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3 years ago

Suppose you are covering your desk (shape below) with paper and want to know how many square inches of paper you need.

Mathematics

1 answer:

zavuch27 [327]3 years ago

3 0

Answer:

a. Divide the figure into two rectangles, find the area of each rectangle and add them (See the picture attached).

b. $279\ in^2$

c. The total area of the figure is 279 square inches.

Step-by-step explanation:

a. Divide the figure into two rectangles (See the picture attached), then find the area of each rectangle and finally, add the areas calculated in order to get the total area of the given figure,

b. The area of a rectangle can be found using this formula:

$A=lw$

Where "l" is lenght and "w" is the width.

Area of Rectangle A

You can identify that:

$l_A=19\ in\\\\w_A=11\ in$

Then, its area is:

$A_A=(19\ in)(11\ in)=209\ in^2$

Area of Rectangle B

You can identify that:

$l_B=10\ in\\\\w_B=18\ in-11\ in=7\ in$

Then, its area is:

$A_B=(10\ in)(7\ in)=70\ in^2$

Total area

$A_T=209\ in^2+70\ in^2=279\ in^2$

c. The total area of the figure is 279 square inches.

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Where can the perpendicular bisectors of an acute triangle intersect?

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Find the sum of the geometric sequence –3, 15, –75, 375, … when there are 8 terms

arlik [135]

First, we need to solve for the common ratio from the data given by using the equation.

a(n) = a(1) r^(n-1)
15 = -3 r^(2-1)
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Then, we can find the sum by the expression:

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3 years ago

use the general slicing method to find the volume of The solid whose base is the triangle with vertices (0 comma 0 ), (15 comma

lyudmila [28]

Answer:

volume V of the solid

$\boxed{V=\displaystyle\frac{125\pi}{12}}$

Step-by-step explanation:

The situation is depicted in the picture attached

(see picture)

First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each

[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]

Now, we slice our solid into n slices.

Each slice is a quarter of cylinder 5/n thick and has a radius of

-k(5/n) + 5 for each k = 1,2,..., n (see picture)

So the volume of each slice is

$\displaystyle\frac{\pi(-k(5/n) + 5 )^2*(5/n)}{4}$

for k=1,2,..., n

We then add up the volumes of all these slices

$\displaystyle\frac{\pi(-(5/n) + 5 )^2*(5/n)}{4}+\displaystyle\frac{\pi(-2(5/n) + 5 )^2*(5/n)}{4}+...+\displaystyle\frac{\pi(-n(5/n) + 5 )^2*(5/n)}{4}$

Notice that the last term of the sum vanishes. After making up the expression a little, we get

$\displaystyle\frac{5\pi}{4n}\left[(-(5/n)+5)^2+(-2(5/n)+5)^2+...+(-(n-1)(5/n)+5)^2\right]=\\\\\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2$

But

$\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2=\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}((5/n)^2k^2-(50/n)k+25)=\\\\\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)$

we also know that

$\displaystyle\sum_{k=1}^{n-1}k^2=\displaystyle\frac{n(n-1)(2n-1)}{6}$

and

$\displaystyle\sum_{k=1}^{n-1}k=\displaystyle\frac{n(n-1)}{2}$

so we have, after replacing and simplifying, the sum of the slices equals

$\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)=\\\\=\displaystyle\frac{5\pi}{4n}\left(\displaystyle\frac{25}{n^2}.\displaystyle\frac{n(n-1)(2n-1)}{6}-\displaystyle\frac{50}{n}.\displaystyle\frac{n(n-1)}{2}+25(n-1)\right)=\\\\=\displaystyle\frac{125\pi}{24}.\displaystyle\frac{n(n-1)(2n-1)}{n^3}$

Now we take the limit when n tends to infinite (the slices get thinner and thinner)

$\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}\displaystyle\frac{n(n-1)(2n-1)}{n^3}=\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}(2-3/n+1/n^2)=\\\\=\displaystyle\frac{125\pi}{24}.2=\displaystyle\frac{125\pi}{12}$

and the volume V of our solid is

$\boxed{V=\displaystyle\frac{125\pi}{12}}$

3 0

3 years ago

Given that g(x)=x-3/x+4 find each of the following.

maks197457 [2]

Given that the function g(x)=x-3/x+4, the evaluation gives:

g(9) = 6/13.
g(3) = 0.
g(-4) = undefined.
g(-18.75) = 1.07.
g(x+h) = x+h-3/x+h+4

<h3>How to evaluate the function?</h3>

In this exercise, you're required to determine the value of the function g at different intervals. Thus, we would substitute the given value into the function and then evaluate as follows:

When g = 9, we have:

g(x)=x-3/x+4

g(9) = 9-3/9+4

g(9) = 6/13.

When g = 3, we have:

g(x)=x-3/x+4

g(3) = 3-3/3+4

g(3) = 0/13.

g(3) = 0.

When g = -4, we have:

g(x)=x-3/x+4

g(-4) = -4-3/-4+4

g(-4) = -1/0.

g(-4) = undefined.

When g = -18.75, we have:

g(x)=x-3/x+4

g(-18.75) = -18.75-3/-18.75+4

g(-18.75) = -15.75/-14.75.

g(-18.75) = 1.07.

When g = x+h, we have:

g(x)=x-3/x+4

g(x+h) = x+h-3/x+h+4

Read more on function here: brainly.com/question/17610972

#SPJ1

8 0

2 years ago