Question 6 of 12 View Policies Current Attempt in Progress Solve the given triangle. Round your answers to the nearest integer. Ax Y≈ b= eTextbook and Media Sve for Later 72 a = 3, c = 5, B = 56°
Answers
The angles A, B, and C are approximately 65°, 56° and 59°, respectively.
Given data:
a = 3, c = 5, B = 56°
In a triangle ABC, we have the relation:
a/sin(A) = b/sin(B) = c/sin(C)
The given angle B = 56°
Thus, sin B = sin 56° = b/sin(B)
On solving, we get b = c sin B/ sin C= 5 sin 56°/ sin C
Now, we need to find the value of angle A using the law of cosines:
cos A = (b² + c² - a²)/2bc
Putting the values of a, b and c in the above formula, we get:
cos A = (25 sin² 56° + 9 - 25)/(2 × 3 × 5)
cos A = (25 × 0.5543² - 16)/(30)
cos A = 0.4185
cos⁻¹ 0.4185 = 65.47°
We can find angle C by subtracting the sum of angles A and B from 180°.
C = 180° - (A + B)C = 180° - (65.47° + 56°)C = 58.53°
Thus, the angles A, B, and C are approximately 65°, 56° and 59°, respectively.
To know more about angles visit:
https://brainly.com/question/31818999
#SPJ11
Related Questions
Which of the following correlation coefficients represents the strongest relationship between two variables? -.75 +.60 .00 +.30
Answers
The correlation coefficient that represents the strongest relationship between two variables is -0.75.
In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.
The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.
To know more about correlation coefficients, visit,
https://brainly.com/question/4219149
#SPJ4
Which of the following structures (G,∘) are groups? (a) G=P(X),A∘B=A△B (symmetric difference); (b) G=P(X),A∘B=A∪B; (c) G=P(X),A∘B=A\B (difference); (d) G=R,x∘y=xy; (e) G is the set of positive real numbers, x∘y=xy; (f) G={z∈C:∣z∣=1},x∘y=xy; (g) G is the interval (−c,c), x∘y= x+y/(1+xy/c²)
[this example describes the addition of velocities in Special Relativity];
Answers
(e) G is the set of positive real numbers, x∘y = xy.
To determine which of the given structures (G,∘) are groups, we need to verify whether they satisfy the four group axioms: closure, associativity, identity element, and inverse element.
(a) G = P(X), A∘B = A△B (symmetric difference):
This structure is not a group because it does not satisfy closure. The symmetric difference of two sets may result in a set that is not in G (the power set of X).
(b) G = P(X), A∘B = A∪B:
This structure is not a group because it does not satisfy inverse element. The union of two sets may not result in a set with the required inverse element.
(c) G = P(X), A∘B = A\B (difference):
This structure is not a group because it does not satisfy associativity. Set difference is not an associative operation.
(d) G = R, x∘y = xy:
This structure is not a group because it does not satisfy the inverse element. Not every real number has a multiplicative inverse.
(e) G is the set of positive real numbers, x∘y = xy:
This structure is a group. It satisfies all the group axioms: closure (the product of two positive real numbers is also a positive real number), associativity, identity element (1 is the identity element), and inverse element (the reciprocal of a positive real number is also a positive real number).
(f) G = {z ∈ C: |z| = 1}, x∘y = xy:
This structure is not a group because it does not satisfy closure. The product of two complex numbers with modulus 1 may result in a complex number with a modulus other than 1.
(g) G is the interval (−c,c), x∘y = x + y/(1 + xy/c²):
This structure is not a group because it does not satisfy closure. The sum of two numbers in the interval (−c,c) may result in a number outside this interval.
In summary, the structures (G,∘) that form groups are:
(e) G is the set of positive real numbers, x∘y = xy.
Learn more about inverse element here
https://brainly.com/question/32641052
#SPJ11
Please help me understand this math problem! :D
Answers
Answer:
48 cm^2
Step-by-step explanation:
First find the area of each shape.
2 triangles- [bxh]x1/2
(4 times 3)(divided by 2) = 6, but there are 2 triangles so 6+6=12
Square- (l x w)
3 times 3 (You get the other three from the other side of the rectangle) =9
Left rectangle- (l x w)
3 times 4 = 12
Right rectangle- (l x w)
5 times 3 (You get the three from the side of the square) = 15
Total: 2 triangles Area + Square Area + Left rectangle Area+ Right rectangle Area = Surface Area
12 + 9 + 12 + 15 = 48 cm^2
Hope this helps!!
need answer with work out!!
