Find the solution to the differential equation dzdt=7te7z that passes through the origin.
Answers
The answer is \(z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$\)
What do you understand by differential equation?
An ordinary derivative or a partial derivative can both be found in a differential equation. The differential equation describes the relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.
Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variables x and y are related because y is an unidentified function of x. The derivative of y is also on the equation's left-hand side.
Given equation:
\($$\begin{aligned}&e^{-7 z} d z=7 t d t \\&:(-1 / 7) e^{-7 z}=3.5 t^2+C\end{aligned}$$\)
\($C=-1 / 7$\)
\($$(-1 / 7) e^{-7 z}=3.5 t^2-1 / 7$$\)
\($$e^{-7 z}=1-24.5 t^2$$\)
\($$\begin{aligned}-7 z &=\ln \left(1-24.5 t^2\right) \\z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$\)
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Related Questions
Find the value of x. (4x + 12)° 64°
Answers
Answer:
C. 13Step-by-step explanation:
the angle of measure 4x + 12 and the angle of measure 64 are Vertically opposite angles then they are equal in measure
therefore
4x + 12 = 64
⇔ 4x = 64 - 12
⇔ 4x = 52
⇔ x = 52/4
⇔ x = 13
A gene carries the______ for a trait.
Answers
Whats the measure of the unknown angle . Will mark b if correct
Answers
Answer:
93
Step-by-step explanation:
Will mark brainliest plz help
Answers
A
Explanation
NR=3.6
NP=0.9
NQ is slightly longer that NP so that means it probably equal approximately 1
So then you subtract 3.6-1=2.6
It’s probably 2.61 because NQ isn’t exactly 1
Hope that helps please give brainliest
what four intgers would give my the product -24
Answers
The four intgers would give my the product -24, can be, -2,2,2,3
or, _-2, 4, 3 , 1.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
-24
we know,
-24
= -4 * 6
= -2*2 * 2*3
Hence, The four intgers would give my the product -24, can be, -2,2,2,3
or, _-2, 4, 3 , 1.
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According to this model, how high would the ticket price have to be for the theater to make $0 in revenue? Explain your reasoning.
Answers
We have calculated that 48 students passed Mathematics only in the first year of the school.
What is Equation?Equation is a mathematical statement that expresses two expressions having the same value. It is usually represented by an equals sign (=). An equation can involve variables, numbers, operations and functions. It is an important tool to solve real-world problems, as it helps to relate different variables. Equations can be used to determine unknown quantities, or to predict future outcomes.
Firstly, let us denote the number of students who passed mathematics only as M, and the number of students who passed Science only as S. As twice as many students passed Science as Mathematics, we can say that 2S = M.
Now, let us add up the number of students who passed both Mathematics and Science and the number of students who passed Mathematics only to get the total number of students who passed Mathematics. This is given by M+34.
Next, we can add up the number of students who passed both Mathematics and Science and the number of students who passed Science only to get the total number of students who passed Science. This is given by S+34.
Now, since we know that there were 116 students who passed at least one subject, we can subtract the sum of M+34 and S+34 from 116 to get the number of students who passed neither subject. This is given by 116 - (M+34 + S+34) = 116 - (2S+68).
Finally, substituting 2S = M, we can calculate that the number of students who passed Mathematics only is M = 116 - 68 = 48.
In conclusion, we have calculated that 48 students passed Mathematics only in the first year of the school.
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Lily drives 90 miles in 2 hours. If she drives at the same rate, how far does lily travel in each of the following time intervals: 1 hour, 1/2 hour, and 3 hours? Please solve in at least two different ways. You could make a bar model, double number line, ratio table, or graph.
How far does she travel in 1/2 hour?
