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3 years ago

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Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard

is 10 cm by 10 cm. The volume V(x) in cubic cm of the open top box is a function of the side length x in cm of the square cutouts

1 answer:

Bumek [7]3 years ago

5 0

Answer:

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

The domain for x is all real numbers greater than zero and less than 5 com

Step-by-step explanation:

<em><u>The question is</u></em>

What is the volume of the open top box as a function of the side length x in cm of the square cutouts?

see the attached figure to better understand the problem

Let

x -----> the side length in cm of the square cutouts

we know that

The volume of the open top box is

$V=LWH$

we have

$L=(10-2x)\ cm$

$W=(10-2x)\ cm$

$H=x)\ cm$

substitute

$V(x)=(10-2x)(10-2x)x\\\\V(x)=(100-40x+4x^{2})x\\\\V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

Find the domain for x

we know that

$(10-2x) > 0\\10> 2x\\ 5 > x\\x < 5\ cm$

so

The domain is the interval (0,5)

The domain is all real numbers greater than zero and less than 5 cm

therefore

The volume of the open top box as a function of the side length x in cm of the square cutouts is

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

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Help 80 points A concrete planter is formed from a square-based pyramid that was inverted and placed

Rufina [12.5K]

Answer:

<h3>(A)</h3>

The slant height of the pyramid refers to the height of a face of the pyramid.

Notice that each slant height forms a right triangle like the image attached shows, where the hypothenuse is the slant height. Additionally, the bottom leg is 1 yard, because is half of the base side, and the other leg is 2 yard. Using Pythagorean's Theorem, we have

$h^{2} =1^{2} +2^{2} \\h=\sqrt{1+4}=\sqrt{5}$

Therefore, the slant height is the square root of 5 yard.

<h3>(B)</h3>

The surface area of the composite figure is the sum of the surface area of both volumes.

<h3>Surface area of the cube.</h3>

$S_{cube}=5(2yd)^{2} =20 yd^{2}$

Notice that we only included 5 faces of the cube, that is because the sixth is the base of the pyramid, so if we include it here, we would have the wrong total surface area.

<h3>Surface area of the pyramid.</h3>

$S_{pyramid}=\frac{1}{2}pl$

Where $p$ is the perimeter of the base and $l$ is the slant height.

$S_{pyramid}=\frac{1}{2}(8yd)(\sqrt{5}yd )=4\sqrt{5}yd ^{2}$

Therefore, the surface od the composite figure is

$S_{total}=20yd^{2} +4\sqrt{5} yd^{2} \approx 29.94 yd^{2}$

<h3>(C)</h3>

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$V_{concrete}=V_{cube} -V_{pyramid}=l^{3}- \frac{1}{3}l^{2}h$

Where $l=2yd$ and $h=2yd$

$V_{concrete}=2^{3}-\frac{1}{3}(2)^{2} (2)=8-\frac{8}{3} \approx 5.33 yd^{3}$

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3 years ago

Given f(×) and g(×) = f(kx), use the graph to determine the value of k

Vitek1552 [10]

The value of k is 3

Solution:

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The points on the line are (-6, -2) and (0, 4).

Here, $x_1=-6, y_1=-2, x_2=0, y_2=4$

Formula to find equation of a line:

$$\frac{y-y_1}{x-x_1} =\frac{y_2-y_1}{x_2-x_1}$

$$\frac{y-(-2)}{x-(-6)} =\frac{4-(-2)}{0-(-6)}$

$$\frac{y+2}{x+6} =\frac{4+2}{6}$

$$\frac{y+2}{x+6} =\frac{1}{1}$

Do cross multiplication.

y + 2 = x + 6

y = x + 4

f(x) = x + 4

Given that g(x) = f(kx)

g(x) = kx + 4

The point in the graph of g(x) is ( -2, -2).

g(-2) = k(-2) + 4

we know that g(-2) = -2.

-2 = -2k + 4

Subtract 4 from both sides.

-6 = -2k

Divide by -2 on both sides.

3 = k

k = 3

The value of k is 3.

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True [87]

The correct answer is c

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3 years ago

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ankoles [38]

Answer:

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Answer:

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Step-by-step explanation:

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