Answers
The volume of the figure is the sum of the volume of the square prism and the volume of the square pyramid which is 67.2cm³
What is the volume of the figure?To calculate the volume of the figure, we need to find the volume of the square prism and the volume of the square pyramid.
The volume of a square prism is given as;
V = L³
l = length of the sides;V = 4³
V = 64cm³
The volume of the square pyramid is given as;
V = 1/3lh
l = length of baseh = height of pyramidV = 1/3 * 4 * 2.4
V = 3.2cm³
The volume of the figure is 64cm³ + 3.2cm³ = 67.2cm³
Learn more on volume of square pyramid here;
https://brainly.com/question/15219357
#SPJ1
Solve each matrix equation. [7 -5 3 0 1 3 8 4 -2]X + [5 -9 0]= [54 -12 96]
Answers
The matrix equation [7 -5 3 0 1 3 8 4 -2]X + [5 -9 0] = [54 -12 96] has no solution.
In order to solve the matrix equation, we need to find the matrix X that satisfies the equation [7 -5 3 0 1 3 8 4 -2]X + [5 -9 0] = [54 -12 96]. This equation represents a system of linear equations in matrix form.
Let's denote the matrix X as [x y z]. Expanding the equation, we have:
[7 -5 3 0 1 3 8 4 -2][x] [5] [54]
[y] + [-9] = [-12]
[z] [0] [96]
Using matrix multiplication, we can write the expanded equation as:
[7x - 5y + 3z] [5] [54]
[ x + 3y + 8z] + [-9] = [-12]
[4x - 2y ] [0] [96]
Now we can equate the corresponding entries on both sides of the equation:
7x - 5y + 3z = 5 --> (1)
x + 3y + 8z = -9 --> (2)
4x - 2y = 0 --> (3)
To solve the system of equations, we can use various methods such as substitution, elimination, or matrix inversion. However, upon closer inspection, we can see that the third equation (3) is a linear combination of the first two equations (1) and (2). This means that the system of equations is dependent and has infinitely many solutions, or it could be inconsistent.
To check for consistency, we can attempt to find a solution that satisfies all three equations. However, when we solve the system of equations, we will find that there is no solution that satisfies all three equations simultaneously. Therefore, the given matrix equation has no solution.
In summary, the matrix equation [7 -5 3 0 1 3 8 4 -2]X + [5 -9 0] = [54 -12 96] has no solution. This is because the system of equations represented by the matrix equation is inconsistent and does not have a solution that satisfies all three equations simultaneously.
Learn more about matrix here:
brainly.com/question/28180105
#SPJ11
this is long so if you can't answer it all in one i can repost the question Some students at MDVS are planning on planting a garden this spring. They want to plant squash, pumpkins, corn, beans, and potatoes. They plan for the field layout in feet is shown in the figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:
a) Write an expression that represents the length of the North side of the field.
b) Simplify the polynomial expression that represents the North side of the field.
c) Write a polynomial expression that represents the perimeter of the beans field.
d) Simplify the polynomial expression that represents the perimeter of the beans field. State one reason why the perimeter would be useful to the Garden Club.
e) Write a polynomial expression that represents the area of the potato field.
f) Simplify the polynomial expression that represents the area of the potato field in descending order. State one reason why the calculated area would be useful to the Garden Club.
g) Write and simplify the polynomial expression that represents the area of the bean field if = 3. What unit would the area of the bean field have?
h) The Club would like their bean plants to grow to a height of ( + 2). Write a polynomial expression to find the volume of the bean plants if they reach a height of ( + 2).
i) Simplify the polynomial expression that represents the volume of the bean plants if they reach a height of ( + 2) feet in descending order.
j) The club realized they forgot to include a zucchini field into the field layout. They plan to use half the length and half the width of the squash field to plant zucchini. Write a polynomial expression that represents the area of the new zucchini field.
k) Simplify the polynomial expression that represents the area of the newly added zucchini field.
l) (don't do this one if you want to Write and simplify polynomial expressions that represent the perimeter and area of the cornfield. (Extra-credit)
Answers
Answer:
Step-by-step explanation:
the answer to that one is to math is how long you want to have you crops and two is how much money you will have in your pocket so that you can have another crops to take care of and also have a helper to help you grow crops for that issue
what is the equation of the line with a slope of -3 and passes through the point (-6,-3)
Answers
Answer:
f(x) = -3x - 21
Step-by-step explanation:
Graphed this equation and it passes through (-6, -3), also known as Point A.
