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2 years ago

The surface area of the rectangular prism below is 286in2. Find the height.

Mathematics

1 answer:

Rudiy272 years ago

4 0

Answer: $7in$

Step-by-step explanation:

$Formula: A=2(wl+hl+hw)$

Solve for h;

Let's begin by dividing by 2.

$\frac{A}{2}=wl+hl+hw$

Subtract wl because it's the only term that doesn't have h.

$\frac{A}{2}-wl=hl+hw$

Plug your values into the formula.

$\frac{286in^2}{2}-(5in)(9in) =h(9in)+h(5in)\\143in^2-45in^2=9inh+5inh\\98in^2=14inh$

Divide by 14 to isolate h.

$\frac{98in^2}{14in}=h$

$7in=h$

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Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2

butalik [34]

To solve this question, we use the factor theorem, and using it, the polynomial function is:

$f(x) = x^3 - 2x^2 - 3x + 6$

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The factor theorem means that if k is a root of f(x), f(k) = 0.

Thus, applying the factor theorem for this question, we have to choose the function for which: $f(2) = 0, f(\sqrt{3}) = 0, f(-\sqrt{3}) = 0$

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Function 1:

$f(x) = x^3 - 2x^2 - 3x + 6$

Testing the values:

$f(2) = 2^3 - 2(2)^2 - 3(2) + 6 = 8 - 8 - 6 + 6 = 0$

$f(\sqrt{3}) = \sqrt{3^3} - 2(\sqrt{3})^2 - 3\sqrt{3} + 6 = \sqrt{3^2\times3} - 6 - 3\sqrt{3} + 6 = 3\sqrt{3} - 3\sqrt{3} = 0$

$f(-\sqrt{3}) = -\sqrt{3^3} - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 = -\sqrt{3^2\times3} - 6 + 3\sqrt{3} + 6 = -3\sqrt{3} + 3\sqrt{3} = 0$

Thus, since all three conditions are satisfied, $f(x) = x^3 - 2x^2 - 3x + 6$ is the polynomial function.

A similar question is given at brainly.com/question/11378552

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2 years ago

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2 years ago

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2 years ago

The snowiest city receive an average of 113.9 more inches of snow than the second snowiest city. The second snowiest city reciev

steposvetlana [31]

Answer:

The snowiest city receive 347.7 inches on average each year.

Step-by-step explanation:

We want to find the amount of snow the snowiest city receives on average every year, "x". It is known that this city receives 113.9 more inches than the second snowiest, which receives 223.8 inches on average every year. Therefore, the expression for "x" is:

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