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lions [1.4K]
3 years ago
7

A shipping company is loading cube shaped crates into a larger cube shaped container the smaller cubes have side lengths 21/2 fe

et,and the larger shipping container has side lengths of 10 feet. How many crates will fit in the largest shipping container?Explain your reasoning
Mathematics
1 answer:
zheka24 [161]3 years ago
7 0

Answer:

64 crates

Step-by-step explanation:

Smaller Cube Side Length = 2 1/2 feet, or, 2.5 feet

Larger Container (Cube) Side Length = 10 feet

We find volume of larger container and find volume of small crates. We divide the large volume by volume of each crate. This will give us number of crates we can fit.

Volume of Cube = x^3

Where x is the side length of the cube

Now,

Small Crate Volume = (2.5)^3 = 15.625 cubic feet

Large Container Volume = 10^3 = 1000 cubic feet

Number of crates that would fit = 1000/15.625 = 64

So, 64 crates will fit in the largest shipping container

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Forgot to do this over winter break. Its due tomorrow and I haven't used my brain for 2 weeks. HELPPP (may have to zoom in)
ANEK [815]
1. 60,30,90 right triangle. y will be hypotenuse/2, x will be
hypotenuse*sqrt(3)/2. So x = 16*sqrt(3)/2 = 8*sqrt(3), approximately 13.85640646 
y = 16/2 = 8  
2. 45,45,90 right triangle (2 legs are equal length and you have a right angle).
X and Y will be the same length and that will be hypotenuse * sqrt(2)/2. So 
x = y = 8*sqrt(2) * sqrt(2)/2 = 8*2/2 = 8 
 3. Just a right triangle with both legs of known length. Use the Pythagorean theorem 
x = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13  
4. Another right triangle with 1 leg and the hypotenuse known. Pythagorean theorem again. 
y = sqrt(1000^2 - 600^2) = sqrt(1000000 - 360000) = sqrt(640000) = 800  5. A 45,45,90 right triangle. One leg known. The other leg will have the same length as the known leg and the hypotenuse can be discovered with the Pythagorean theorem.  x = 6. y = sqrt(6^2 + 6^2) = sqrt(36+36) = sqrt(72) = sqrt(2 * 36) = 6*sqrt(2), approximately 8.485281374  
6. Another 45,45,90 triangle with the hypotenuse known. Both unknown legs will have the same length. And Pythagorean theorem will be helpful. 
x = y. 
12^2 = x^2 + y^2 
12^2 = x^2 + x^2 
12^2 = 2x^2 
144 = 2x^2 
72 = x^2 
sqrt(72) = x 
6*sqrt(2) = x 
x is approximately 8.485281374  
7. A 30,60,90 right triangle with the short leg known. The hypotenuse will be twice the length of the short leg and the remaining leg can be determined using the Pythagorean theorem. 
y = 11*2 = 22. 
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8. A 30,60,90 right triangle with long leg known. Can either have fact that in that triangle, the legs have the ratio of 1:sqrt(3):2, or you can use the Pythagorean theorem. In this case, I'll use the 1:2 ratio between the unknown leg and the hypotenuse along with the Pythagorean theorem. 
x = 2y 
y^2 = x^2 - (22.5*sqrt(3))^2 
y^2 = (2y)^2 - (22.5*sqrt(3))^2 
y^2 = 4y^2 - 1518.75 
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y^2 = 506.25 = 2025/4 
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y = 22.5
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x = sqrt(16^2 + 30^2) = sqrt(256 + 900) = sqrt(1156) = 34  
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8 0
3 years ago
A ball is thrown directly up in the air from a height of 5 feet with an initial velocity of 60 ft/s. Ignoring air resistance, ho
Mice21 [21]

Answer:

3.8 seconds

Step-by-step explanation:

Given equation

h= -16t^2 + 60t + 5

When the ball hits the ground then height is 0

So we replace h with 0 and solve for t

0= -16t^2 + 60t + 5

a= -16 , b= 60 and c= 5

Apply quadratic formula to solve for t

t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

=\frac{-60+\sqrt{60^2-4\left(-16\right)\cdot \:5}}{2\left(-16\right)}[/tex[tex]=\frac{-60+-\sqrt{3920}}{-32}

=\frac{-60+-28\sqrt{5}}{-32}

=\frac{4(-15+-7\sqrt{5})}{-32}

=\frac{(-15+-7\sqrt{5})}{-8}

Now make two fractions and solve for x

t= -\frac{7\sqrt{5}-15}{8}=-0.0815

t= \frac{7\sqrt{5}+15}{8}=3.83

So answer is 3.8 seconds


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3 years ago
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Answer:

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125/ 2

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2 years ago
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Answer:

ratio: 104:1875

Step-by-step explanation:

toy jeep = 12.5 inches

12.5 inches = 1.04 feet

real jeep = 18.75 feet

1.04 / 18.75 = 0.055

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5 0
3 years ago
Read 2 more answers
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grandymaker [24]
700 is 100 times bigger than 7
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