How many significant figures should be included in the answer to the following calculation? (3.4876)/(4.11+1.2
Answers
The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.
To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.
First, let's analyze the number of significant figures in the given values:
- 3.4876 has five significant figures.
- 4.11 has three significant figures.
- 1.2 has two significant figures.
To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:
4.11 + 1.2 = 5.31
Now, we divide 3.4876 by 5.31:
3.4876 / 5.31 = 0.6567037...
Now, let's determine the number of significant figures in the result.
Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.
In this case, the value with the fewest significant figures is 5.31, which has three significant figures.
Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.
To learn more about significant figures click here:
brainly.com/question/31437050
#SPJ11
John's family visited his grandmother over the weekend. the drive to her house was 2 hours at their usual speed. the trip back took 15 min longer because traffic was bad and they had to drive 5 mph slower. how many miles away is Johns's grandmother's house?
Answers
The distance to Johns's grandmother's house is 90 miles.
SpeedSpeed is the ratio of total distance to total time taken, it is given by:
Speed = distance / time
Let x represent the speed that John used and d represent the distance, hence:
x = d/2
Also when taken 15 minute longer (0.25 hours):
x - 5 = d/(2 + 0.25)
x = d/2.25 + 5
Equating:
d/2 = d/2.25 + 5
d = 90 miles
The distance to Johns's grandmother's house is 90 miles.
Find out more on speed at: https://brainly.com/question/4931057
Answer:
The distance to Johns's grandmother's house is 90 miles.
Speed
Speed is the ratio of total distance to total time taken, it is given by:
Speed = distance / time
Let x represent the speed that John used and d represent the distance, hence:
x = d/2
Also when taken 15 minute longer (0.25 hours):
x - 5 = d/(2 + 0.25)
x = d/2.25 + 5
Equating:
d/2 = d/2.25 + 5
d = 90 miles
The distance to Johns's grandmother's house is 90 miles.
20 POINTS!!!!!!!
pic shown below :)
Answers
Answer:
16,849,464 ft³
Step-by-step explanation:
subtract the two volumes of the pyramids.
What is the probability of drawing a queen or a heart from a standard deck of 52 cards?
Reminder: the four card families
Answers
Answer:
13 hearts, plus 3 other queens- so 16 out of 52, simplified 4 out of 13.
A book is 52 pages i read 18 already i am gonna read 10 pages every day how many days will it take to finish the book
Answers
Answer
4
Step-by-step explanation:
just keep reading 10 pages a day and you'll find your answer
(1 point) a park bench can seat 4 people. how many seating arrangements are possible if 4 people out of a group of 12 want to sit on the park bench?
Answers
out of a group of 12, the possible arrangements are possible are 495.
What do you mean by arrangements in permutation and combinations?
Finding the total number of different configurations for a collection of elements is a straightforward definition of the term permutation. According to permutation, the arrangement is classified as a non-distinct item, which essentially classifies things that are impossible to identify from one another.
according to the question, out of 12 people, 4 are to be chosen
so the possible arrangements are 12C4 =495
Hence, the possible arrangements are 495.
to learn about arrangements from the given link,
https://brainly.com/question/1216161
#SPJ4
20 applicants from a pool of 90 applications will be hired. How many ways are there to select the applicants who will be hired?
Answers
The ways are the \(C_{20} ^{90}\) which are we there to select the applicants who will be hired with the help of combination.
According to the statement
we have to find that the number of ways are there to select the applicants who will be hired.
So, For this purpose, we know that the
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Here we use the combination.
And from the given information:
20 applicants from a pool of 90 applications will be hired.
And according to this the combination becomes:
\(C_{20} ^{90}\)
then solve it
\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)
\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)
Then after solve it
\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)
Now open another factorial
\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)
Now solve this then
\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).
