You want to measure the height of a tree in
front of your house. You are standing 25
feet away from the tree, and you are
looking at the top of the tree with an angle
of elevation of 52º. What is the height of
the tree? Round to the nearest foot.

Answer:

The approximate area of the region using the midpoint rule with n = 2 is about 2.8418 square units.

Step-by-step explanation:

We want to use the midpoint rule with n = 2 to approximate the area of the region bounded by the graphs of:

[tex]\displaystyle y=\sqrt[3]{16-x^3}, y=x\text{ and } x=0[/tex]

This is shown in the graph below. Our area of interest is between the green, red, and blue lines.

First, find the intersection point of the two graphs:

[tex]\displaystyle x=\sqrt[3]{16-x^3}\Rightarrow x=2\Rightarrow (2, 2)[/tex]

Therefore, we will want to approximate from x = 0 to x = 2.

Note that the red graph (cubic root) is greater than the linear function for all x in the interval [0, 2].

Since the cubic function is greater than the linear function for all x in [0, 2], the area of the region will be the linear function subtracted from the cubic function. Hence:

[tex]\displaystyle \text{Area}=\int_{0}^2\sqrt[3]{16-x^3}-x\, dx[/tex]

We will let:

[tex]f(x)=\sqrt[3]{16-x^3}-x[/tex]

The midpoint rule is given by:

[tex]\displaystyle \text{Area}\approx \sum_{i=1}^nf\left(\frac{x_{i-1}+x_i}{2}\right)\Delta x[/tex]

Since the area is on the interval [0, 2] and n = 2, find the width:

[tex]\displaystyle \Delta x=\frac{2-0}{2}=1[/tex]

Hence, our x-coordinates are x₀ = 0, x₁ = 1, and x₂ = 2.

Therefore, by the midpoint rule:

[tex]\displaystyle \text{Area}\approx \sum_{i=1}^2f\left(\frac{x_{i-1}+x_i}{2}\right)(1)[/tex]

Substitute:

[tex]\displaystyle \text{Area}\approx (1)\left(f\left(\frac{0+1}{2}\right)+f\left(\frac{1+2}{2}\right)\right)[/tex]

Evaluate:

[tex]\displaystyle \text{Area}\approx\displaystyle f\left(0.5\right)+f(1.5)[/tex]

Evaluate:

[tex]\displaystyle \text{Area}\approx(\sqrt[3]{16-(.5)^3}-(.5))+(\sqrt[3]{16-(1.5)^3}-(1.5))}\approx 2.8418[/tex]

Hence, the approximate area of the region is about 2.8418 square units.

Notes:

The exact area is 2.80436... square units.

Answer:

2.8147

Step-by-step explanation:

See the attached writeup!

It's a windy explanation because really short explanations are impossible.  If you're using a textbook, its explanation may be shorter, but probably unclear.

Answer:

B. What was the highest temperature this month?

Step-by-step explanation:

Rory is recording the highest temperature for the duration of the day for month's worth of data.

B. is the easiest one to answer, as you simply will have to look for the greatest number within the set, and that will be the answer.

A. is too broad, and does not imply that only the "high temperature" is needed, rather just a leveled temperature within day in that month.

C. is the opposite of what Rory had recorded, and without data, he cannot answer it.

D. is answerable as well, but, again, the only temperature recorded is the high temperature. Temperature can fluctuate depending on the time of the day, and can be in the 50s one hour and the 90s in another.

~

Answer:

10 tubes

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

15/1.5=10

Answer:

a = x² + 3x - 40

Step-by-step explanation:

a = l * w

a = (x - 5)(x + 8)

a = x(x + 8) - 5(x + 8)

a = (x² + 8x) + (- 5x - 40)

a = x² + 3x - 40

Answer:

Step-by-step explanation:

Answer:

It's the first graph.

Step-by-step explanation:

The data points resemble the data in the table more than the second.

Answer: C: on the science test because the y-intercept is greater

Step-by-step explanation: I got the question right on edge.

Answer:

C

Step-by-step explanation:

Answer:3495250

Step-by-step explanation:

~geometric sequence

common ratio: r=4

formula: Sn=a1(1-r^n)/1-r

Sn=10(1-(4)^10)/1-4

=-10485750/-3

=3495250

The sum of the first 10 terms of the following series, to the nearest integer. 10, 40,160 would be 3495250.

Let's suppose its initial term is a multiplication factor is r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

The given geometric sequence is

10, 40,160

common ratio: r=4

a = 10

n=10

We know that

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

[tex]S_{10} = \dfrac{10(4^{10}-1)}{4-1}\\S_{10} = \dfrac{10\times 1048575}{3}\\S_{10} = \dfrac{10485750}{3}\\S_{10} = 3495250[/tex]

Learn more about sum of terms of geometric sequence here:

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Answer:

The surface area is 76 square yards.

