle of the second half of the data set of the lengths in minutes, which is 39.Maximum: this is the largest length in minutes, which is, 51.3. Range of the data = max - min = 51 - 9 = 42
4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5
Interquartile range for the data set = 22.5
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(1 point) suppose y′1y′2==t6y1 4y2 sec(t),sin(t)y1 ty2−2.
Answers
y1'y2 = (t^6/4) y1 tan(t) y2 + (sin(t)/t) y1 ln|y2| - 2y1 + C y2^2
This is the general solution to the differential equation.
To solve this differential equation, we can use the method of integrating factors.
First, we rearrange the equation to get it into a standard form:
y′1y′2 = t^6y1/(4y2) sec(t), sin(t)y1/(ty2) - 2
y′1y′2 = (t^6/4) (y1/y2) sec(t), (sin(t)/t) (y1/y2) - 2(y1/y2)
Now, we introduce an integrating factor e^(-2ln(y2)) = 1/y2^2:
y′1y′2/y2^2 = (t^6/4) (y1/y2^3) sec(t), (sin(t)/t) (y1/y2^3) - 2/y2^2
Now, we can integrate both sides with respect to t:
y1'y2^-2 = (t^6/4) ∫ y1/y2^3 sec(t) dt + (sin(t)/t) ∫ y1/y2^3 dt - 2/y2^2 ∫ dt
y1'y2^-2 = (t^6/4) y1/y2^2 tan(t) + (sin(t)/t) ln|y1/y2| - 2/y2^2 t + C
where C is the constant of integration.
Multiplying both sides by y2^2, we get:
y1'y2 = (t^6/4) y1 tan(t) y2 + (sin(t)/t) y1 ln|y2| - 2y1 + C y2^2
This is the general solution to the differential equation.
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Two step equation help me pls step by step
The questions 36 and 37
Answers
Answer:
Step-by-step explanation:
SOLVING
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Question 36
6=-2(7-c)
Use distribution to multiply -2 by parenthesis
6=-14+2c
Add to both sides 14
20=2c
Divide 2 into both sides
10=c
Question 375(h-4)=8
Use distribution to multiply 5 by the parenthesis
5h-20=8
Add to both sides 20
5h=28
Divide 5 into both sides
\(h=\frac{28}{5}\)
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In 2016, taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile.
In equation form, Fare = 2.85 + 2.7 (miles).
At the end of a month, a businessman collects all his taxicab receipts and calculates some numerical summaries. he paid was $15.45 with a standard deviation of $10.20.
What are the mean and standard deviation of the lengths of his cab rides in miles?
O Mean = 5.722 miles, Standard deviation = 3.778 miles
O Mean = 44.715 miles, Standard deviation = 27.54 miles
O Mean 4.667 miles, Standard deviation = 3.778 miles
O Mean 5.722 miles, Standard deviation = 2.722 miles
O Mean 4.667 miles, Standard deviation = 2.722 miles
Answers
The mean and standard deviation of the lengths of cab rides in miles is: Mean = 4.667 miles, Standard deviation = 3.778 miles
To find the mean and standard deviation of the lengths of the businessman's cab rides, we need to use the given information. The fare equation, Fare = 2.85 + 2.7 (miles), tells us that the cost of the ride is a linear function of the distance traveled.
From the given data, we know that the businessman paid a total of $15.45 at the end of the month. This total cost is the sum of the initial fee and the cost per mile multiplied by the total distance traveled. So we can set up the equation 15.45 = 2.85 + 2.7(miles) to find the mean.
Simplifying the equation, we have 12.6 = 2.7(miles), and solving for miles gives us miles ≈ 4.667. Therefore, the mean length of the cab rides is approximately 4.667 miles.
To calculate the standard deviation, we are given that the standard deviation of the total cost is $10.20. Since the total cost is determined by the distance traveled, the standard deviation of the lengths of the cab rides will also be the same. Hence, the standard deviation of the lengths of the cab rides is approximately 3.778 miles.
Therefore, the correct answer is: O Mean 4.667 miles, Standard deviation = 3.778 miles.
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An urn contains 1 red and 3 white balls. Two balls will be randomly selected, with replacement. If equals the number of red balls in the sample, find the probability distribution for
Answers
The probability distribution for red ball is 1/16.
we have,
Red ball = 1
White ball= 3
Total ball = 4
Probability of getting a red ball both time
= 1/4 x 1/4
= 1/16
Thus, the required probability is 1/16.
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