So, The ways are the \(C_{20} ^{90}\) which are we there to select the applicants who will be hired with the help of combination.
Learn more about combination here
https://brainly.com/question/11732255
#SPJ4
PLEASE HELP FAST ITS DUE SOONNN
Answers
Answer:
ST = CHORD
PR = RADIUS
MN = DIAMETER
Step-by-step explanation:
Answer:
ST) Chord/// PR) Radius/// MN) Diameter
A movie theater has two rooms. Room A has 9 rows of seats with 18 seats in each row. How many seats are there in room A? Fill in the blank. There are ___ seats in Room A. *
Answers
Answer:
162 seats
Step-by-step explanation:
A movie theater has two rooms. Room A has 9 rows of seats with 18 seats in each row.
From the question:
1 row = 18 seats
9 rows = x seats
Cross Multiply
1 row × x = 9 rows × 18 seats
x = 9 rows × 18 seats/1 row
x = 162 seats
There are 162 seats in Room A.
Which fraction correctly shows the probability of14 favorable outcomes and 37 possible outcomes?
Answers
Answer: 14/37
Step-by-step explanation:
the admissions officer for the graduate programs at the university of pennsylvania believes that the average score on the lsat exam at his university is significantly higher than the national average of 1,300. an accepted standard deviation for lsat scores is 125. a random sample of 25 scores had an average of 1,375. a. state the appropriate null and alternative hypotheses. b. calculate the value of the test statistic c. calculate the p-value. d. use the p-value to test the hypotheses and conduct the test at the 0.025 leve
Answers
(a) The Null And Alternate hypothesis are stated below,
(b) The value of test-statistic is 3,
(c) The "p-value" is 0.0013,
(d) The hypothesis is rejected because p-value is less than 0.025.
Part (a) : The appropriate null and alternative hypotheses are:
Null hypothesis (H₀): The average LSAT score at the University of Pennsylvania is equal to or less than the national average of 1,300.
Alternative hypothesis (Hₐ): The average LSAT score at the University of Pennsylvania is significantly higher than the national average of 1,300.
Part (b) : To calculate the test-statistic, we use formula : t = (x' - μ)/(s / √n),
where x' = sample mean, μ = hypothesized population mean, s = sample standard deviation, and n = sample size.
Substituting the given values,
We get,
t = (1375 - 1300)/(125 / √25) = 3;
So, the value of the test statistic is 3.
Part (c) : To calculate "p-value", we need to find the probability of getting a t-value as extreme or more extreme than 3, assuming that the null hypothesis is true.
We know that for a two-tailed test at a significance level of 0.03, the p-value is approximately 0.0013.
Part (d) : To test the hypotheses using the p-value, we compare it to the significance-level.
Since the p-value is less than 0.025 (half of the significance level for a two-tailed test), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim.
Learn more about Hypothesis here
https://brainly.com/question/17099835
#SPJ4
The given question is incomplete, the complete question is
The admissions officer for the graduate programs at the university of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300. an accepted standard deviation for LSAT scores is 125. random sample of 25 scores had an average of 1,375.
(a) State the appropriate null and alternative hypotheses.
(b) Calculate the value of the test statistic
(c) Calculate the p-value.
(d) Use the p-value to test the hypotheses and conduct the test at the 0.025 level.
Look at ivan’s check register. ivan spent $158.29 on groceries. he then transferred $250 to his savings account. a check register. a is the amount debited for groceries. d is the amount debited for a transfer. the letter represents where the amount of $158.29 should be written. the letter represents where the amount of $250 should be written.
Answers
The letter A represents where the amount of $158.29 should be written.
The letter D represents where the amount of $250 should be written.
What is a Cash Register?This refers to the automated machine that is used to handle cash transactions and also for making calculations.
Hence, we can see that from the complete information, Ivan has a cash register where he records the amount he spends on groceries which is $158.29, and also the transaction of sending $250 to his savings account.
However, in the cash register, Ivan uses the letter A to show where the amount of $158.29 should be written and the letter D represents where the amount of $250 should be written.
Read more about check registers here:
https://brainly.com/question/27155313
#SPJ4
Answer:
A and D
Edge 2022
analyze relationships (lots of points for correct answer!!)
if u answer correctly and on spot, ill give u a thanks on ur account
Answers
The equation showing the relationship between the number of free balls and the number of bats purchased is b = 6f.
