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2 years ago

A 28 foot ladder is propped against a wall. The base of the ladder is 19 ft from the wall how far up the wall does the ladder go

Mathematics

1 answer:

docker41 [41]2 years ago

8 0

Answer:

20.6

Step-by-step explanation:

The problem can be solved by applyPythagoreanean theory

a^2+b^2= c^2

19^2 + b^2= 28^2

361 + b^2= 784

b^2= 784-361

= 423

b= √423

= 20.6

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Answer:

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Step-by-step explanation:

Find the missing side of the rectangle, use Pythagorean:

b² = 25² - 7² = 576
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2 years ago

What is pi and why is it important

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dimulka [17.4K]

Hi! Basically, the problem is asking us to find the values of a, b, and c in the equation $f(x)=a x^{2} +bx+c$ . Since we have three unknowns, we just need three equations. We can find these equations by using the data in the table.

First let's plug x = 0 and f(x) = 0.
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3 years ago

Read 2 more answers

You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

Aleksandr [31]

Answer:

Therefore the circumference of the circle is $=\frac{20\pi}{4+\pi}$

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

$\Rightarrow s=\frac{10-\pi r}{2}$

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

$A=\pi r^2+ (\frac{10-\pi r}{2})^2$

$\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2$

$\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}$

$\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25$

For maximum or minimum $\frac{dA}{dr}=0$

Differentiating with respect to r

$\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi$

Again differentiating with respect to r

$\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}$ > 0

For maximum or minimum

$\frac{dA}{dr}=0$

$\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0$

$\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}$

$\Rightarrow r=\frac{10}{4+\pi}$

$\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0$

Therefore at $r=\frac{10}{4+\pi}$ , A is minimum.

Therefore the circumference of the circle is

$=2 \pi \frac{10}{4+\pi}$

$=\frac{20\pi}{4+\pi}$

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