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3 years ago

Which polynomial is a difference of squares?

Mathematics

2 answers:

Svetllana [295]3 years ago

7 0

<u>Answer</u>

D.25x2 – 36

<u>Explanation</u>

A. x² – 16x + 64

product = 64

sum = -16

factors: -8 and -8

x² – 16x + 64 = x² - 8x - 8x + 64

= x(x - 8) - 8(x - 8)

= (x - 8)(x-8) = (x-8)² ⇒ Not a difference of squares

B.x² + 4 = (x² + 2²) ⇒ Not a difference of squares

C.9x² – x – 36

product = - 324

sum = -1

Factors: none

9x² – x – 36 ⇒ Has no perfect roots.

D.25x² – 36

25x² – 36 = (5x)² - 6² ⇒ This is the difference of squares.

Greeley [361]3 years ago

5 0

Hello,

Answer D

25x²-36=(5x)²-6²

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We have been given an expression $(8.5\times 10^3)(2\times 10^5)$ . We are asked to find the solution to our given expression expressed as scientific notation.

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kari74 [83]

<h3>Given:</h3><h3>Large cone:</h3>

r= 8 cm
h= 20 cm

<h3>Small cone:</h3>

r= 4 cm
h= 10cm

r: radius
h: height

The volume of the frustum of the given cone.

<h3>Solution:</h3>

Frustum is a part of a cone formed by cutting off the top by a parallel plane.

$\large\boxed{Formula: V= \frac{1}{3}\pi{r}^{2}h}$

Let's solve!

First, let's find the volume of the smaller cone.

Substitute the values according to the

formula.

$V= \frac{1}{3}×\pi×{4}^{2}×10$

$V= 167.5516082 \: {cm}^{3}$

Now, we can round off to the nearest hundredth.

The value in the thousandths place is smaller than 5 so we won't have to round up.

$\boxed{V= 167.55 \: {cm}^{3}}$

Next, let's find the volume of the bigger cone.

Substitute the values according to the formula.

$V= \frac{1}{3}×\pi×{8}^{2}×20$

$V= 1340.412866 \: {cm}^{3}$

Now, we can round off to the nearest hundredth.

The value in thousandths place is smaller than 5 so we won't have to round up.

$\boxed{V=1340.41 \: {cm}^{3}}$

Now, we can find the volume of the frustum.

We'll have to minus the volume of the smaller cone from the bigger cone.

$V= 1340.41-167.55$

$\large\boxed{V= 1172.86 \: {cm}^{3}}$

<u>Hence, the volume of the frustum is 1172.86 cubic centimeters.</u>

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