Answers
Answer:
22.5 miles 1/2 hour - 45 miles 1 hour - 67.5 miles 1.5 hours - 135 miles 3 hours
Step-by-step explanation:
If Lily travels 90mph in 2 hours she would travel 45mph each hour. So now just take 45 times 1, 1.5, and 3 to get your answers. So in half an hour she would travel 22.5 miles
HELPP 65 POINTS I NEED THEM ALL
It can be expensive to go to the movie theater. The scatter plot shown here gives the average cost in
U.S. dollars of a movie ticket in the U.S. for each year from 1980 to 2013. Using this data, how much do
you think a movie ticket will cost in the years 2020 and 2030? Download the worksheet and complete it.
1. How has the cost of a movie ticket changed over the last 30 years? What has been the general
trend? How can you tell this from the graph? (2 points)
2. What years did the cost of movie ticket decrease compared to the year before? How can you tell
from the graph when the price is decreasing? (2 points)
Student Name:
Predicting Movie Ticket Costs Activity
3. There was a time where the cost of a movie ticket stayed relatively the same over several years.
For what years did the cost stay relatively the same? How can you tell this from the graph? (2
points)
4. The graph could be divided up into three different periods of relatively consistent ticket price
change: The years 1980 – 1988, 1989 – 1993 and 1994 – 2011. Can you find a typical rate of
change in the price of a ticket for each of these time periods? In other words, on average, by
how much did the price of a ticket increase by each year during each of these time periods?
(2 points)
5. Predict the cost of a ticket in 2012 – 2015. Plot your predictions and give your actual predictions
for each year below. How did you determine how much a ticket would cost each year? (2 points)
6. What might have been the cost of a ticket during the years 1975 – 1979? Plot your estimates on
the grid and give your actual predictions for each year below. How did you determine how much
a ticket would cost each year? (2 points)
Predicting Movie Ticket Costs Activity
7. Find a line of best fit to represent the data. Let y = ticket price and x = the number of years since
1980 (1980 is year zero, 1981 is year one). Approximate a line to represent the data, a slope, a y-intercept and equation that models your line of best fit. (2 points)
8. Use your equation (or graph or a table) to predict the cost of a movie ticket in the years 2020
and 2030. Be sure to show how you came to each answer. (2 points)
Answers
Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.
What do you mean by rates?
A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
1. Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.
2. From 1988 to 1989 the cost of a ticket decreased. Also from 1991 to 1992 the cost decreased a little. The graph slants a little downward.\
3. From 1990 to 1994 the cost stayed pretty much the same. Those years on the graph look almost level... not sloping upward or downward.
4. 1980-1988 price increased from about $2.75 to about $4.25 $1.50 over 8 years = $0.19 per year 1989-1993 price increased from about $4.00 to about $4.20 = $0.20 over 4 years = $0.05 per year 1994-2011 price increased from about $4.20 to about $8.00 $3.80 over 7 years = $0.54 per year
5. Maybe 2012 will be $8.20, 2013 will be $8.30, 2014 will be $8.50, 2015 will be $8.60 ish
Maybe I should make the price go up about $0.17 cents per year ... on average.
6. 1979 maybe $2.52
1978 maybe $2.36
1977 maybe $2.19
1976 maybe $2.02
975 maybe $1.85
I figured that the price was going down, on average, at about $0.17 per year.
7. one possibility might be y=$5.30/31 x + $2.70 or y = 0.17x+2.7.
8.Using the equation that we fit to this data y = 0.17x + 2.7 we get 0.17(40) + 2.7= $9.50 for the year 2020 and for the year 2030 we get 0.17(50)+2.7 $11.20
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Answer:
Step-by-step explanation:
its b like this the aetter number g
If is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with and being relatively prime positive integers, what is
Answers
The probability value of (m, n) is (1, 2^1005).
Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.
We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.
Thus, the probability is:
P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004
We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.
Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|
where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.
By the inclusion-exclusion principle:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)
where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.
This simplifies to:
(1/2) ⋅ (2^1004 + (-1)^1005)
Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).
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Complete question:
If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?
The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.
If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.
We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.
Thus, the probability is:
P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004
We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.
Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|
where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.
By the inclusion-exclusion principle:
|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)
where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.
This simplifies to:
\((1/2) * (2^{1004} + (-1)^1005)\)
Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)
Hence, (m, n) = (\(1, 2^{1005\)).