Given:
Kellen loves baseball he saw the ad below:
Bats purchased free baseballs
2 12
3 18
12 72
Number of balls received free is f and the number of bats purchased is b.
2*b = 12f
divide by 2 on both sides
2b/2 = 12f/2
b = 12f/2
b = 6f
Therefore The equation showing the relationship between the number of free balls and the number of bats purchased is b = 6f.
Learn more about the equation here:
https://brainly.com/question/10413253
#SPJ1
Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
7x²
3x-5
2x+6 x+3
OA.
OB.
O C.
O D.
O E.
21x³-35x2
2x² +12x+18
7x²
6x-10
7x³ +21x²
6x² +8x-30
6x-10
7x²
6x² +8x-30
7x³+21x²
Answers
The quotient of the rational expressions shown above is given by, Answer: option (C) 7x²/6x-10
To simplify the expression 7x² / 3x-5 / 2x+6 / x+3
We need to perform the following steps:
Invert the divisor.
Change the division to multiplication.
Factor the numerator and denominator.
First, divide the first term in the numerator (7\(x^2\)) by the first term in the denominator (2x) to get 3.
Then multiply (2x + 6) by 3 to get 6x + 18 Subtract this from the numerator.
2x + 6 | 7\(x^2\) + 3x - 5
- (6x + 18)
_______
-3x - 23
Then subtract the following term from the numerator: -3x.
Dividing -3x by 2x gives -3/2.
Multiply (2x + 6) by -3/2. The result is -3x - 9.
Subtract this from the previous result.
3 - (3/2)x
_________
2x + 6 | - 14
The result of polynomial long division is -14.
Therefore, the quotient of the rational expression is (7\(x^2\) + 3x - 5) / (2x + 6) -14.
So the correct answer is option D: -14.
Cancel out any common factors.
Multiply the remaining terms to get the answer.
For more related questions on rational expressions:
https://brainly.com/question/30968604
#SPJ8
what is the geometric mean of 3 and 24?
Answers
Answer:
for GM, you find out the square root of the product of the numbers provided.
\( = \sqrt{3 \times 24} \\ = \sqrt{72} \\ = 6 \sqrt{2} \)
since 72 can be broken down into the product of 36 and 2. 6 being the square root of 36 comes out, leaving 2 behind.
that should be it i’m pretty sure
Find the circumference of the circle pictured above Round your answer to the nearest. hundredth 6
Answers
To find the circumference we have to calculate
\(s=2\pi r\)where r=6
therefore we have that the answer is
\(2\pi\cdot6=12\pi=37.699\approx37.70\)Combine these radicals 3[/2] - 5 [/2]
Answers
On combining the radicals 3\(\sqrt{2}\) and -5\(\sqrt{2}\) we get the answer
- 2\(\sqrt{2}\).\(\sqrt{2}\)
Square Root : The root of a number in math is a number that when multiplied by itself produces the original number. For example, the square root of 49 is 7 because 7×7=49. In this case, because 7 is multiplied by itself twice to produce 49, we call 7 the square root of 49.
Given are the two radicals 3\(\sqrt{2}\) and -5\(\sqrt{2}\)
Explanation:
Subtracting both the numbers, we get
= 3\(\sqrt{2}\) + (- 5\(\sqrt{2}\))
opening brackets, we get
= 3\(\sqrt{2}\) - 5\(\sqrt{2}\)
Taking common \(\sqrt{2}\) from both the digits, we get
= ( 3 - 5 ) \(\sqrt{2}\)
On subtracting, we get
= - 2\(\sqrt{2}\)
Therefore, on combining the radicals 3\(\sqrt{2}\) and -5\(\sqrt{2}\) we get the answer
- 2\(\sqrt{2}\).
To learn more about square root visit : brainly.com/question/3120622
#SPJ9
Anyone help with this question
Answers
625^-1/2=0.04
Then
0.04^-1/4=2.3606797
Finally
2.36^2=5
Therefor the answer is 5
(If rounded may vary)
A day’s production of n manufactured parts contains x parts that do not conform to customer requirements. Assume that the selected parts are independent. What is the probability that the second nonconforming part is obtained in y tests?