Step-by-step explanation:

A = 2(wl + hl + hw)

2 · (2 · 4 + 5 · 4 + 5 · 2)

76

Answer:

Step-by-step explanation:

x=13

Sorry you asked me to jurry so i do not have time to explain

Answer:

14

Step-by-step explanation:

If you do 42/3 you get 14. Which to check your answer you can do 14 x 3 and you would get 42. Hope this helps.

The answer is 14.

I am answering dis for you to give da other person brainliest!

Answer:

Point form: 2.2

Equation form: x=2, y=2

Answer:

3x-y+2x+y =4+6

5x. =10

x =2

y=6-4

y=2

Answer:

3x-1y

Step-by-step explanation:

i think that Is that

Answer:

what is 4x+3y-x-4y?

Simplify the expression.

Final answer: 4x+3y-x-4y = 3x-y

Step-by-step explanation:

I hope that this answer helps you to understand your question more thoroughly. If you have any other questions, please put them below.

Have a great rest of your day/night!

Answer:30 on delta math!

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Answer:

Because 3 and 2 are vertical angles

Step-by-step explanation:

Vertical angles are always equal or congruent

[tex]Area = pi * r^{2} \\5 = 3.142 * r^{2} \\r^{2} = 5 / 3.142\\r^{2} = 1.59\\r = \sqrt{1.59} \\r = 1.26cm[/tex]

Let's take the first value of x and y.

When x = 4, y = -3. This also gives us point

(4, -3). We need another point to find the slope.

From the table I see the point (5, -4.5)

.

See it?

Let m = slope

m = (-4.5 -(-3))/(5-4)

m = (-4.5 + 3)/1

m = (-1.5)/1

m = -1.5

Now, use the slope m and one of the points to plug into the point-slope formula.

Here is the point-slope formula:

y - y_1 = m(x - x_1)

I will use the point (4, -3) and m.

y - (-3) = -1.5(x - 4)

y + 3 = -1.5x + 6

The slope-intercept form we want is

y = mx + b.

y = -1.5x + 3

Answer:

it's answer is B

Step-by-step explanation:

f (x)=x (x-2)+3 (x-2)

=x2+x-6

Answer:

N O T H I N G

Step-by-step explanation:

L O L

Answer:i think it would be 5 but 382

Step-by-step explanation:

The the z-score for given mean and standard deviation is 3.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Given that, x=273, μ=258 and σ=5

We know that, Z=(x-μ)/σ

Z=standard score, x=observed value, μ=mean of the sample and σ=standard deviation of the sample

Now, Z=(273-258)/5

Z=15/5

Z=3

Therefore, the z-score is 3.

Learn more about the standard deviation visit:

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Answer:5.5

Step-by-step explanation:

The key is to divide by 2.54. It was not terminating so I rounded.

Step-by-step explanation:

your present age = 20/4 =5

Answer:

Your present is age 5

your present age = 20/4 = 5

Answer:

[tex](1,8) \to (2,11)[/tex]

Step-by-step explanation:

Given

[tex](x,y) \to (x + 1,y+3)[/tex]

Required

Translation of [tex](1,8)[/tex]

We have:

[tex](x,y) \to (x + 1,y+3)[/tex]

This gives:

[tex](1,8) \to (1 + 1,8+3)[/tex]

[tex](1,8) \to (2,11)[/tex]

Answer:

The answer should be both 6-8 and 4-6

Step-by-step explanation:

Considering 6 is at the end and the start it is able to go into both places.

Answer:

Step-by-step explanation:

this is the answer on edmentum

The matching will be given below.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The value of sin C will be

sin C = 3 / 5

The value of sin D will be

sin D = 4 / 5

The value of cos C will be

cos C = 4 / 5

The value of cos D will be

cos D = 3 / 5

The value of tan C will be

tan C = 3 / 4

The value of tan D will be

tan D = 4 / 3

The product of sin D and cos D will be

sin D × cos D = (4 / 5) × (3 / 5)

sin D × cos D = 12 / 25

The product of tan C and tan D will be

tan C × tan D = (3 / 4) × (4 / 3)

tan C × tan D = 1

The product of cos C and tan D will be

cos C × tan D = (4 / 5) × (4 / 3)

cos C × tan D = 16 / 15

Then the matching will be given below.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

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Answer:

w ≤ 35

Step-by-step explanation:

Answer:

the standard error is 153.125

Step-by-step explanation:

given that

The random sample is 256

The sample mean is $35,420

And, the standard deviation is $2,450

We need to find out the standard error

We know that

= standard deviation ÷ √random sample

= 2450 ÷ √256

= 2450 ÷ 16

= 153.125

Hence, the standard error is 153.125