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PLEASE HURRY MY SCHOOL ENDS TOMORROW AND BEED THIS DONE
Candace purchased 6 gallons of gas for $13.56. What is the constant of proportionality that relates the cost in dollars, y, to the number of gallons, x?
Answers
Answer
we need to use the formula for direct variation, which is:
y = kx
where y is the cost in dollars
x is the number of gallons
k is the constant of proportionality.
We can use the given information to set up an equation for the relationship between y and x:
13.56 = k(6)
Solving for k, we can divide both sides by 6:
k = 13.56/6
k = 2.26
Therefore, the constant of proportionality that relates the cost in dollars, y, to the number of gallons, x, is 2.26.
Mary spent half of her allowance going to the movies . She washed the family car and earned seven dollars . What is her weekly allowance if she ended with seventeen dollars ?
Answers
The problem says that after Mary has spent half of her allowance at the movies she was left with 18 dollars so that means that the equation must be equal to 18.
The equation you want to set up is
0.5x+7=18
Where, 18-7=11
0.5x=11
11/.5 = x
x = $22
Thus, Mary has a weekly allowance of 22 dollars.
How to find proportional parts in triangles and parallel lines?
Answers
If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides. If DE = BC, then ADDB=AEEC.
If a line parallel to one side of a triangle contacts the other two sides, the two sides are proportionately divided.
The formula for a proportional equation is y = kx. The letters y and x denote the variables in the equation. The letter k represents the proportionality constant, which is fixed.
Because matching angles produce the AA similarity shortcut, when a line is drawn parallel to one side of a triangle, two similar triangles are generated. Because the triangles are comparable, the parallel line segments are proportionate segments.
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Point / lies between points w and F. WI = 7x - 3.
IF = 2x + 4. WF = 15x – 21. What is the measure of
WF?
Answers
Answer:
WF = 9x + 1
Step-by-step explanation:
Here in this question, we are interested in calculating the measure of WF
By mathematical convention;
WF = WI + IF
WF = 7x-3 + 2x + 4
WF = 7x + 2x -3 + 4
WF = 9x + 1
INCREASE OR DECREASE? MATH HELP PLZ
Answers
Answer:
decreasing
Step-by-step explanation:
Answer:
decreasing.
Step-by-step explanation:
this is bc its negative, therefore its decreasing. heres a picture also (as you can see, the purple line is increasing and the black line is decreasing, so its decreasing)
hope this helped!
CAN SOMEONE HELP ME WITH #2 PLEASE????
Answers
Answer:
Step-by-step explanation:
Need help with this please
Answers
Answer:
450
Step-by-step explanation:
base times height is the formula so 75x12
I need it simplified help
Answers
The answer is 23/40
To simplify this expression, we need to find a common denominator for each pair of fractions that are being added or subtracted.
The common denominator for 1/4 and 1/5 is 20, so we can rewrite 1/4 as 5/20 and 1/5 as 4/20. Then, we can subtract these fractions to get 1/20.
The common denominator for -3/4 and 1/8 is 8, so we can rewrite -3/4 as -6/8. Then, we can add these fractions to get -5/8.
Now, we can combine the two simplified fractions by finding a common denominator of 40. We can do this by multiplying 20 and 8, which gives us 160.
Then, we can rewrite 1/20 as 2/40 and -5/8 as -25/40. Adding these fractions together gives us:
2/40 - 25/40 = -23/40.
The absolute value of any number is always positive so it becomes 23/40.
The simplified version of (1/4 - 1/5) + (-3/4 + 1/8) is 23/40.
If a data set has 25 values and a standard deviation 9.4, then the variance is
Answers
If a data set has 25 values and a standard deviation 9.4, then the variance is equal to 88.36.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
\(Z=\frac{\bar{x}\;-\;\mu}{ \delta }\)
Where:
x is the sample mean or observed data.u is the mean.δ is the standard deviation.In Statistics, the standard deviation of a data sample is the square root of the variance and as such, this given by:
Variance = δ²
Taking the square of standard deviation, the variance would be given by:
Variance = δ²
Variance = 9.4²
Variance = 88.36.
