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3 years ago

Please help me! Need answer quick!

Mathematics

1 answer:

aksik [14]3 years ago

6 0

Let h = height of triangle

h^2 + 12^2 = 15^2

h^2 + 144 = 225

h^2 = 225 - 144

h^2 = 81

sqrt{h^2} = sqrt{81}

h = 9 cm

For part B, we need to find surface area because it represents the perimeter of this 3-D figure. The formula needed is SA = B + LA.

1. First find the lateral area.

LA = perimeter of triangle • height

LA = ph

p = 15 + 15 + 24

p = 30 + 24

p = 54 cm

LA = (54)(9)

LA = 486 cm^2

2. We now find the base of each triangle. This is found by finding the area of each triangle and multiplying by 2.

A = (1/2)bh

A = (1/2)(24)(9)

A = 108 cm^2

A = 2•108 cm^2

A = 216 cm^2 = our B in the surface area formula.

SA = B + LA

SA = 216 cm^2 + 486 cm^2

SA = 702 cm^2

The amount of cardboard needed is 702 cm^2.

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3 years ago

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Answer:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

Step-by-step explanation:

We want to find a third degree polynomial with zeros x = 2 and x = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since x = 2i is a root, x = -2i must also be a root.

Hence, we will have the three factors:

$\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))$

Where a is the leading coefficient.

Expand and simplify the second and third factors:

$\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}$

Hence:

$\displaystyle f(x) = a(x-2)(x^2+4)$

Since f(-1) = 30:

$\displaystyle \begin{aligned} f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}$

In conclusion, third degree polynomial function is:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

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