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3 years ago

How many times does the graph of 4x = 32 - x2 cross the x-axis? 0 1 2

Mathematics

2 answers:

garri49 [273]3 years ago

7 0

Answer:

How many times does the graph of 4x = 32 - x2 cross the x-axis?

What are the solutions to the equation?

✔ 4, -8

Step-by-step explanation:

Yakvenalex [24]3 years ago

4 0

Answer:

Step-by-step explanation:

4x = 32 - x2 would be much clearer if written as 4x = 32 - x^2. Please use

" ^ " to indicate exponentiation.

Rewrite 4x = 32 - x^2 in the standard form of a quadratic: x^2 + 4x - 32

Then the coefficients are a = 1, b = 4 and c = -32.

Find the discriminant. It is b^2-4ac.

Here, b^2-4ac = 4^2 - 4(1)(-32), or 16 + 128, or 144.

Because the discriminant is positive, we know immediately that this quadratic has two real, unequal roots.

So, the answer to this question is "the graph of 4x = 32 - x^2 cross the x-axis in two places."

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A billboard designer has decided that a sign should have 4-ft margins at the top and bottom and 1-ft margins on the left and rig

givi [52]

An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,

The total area of the billboard, A= x·y

The total printed area of the billboard, $A_p=(x-2)(y-8)$

Given in problem that the area of the billboard is 3600 ft².

x·y = 3600

y = (3600)/x

Substituting the value of y in the equation of the total printed area of the billboard,

$A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}$

Now, the value of x is needed to be minimum, therefore, differentiating the given function,

$\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}$

Equate the differentiated function with 0,

$0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.$

Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

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2 years ago

A chef uses a circular pan with a 24-inch diameter to make a pizza. What is the area of pizza

RUDIKE [14]

Answer:

<u>The area of a pizza made in that circular pan is 452.39 inches²</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Diameter of the circular pan = 24 inches

Radius of the circular pan = 24/2 = 12 inches

2. What is the area of the pizza?

Let's use the formula of the area of a circle, this way:

Area = π * r²

Substituting with the real values, we have:

Area = 3.1416 * 12²

Area = 452.39 inches²

<u>The area of a pizza made in that circular pan is 452.39 inches²</u>

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3 years ago

Can someone give me the answer.

AysviL [449]

Answer:

1 inch

Step-by-step explanation:

Basically cause both b and c tend to form an equidistant triangle which makes them have the same distance

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2 years ago

It takes 4 people 2 days to build a patio. How long will it take 2 people, working at the same rate, to buid the patio?

kifflom [539]

Answer:

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Step-by-step explanation:

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Think about it, for half the people, it should take double the time.

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3 years ago

Solve the equation 5*e^x=15.76

liq [111]

Divide both sides by 5

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3 years ago