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Find the probability of being dealt a jack given that you were dealt a card above a 9 (count aces high).
Answers
The probability of being dealt a jack, given that you were dealt a card above a 9 (counting aces high), depends on the number of cards above a 9 in the deck.
The explanation below will consider a standard deck of 52 cards.
In a standard deck of 52 cards, there are 4 jacks. Given that you were dealt a card above a 9, there are 12 cards (10, J, Q, K, and A) that satisfy this condition. Among these 12 cards, there is 1 jack.
Therefore, the probability of being dealt a jack, given that you were dealt a card above a 9, can be calculated as the number of favorable outcomes (1 jack) divided by the number of possible outcomes (12 cards above a 9).
Hence, the probability is 1/12, which can also be expressed as approximately 0.083 or 8.33%. This means that there is an approximately 8.33% chance of being dealt a jack when you are already dealt a card above a 9 in a standard deck of 52 cards.
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assume that the histograms are drawn on the same scale. which of the histograms has the largest interquartile range (iqr)?
Answers
The interquartile range (IQR) is a measure of variability in a data set and is calculated as the difference between the first and third quartiles.
A larger IQR indicates a greater spread of data. Assuming that the histograms are drawn on the same scale, the histogram with the largest IQR would be the one with the widest spread of data. This can be determined by examining the width of the boxes in each histogram. The box represents the IQR, with the bottom of the box being the first quartile and the top of the box being the third quartile. The histogram with the widest box would have the largest IQR. It is important to note that a larger IQR does not necessarily mean that the data is more spread out than other histograms, as it only measures the middle 50% of the data and ignores outliers. Therefore, it is important to consider other measures of variability and the overall shape of the distribution when interpreting histograms.
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Whats the slope using rise/run?
Answers
Answer:
-4,1
Step-by-step explanation:
Y is at -1,1
X is at -5,0
subracting we get -4,1
since it’s rise over run
-4,1
so -4
Help needed ASAP will give brainliest (Not a test or assignment)
Answers
Answer:
variable
numerical expression
constant
coefficient
variable term
like terms
algebraic expression
numerical expression
Step-by-step explanation:
Bentley is deciding between two truck rental companies. Company A charges an initial fee of $50 for the rental plus $2 per mile driven. Company B charges an initial fee of $10 for the rental plus $3 per mile driven. Let AA represent the amount Company A would charge if Bentley drives xx miles, and let BB represent the amount Company B would charge if Bentley drives xx miles. Graph each function and determine the interval of miles driven, x,x, for which Company A is cheaper than Company B.
Company A is cheaper than Company B when x ___ _ ___
Answers
Answer:
after 41 miles A is cheaper than B
Step-by-step explanation:
not sure if this is what the question is asking for
Jaxon goes to a store an buys an item that costs xx dollars. He has a coupon for 20% off, and then a 4% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Jaxon paid at the register
Answers
An expression in terms of xx that represents the total amount that Jaxon paid at the register is 1.04 (xx - 0.20(xx)).
What is the total cost?The total cost is the amount calculated after any discount for an item and along with the tax incurred for an item to be purchased.
For the given situation,
Jaxon goes to a store and buys an item that costs xx dollars.
He has a discount coupon for 20%
Convert percentages to decimals = 0.20
The tax percentage is 4%
Convert percentages to decimals = 0.04
The discounted amount will get less than the cost price. So,
⇒ xx - 0.20(xx)
The tax amount for the item will get added to the final cost of the item. Thus the expression becomes,
⇒ 1.04 (xx - 0.20(xx))
Hence we can conclude that the expression for the total cost is 1.04 (xx - 0.20(xx))
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Consider the probability distribution of the random variable X
X P(X)
0 0.1
1 0.2
2 0.3
3 ?
a. Find the missing (?) probability value
b. Find E(X).
c. Find Var(X) and x.
d. If Z = 1 + 2/3X, find E(Z), Var(Z) and z.
