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2 years ago

The surface area of a cube is 400 millimeters what is the surface area of a similar cube that is larger by a scale factor of 3

1 answer:

3 0

Larger by 3 means that the legnths of the sides are larger by 3 times
so we have a cube that has area of 400
surface area=legnth times width times 6 since it is a cube and legnth=width
so
SA=w^2 times 6

6w^2=400
divide by 6
w^2=200/3
square root both sides
w=√(200/3)
so w is 3 times larger
(3w)^2 times 6 is new area

w=√(200/3)
(3√(200/3))^2 times 6=9(200/3) times 6=600 times 6=3600

answer is 3600 ml^2

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A gardener already has four and one over 2 ft of fencing in his garage. He wants to fence in a square garden for his flowers. Th

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<h2>Answer:</h2>

$6\frac{1}{2}$ <u>, "six and one over two ft".</u>

<h2>Step-by-step explanation:</h2>

Let's considerate the fact that the garden has a <u>square shape</u>.

<h3>1. Finding values of interest.</h3>

Amount of fence that the gardener already has: $4\frac{1}{2}$ ft.

Length of one side: $2\frac{3}{4}$ ft.

If one side measures $2\frac{3}{4}$ ft, and the square garden has 4 sides of equal length, because it's a square, then we must multiply the measure of one side by 4 to find the total length of fence needed:

$4*(2\frac{3}{4})=\\ \\4*(2+\frac{3}{4})=\\ \\(4*2)+(4*\frac{3}{4})=\\ \\8+(\frac{12}{4} )=\\ \\8+3=\\ \\11$

The gardener already has $4\frac{1}{2}$ , which equals $4 + \frac{1}{2}$ . Hence, the difference between the amount needed and the amount that the gardeneralready has will give us the remaining amount required. Let's do that:

$11-(4+\frac{1}{2} )=\\ \\11-(\frac{8}{2} +\frac{1}{2} )=\\ \\11-\frac{9}{2}= \\ \\\frac{22}{2} -\frac{9}{2}=\\\\ \frac{13}{2}$

<h3>3. Express your result.</h3>

$\frac{13}{2} =\\ \\\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{2}{2} +\frac{1}{2}= \\ \\6+\frac{1}{2}=\\ \\6\frac{1}{2}$

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1st answer: 52 serves

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You are given a vector in the xy plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. Determine the dire

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You are given a vector in the XY plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. The direction of the vector V is;

<h3>How to know the direction of a vector?</h3>

We know that the formula for 2 vectors like this in the x and y directions is; A = xi^ + yj^

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Magnitude of vector = 84 units

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$A = \sqrt(x^2 + y^2)\\\\87 = \sqrt(x^2+ (-66)^2)\\\\87^2= x^2+ 4356\\\\7569 = x^2+ 4356\\\\x= \sqrt(7569 - 4356)\\\\x = 56.68 units$

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Since it points entirely to the negative x-axis, then the angle is;

180 - (-27.15) = 207.15°

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