Please choose n between 15 and 25
Please choose x between 11 and 14
Please choose y between 3 and 10
Then solve the problem. Formula: P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r)
Answers
The P(2nd non-conforming part is obtained in y tests) is given by (n-x) / n * (1-x/n)^(y-1).
The probability that the second nonconforming part is obtained in y tests is given by the formula P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r).Solution:Given, n = between 15 and 25x = between 11 and 14y = between 3 and 10To find: The probability that the second nonconforming part is obtained in y testsFormula used:P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r)Where X represents the number of trials, p represents the probability of success, k represents the number of successful outcomes, and r represents the number of trials.Possible values of x:n - xLet the probability of obtaining a non-conforming part be p, then the probability of obtaining a conforming part would be 1-p.Number of non-conforming parts in n: n-xProbability of selecting the non-conforming part p = x/nProbability of selecting the conforming part 1-p = (n-x)/nP(2nd non-conforming part is obtained in y tests) = P(y-th trial is non-conforming) = P(y-1 conforming trials followed by a non-conforming trial)P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (x/n)^(1-1) * (1-x/n)^(y-1)Therefore, P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (x/n)^(0) * (1-x/n)^(y-1)P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (1) * (1-x/n)^(y-1)Hence, P(2nd non-conforming part is obtained in y tests) is given by (n-x) / n * (1-x/n)^(y-1).
Learn more about Obtained
brainly.com/question/2075542
#SPJ4
A rocket has positive velocity v(t) after being launched upward from an initial height of 0 feet at time =0 seconds_ The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds as shown in the table below 10 20 30 40 50 60 70 80 seconds v(t) (feet_per_second_ 22 29 35 40 44 47 49 Use a midpoint Riemann sum with 3 subintervals of equal length to approximate v(t)dt _ b) Using correct units, explain the meaning of v(t)dt in terms of the rocket's flight
Answers
Using a midpoint Riemann sum with 3 subintervals of equal length to approximate \(\int^{70}_{10}v(t)dt\) is 2020 and \(\int^{70}_{10}v(t)dt\) means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.
From the given question,
An initial height of 0 feet at time t=0 seconds.
The velocity of the rocket is recorded for selected values of over the interval 0 < t < 80 seconds.
(a) Using a midpoint Riemann sum with 3 subintervals of equal length to approximate \(\int^{70}_{10}v(t)dt\).
\(\int^{70}_{10}v(t)dt\)
A midpoint Riemann sum with 3 sub intervals so, n=3
∆t= (70-10)/3
∆t = 60/3
∆t = 20
Intervals: (10, 30), (30,50), (50,70)
Midpoint: 20 40 60
Midpoint Riemann Sum
\(\int^{70}_{10}v(t)dt\) = ∆t[v(20+v(40)+v(60)]
From the table
\(\int^{70}_{10}v(t)dt\) = 20[22+35+44]
\(\int^{70}_{10}v(t)dt\) = 20*101
\(\int^{70}_{10}v(t)dt\) = 2020
(b) Now we have to explain the meaning of v(t)dt in terms of the rocket's flight \(\int^{70}_{10}v(t)dt\).
It means the distance in feet, traveled by rocket A from t=0 seconds to t=70 seconds.
To learn more about a midpoint Riemann sum link is here
brainly.com/question/28174119
#SPJ4
IMPORTANT PLEASE HELP
Fiona owns 80 DVDs. The number of
action DVDs, a, is 8 less than twice the
number of comedy DVDs, c. Which system
of equations describes Fiona's DVDs?
Answers
Answer:
a + c = 80
a = 2c - 8
Step-by-step explanation:
Topic: Algebra
During a rainstorm 2inches of rain fell in 5hours at that rate how many hours will It take for 20 inches of rain to fall
Answers
Answer:
You would get 8in of rain Hope this Helped
Step-by-step explanation:
If you flip a coin 96 times, what is the best prediction possible for the number of times both coins will land on tails
Answers
Answer:
48
Step-by-step explanation:
The best prediction for the number of times both coins will land on tails if you flip a coin 96 times is 48. This is because if each coin flip is independent, the probability of getting tails on a single flip is 0.5. Therefore, the probability of getting tails on both flips is 0.5 * 0.5 = 0.25. So, if you flip a coin 96 times, the expected number of times both coins will land on tails is 96 * 0.25 = 24.