Answers
a. The missing probability value is 0.4.
b. E(X) = 1.4.
c. Var(X) = 0.56 and σx = 0.75.
d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.
The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.
To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.
To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.
Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.
To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.
Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.
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ANALYZE The surface area of a three-dimensional object is the sum of the area of the faces. If represents the length of the side of a cube, write a formula for the surface area S of the cube.
Answers
Step-by-step explanation:
If X represents the length of the side of a cube, the formula for the surface area of the cube, S =?
solution :
the area of each face of the cube = side × side
= X × X = X²
the cube has 6 similar faces, so the surface area of the cube could be:
S = 6 × X² = 6X²
Answer:
Surface Area = 6 × S²
Step-by-step explanation:
the surface area fo the cube :
SA = 6 × lenght × lenghtif lenght = S, the surface area fo the cube :
SA = 6 × lenght × lenght
SA = 6 × S × S
SA = 6 × S²
Volatile organic compounds a are considered a secondary criteria pollutant. b are often odorless and therefore present a great danger to humans. c are responsible for increasing greenhouse gas concentrations. d evaporate easily and contribute to ozone formation.
Answers
Volatile organic compounds (d) evaporate easily and contribute to ozone formation.
The Volatile-organic-compounds (VOCs) are "organic-chemicals" which have high "vapor-pressure" and evaporate readily into atmosphere. They come from various sources, including industrial processes, vehicle emissions, solvents, and household products.
When VOCs are released into the air, they can contribute to the formation of ground-level ozone through complex chemical reactions involving sunlight and other pollutants. Ground-level ozone is a harmful air pollutant and a primary-component of smog.
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
Volatile organic compounds
(a) are considered a secondary criteria pollutant,
(b) are often odorless and therefore present a great danger to humans,
(c) are responsible for increasing greenhouse gas concentrations,
(d) evaporate easily and contribute to ozone formation.
Find the distance between the points (7, -2) and (2, -10).
Answers
Answer:
\(\sqrt{89}\)
Step-by-step explanation:
d = \(\sqrt{(x_{1}-x_{2} )^{2} +(y_{1} -y_{2} )^{2} }\)
d = \(\sqrt{(7-2)^{2} +(-2+10)^{2} }\)
d = \(\sqrt{5^{2} +(-8)^{2} }\)
d = \(\sqrt{25+64}\)
d = \(\sqrt{89}\)
Please show your work
Find the slope when given the following points.
(2, 1) and (5, 3)
Answers
Answer:
2/3
Step-by-step explanation:
We can find the slope using
m = ( y2-y1)/(x2-x1)
= ( 3-1)/(5-2)
= 2/3
Answer:
2/3
Step-by-step explanation:
Use the equation y2-y1/x2-x1
So, 3-1/5-2
2/3
Find a in degrees.
√58
3
7
α
Answers
Answer:
23.20
Step-by-step explanation:
join my stream for an explanation
(ChildOfHermes)
please mark brainliest
im only streaming for 15.5 more hours
Answer:
α ≈ 23.20°
Step-by-step explanation:
given all 3 sides of the triangle , then any of the trig ratios may be used, that is sine, cosine or tangent to find α
tanα = \(\frac{opposite}{adjacent}\) = \(\frac{3}{7}\) , then
α = \(tan^{-1}\) ( \(\frac{3}{7}\) ) ≈ 23.20° ( to the nearest hundredth )
or
sinα = \(\frac{opposite}{hypotenuse}\) = \(\frac{3}{\sqrt{58} }\) , then
α = \(sin^{-1}\) ( \(\frac{3}{\sqrt{58} }\) ) ≈ 23.20° ( to the nearest hundredth )
or
cosα = \(\frac{adjacent}{hypotenuse}\) = \(\frac{7}{\sqrt{58} }\) , then
α = \(cos^{-1}\) ( \(\frac{7}{\sqrt{58} }\) ) ≈ 23.20° ( to the nearest hundredth )