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k0ka [10]
3 years ago
15

A carton can hold 1000 unit cubes that measure 1 inch by 1 inch by 1 inch. Describe the dimensions of the carton using unit cube

s. Can you explain to me how to do this problem to get the answer.

Mathematics
1 answer:
navik [9.2K]3 years ago
6 0
The dimensions of the carton are:

10 x 10 x 10 [inch OR unit cubes - it's the same since cubes' dimensions are 1 x 1 x 1 inch)

I attach the explanation below.

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9. Given the point (6,-8) values of the six trig function.
lozanna [386]

Answer:

Here's what I get.

Step-by-step explanation:

9. (6, -8)

The reference angle θ is in the fourth quadrant.

∆AOB is a right triangle.

OB² = OA² + AB² = 6² + (-8)² = 36 + 64 = 100

OB = √100 = 10  

\sin \theta = \dfrac{-8}{10} = -\dfrac{4}{5}\\\\\cos \theta =\dfrac{6}{10} = \dfrac{3}{5}\\\\\tan \theta = \dfrac{-8}{6} = -\dfrac{4}{3}\\\\\csc \theta = \dfrac{10}{-8} = -\dfrac{5}{4}\\\\\sec \theta = \dfrac{10}{6} = \dfrac{5}{3}\\\\\cot \theta = \dfrac{6}{-8} = -\dfrac{3}{4}

10. cot θ = -(√3)/2

The reference angle θ is in the second quadrant.

∆AOB is a right triangle.

OB² = OA² + AB² = (-√3)² + (2)² = 3 + 4 = 7

OB = √7

\sin \theta = \dfrac{2}{\sqrt{7}} = \dfrac{2\sqrt{7}}{7}\\\\\cos \theta = \dfrac{-\sqrt{3}}{\sqrt{7}} = -\dfrac{\sqrt{21}}{7}\\\\\tan \theta = \dfrac{2}{-\sqrt{3}} = -\dfrac{2\sqrt{3}}{3}\\\\\csc \theta = \dfrac{\sqrt{7}}{2} \\\\\sec \theta = \dfrac{\sqrt{7}}{-\sqrt{3}} = -\dfrac{\sqrt{21}}{3}\\\\\cot \theta = -\dfrac{\sqrt{3}}{2}

3 0
3 years ago
You and your friend are in a canoe race. Your friend is a half mile in front of you and paddling 3 miles per hour. You are paddl
julsineya [31]
Let the time that you caught up with your friend be t, then
8.5 - 3.4t = 8 - 3t
3.4t - 3t = 8.5 - 8
0.4t = 0.5
t = 0.5/0.4 = 1.25
therefore, you will catch up with your friend after 1.25 hours.

b.) time it will take you to cross the finnish line = 8.5/3.4 = 2.5 hours
After 2.5 hours, distance covered by your friend = 3 x 2.5 = 7.5 miles
Therefore, when you cross the finish line, you are 8 - 7.5 = 0.5 miles ahead of your friend.
7 0
3 years ago
Read 2 more answers
The triangles shown have the same perimeter. What is the value of x?
olga nikolaevna [1]

Answer:

18

Step-by-step explanation:

Since you know the perimeters are equal, write your equation.

x+6 + x+6 + x+6 = x + x+6 + 2x-6

combine like terms

3x + 18 = 4x

isolate your x by subtracting 3x from each side

18 = x

check your answer:

3x + 18 = 72

4x = 72

8 0
3 years ago
Luke’s that seven pieces of wood on top of one another if each piece was 4/8 of a foot tall how tall was his pile
Ludmilka [50]

Answer:

6 1/2 feet or 78 inches tall

Step-by-step explanation:

You have to multiply 4/8 by 7/1

First you multiply the nominators: 4 × 7 = 28

Then you multiply the denominators: 8 × 1 = 8

So the fraction would be 28/8 and it simplifies to 7/2

You can turn it into an improper fraction by seeing how many times 2 will go into seven evenly, which would be 6 times with 1 half left over

Therefore it would be 6 1/2 feet or 78 inches tall

8 0
3 years ago
Select the correct answer.<br> Which function is the inverse of ?
Artyom0805 [142]

<u>Answer:</u>

B.    f^{-1}(x) = \frac{x + 3}{9}

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

let \space\ y = f(x)\\\\y = 9x -3\\

• Now make x the subject of the equation:

9x = y + 3\\\\x = \frac{y + 3}{9} \\

• Replace x with f⁻¹(x) and y with x:

f^{-1}(x) = \frac{x + 3}{9}

6 0
2 years ago
Read 2 more answers
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