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3 years ago

14

How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer t

o the nearest square inch
38 in2

63 in2

87 in2

13 in2

2 answers:

uranmaximum [27]3 years ago

8 0

I'm pretty sure its 87 in2 but don't trust me! lol

Harlamova29_29 [7]3 years ago

8 0

A = pi × r^2 = pi × (d/2)^2
So A(large) - A(small) =
$\pi {(12 \div 2)}^{2} - \pi {(8 \div 2)}^{2} \\ = \pi {(6)}^{2} - \pi {(4)}^{2} = 36\pi - 16\pi \\ = 20\pi \: {in}^{2} = 20 \times 3.1415 \: {in}^{2} \\ = 62.8 \: {in}^{2} = 63 \: {in}^{2}$

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What is the factored form of the expression 144x2 - 49?

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Given a function <img src="https://tex.z-dn.net/?f=f%28x%29%3D3x%5E4-5x%5E2%2B2x-3" id="TexFormula1" title="f(x)=3x^4-5x^2+2x-3"

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$\huge\boxed{f(-1) = -7}$

Step-by-step explanation:

In order to solve for this function, we need to substitute in our value of x inside to find f(x). Since we are trying to evalue f(-1), we will substitute -1 in as x to our equation.

$f(-1) = 3(-1)^4 - 5(-1)^2 + 2(-1) - 3$

Now we can solve for the function by multiplying/subtracting/adding our known values.

Starting with the first term to the last term:

$3(-1)^4 = 3$

<u><em>WAIT</em></u><em>!</em><em> How is this possible? </em> $-1^4 = -1$ (according to my calculator), and $3 \cdot -1 = -3$ , not 3!

It's important to note that taking a power of a negative number and multiplying a negative number are two different things. Let's use $-2^2$ as an example.

What your calculator did was follow BEMDAS since it wasn't explicitly told not to.

BEMDAS:

- Brackets

- Exponents

- Multiplication/Division

- Addition/Subtraction

Examining the equation, your calculator used this rule properly. Note that exponents come over multiplication.

So rather than being <em>"-2 squared"</em> - it's <em>"the negative of of 2 squared."</em>

Tying this back into our problem, the squared method would only be true if it looks like $-1^4$ . However, since we're substituting in -1, it looks like $(-1)^4$ , so the expression reads out as "<u><em>-1 to the fourth.</em></u>"

MULTIPLYING -1 by itself 4 times results in $-1\cdot-1\cdot-1\cdot-1=1$ .

Applying this logic to our original term, $3(-1)^4$ :

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Therefore, our first term is 3.

Let's move on to our second and third terms.

Second term: $-5x^2$

$-5(-1)^2$

Applying the same logic from our first term:

$-5(-1 \cdot -1)$
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Combining our terms, we have $3-5-2-3$ .

This comes out to be -7, hence, the value of $f(-1)$ for our function $f(x)=3x^4-5x^2+2x-3$ is <u>-7</u>.

Hope this helped!

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