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3 years ago

15

A gift box in the shape of a rectangular prism measures 8 inches by 8 inches by 10 inches. What is the least amount of wrapping

paper needed to wrap the gift box?

1 answer:

lesantik [10]3 years ago

7 0

You need to calculate the total surface area of the rectangular prism. There are 6 faces total, the two on the top and the bottom will be the same while the area of the other four sides will be the same. Starting with the top and bottom, 8x8=64in^2. Now multiply this by two to get 128in^2. Now the sides will be 8x10=80in^2. Multiply this by four to get 320in^2. Now add 128in^2 plus 320in^2 to get 448in^2.

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If one angle of a set of vertical angles measures 63°, the sum of the vertical angles is °?

algol13

Answer

63rrdddd

Step-by-step explanation:

7 0

3 years ago

Determine and state the coordinates of the center and length of the radius of a circle whose equation is

padilas [110]

First, rewrite the equation in standard form.
The center-radius form of the circle equation<span> is in the format:
(x – h)^</span>2<span> + (y – k)^</span>2<span> = r^</span>2
<span>with the center being at the </span>point<span> (h, k) and the radius being "r".
</span>
(x-3)^2 + (y+4)^2 = 81

From here, you can determine the center and radius. The center is at (3,-4) and the radius is 9.

4 0

3 years ago

2. Use the graph of y=-X2 - 2x + 3 to solve

natita [175]

Answer:

Solution is x=-3 and x =1, because that is zero od function y=-x^2-2x+3

8 0

3 years ago

Consider the following function.

Kryger [21]

Answer:

See below

Step-by-step explanation:

I assume the function is $f(x)=1+\frac{5}{x}-\frac{4}{x^2}$

A) The vertical asymptotes are located where the denominator is equal to 0. Therefore, $x=0$ is the only vertical asymptote.

B) Set the first derivative equal to 0 and solve:

$f(x)=1+\frac{5}{x}-\frac{4}{x^2}$

$f'(x)=-\frac{5}{x^2}+\frac{8}{x^3}$

$0=-\frac{5}{x^2}+\frac{8}{x^3}$

$0=-5x+8$

$5x=8$

$x=\frac{8}{5}$

Now we test where the function is increasing and decreasing on each side. I will use 2 and 1 to test this:

$f'(2)=-\frac{5}{2^2}+\frac{8}{2^3}=-\frac{5}{4}+\frac{8}{8}=-\frac{5}{4}+1=-\frac{1}{4}$

$f'(1)=-\frac{5}{1^2}+\frac{8}{1^3}=-\frac{5}{1}+\frac{8}{1}=-5+8=3$

Therefore, the function increases on the interval $(0,\frac{8}{5})$ and decreases on the interval $(-\infty,0),(\frac{8}{5},\infty)$ .

C) Since we determined that the slope is 0 when $x=\frac{8}{5}$ from the first derivative, plugging it into the original function tells us where the extrema are. Therefore, $f(\frac{8}{5})=1+\frac{5}{\frac{8}{5}}-\frac{4}{\frac{8}{5}^2 }=\frac{41}{16}$ , meaning there's an extreme at the point $(\frac{8}{5},\frac{41}{16})$ , but is it a maximum or minimum? To answer that, we will plug in $x=\frac{8}{5}$ into the second derivative which is $f''(x)=\frac{10}{x^3}-\frac{24}{x^4}$ . If $f''(x)>0$ , then it's a minimum. If $f''(x)$ , then it's a maximum. If $f''(x)=0$ , the test fails. So, $f''(\frac{8}{5})=\frac{10}{\frac{8}{5}^3}-\frac{24}{\frac{8}{5}^4}=-\frac{625}{512}$ , which means $(\frac{8}{5},\frac{41}{16})$ is a local maximum.

D) Now set the second derivative equal to 0 and solve:

$f''(x)=\frac{10}{x^3}-\frac{24}{x^4}$

$0=\frac{10}{x^3}-\frac{24}{x^4}$

$0=10x-24$

$-10x=-24$

$x=\frac{24}{10}$

$x=\frac{12}{5}$

We then test where $f''(x)$ is negative or positive by plugging in test values. I will use -1 and 3 to test this:

$f''(-1)=\frac{10}{(-1)^3}-\frac{24}{(-1)^4}=-34$ , so the function is concave down on the interval $(-\infty,0)\cup(0,\frac{12}{5})$

$f''(3)=\frac{10}{3^3}-\frac{24}{3^4}=\frac{2}{27}>0$ , so the function is concave up on the interval $(\frac{12}{5},\infty)$

The inflection point is where concavity changes, which can be determined by plugging in $x=\frac{12}{5}$ into the original function, which would be $f(\frac{12}{5})=1+\frac{5}{\frac{12}{5}}+\frac{4}{\frac{12}{5}^2 }=\frac{43}{18}$ , or $(\frac{12}{5},\frac{43}{18})$ .

E) See attached graph

5 0

3 years ago

What percent of 59 is 44.1? Round the answer to the nearest<br> hundredth of a percent if necessary.

olga nikolaevna [1]

Answer:

133.78684807256

Step-by-step explanation:

step 1: We need the assumption that 44.1 is 100% since it is our output value

step 2: We need to represent the value we seek in x

step 3: From step 1, it follows that 100% = 44.1

step 4: In the same vein x% = 59

step 5: This give us a pair of simple equations:

100% = 44.1 (1)

x% = 59 (2)

step 6: by simplify dividing equation 1 by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have

$\frac{100}{x} = \frac{44.1}{59}$

step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x}{100 } = \frac{59}{44.1}$

= x = 133.78684807256

Therefore, 59 is 133.78684807256% of 44.1

4 0

3 years ago