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3 years ago

6

Jill has a small treasure box that is 6 in Long. it can hold a volume of 72 inches cubed and the width of the box is 5 in less t

han twice the height of the box. What are the dimensions of the box?

2 answers:

Fofino [41]3 years ago

7 0

V=l*w*h
72=6*4*3
72=72

dusya [7]3 years ago

3 0

Answer:

Step-by-step explanation:

60

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if the "x" is a multiplication symbol, the answer is 2.

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3 years ago

How to solve for x where (2^x)*x =n?

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3 years ago

Find the components of the vertical force Bold Upper Fequalsleft angle 0 comma negative 8 right anglein the directions parallel

nydimaria [60]

Answer with Step-by-step explanation:

We are given that

F=<0,-8>=0i-8j=-8j

$\theta=\frac{\pi}{3}$

The component of force is divided into two direction

1.Along the plane

2.Perpendicular to the plane

1.The vector parallel to the plane will be= $r=cos\frac{\pi}{3}i-sin\frac{\pi}{3}j=\frac{1}{2}i-\frac{\sqrt 3}{2}j$

By using $cos\frac{\pi}{3}=\frac{1}{2},sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Force along the plane will be= $\mid F_x\mid=F\cdot r$

Force along the plane will be = $\mid F_x\mid=F\cdot (\frac{1}{2}i-\frac{\sqrt 3}{2}j)=-8j\cdot(\frac{1}{2}i-\frac{\sqrt 3}{2}j)=8\times \frac{\sqrt 3}{2}=4\sqrt 3$ N

By using $i\cdot i=j\cdoty j=k\cdot k=1,i\cdot j=j\cdot k=k\cdot i=j\cdot i=k\cdot j=i\cdot k=0$

Therefore, force along the plane= $\mid F_x\mid(\frac{1}{2}i-\frac{\sqrt 3}{2}j)=4\sqrt 3(\frac{1}{2}i-\frac{\sqrt 3}{2}j)$

2.The vector perpendicular to the plane= $r=-sin\frac{\pi}{3}-cos\frac{\pi}{3}=-\frac{\sqrt 3}{2}i-\frac{1}{2}j$

The force perpendicular to the plane= $\mid F_y\mid=F\cdot r=-8j(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

The force perpendicular to the plane= $4$ N

Therefore, $F_y=4(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

Sum of two component of force= $F_x+F_y=4\sqrt 3(\frac{1}{2}i-\frac{\sqrt 3}{2}j)+4(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

Sum of two component of force= $2\sqrt 3i-6j-2\sqrt3 i-2j=-8j$

Hence,sum of two component of forces=Total force.

6 0

3 years ago

For your friend's birthday, you have 3 presents to wrap. Find the combined surface area of these 3 gifts so you know how much wr

omeli [17]

The answer is: 5,614 square inches.

The explanation is shown below:

1. The gift on the bottom is a rectangular prism. To calculate its surface area, you must apply the following formula:

$SA=2[(l)(w)+(l)(h)+(h)(w)]$

Where $l$ is the length (20 inches), $w$ is the width (42 inches) and $h$ is the heigth (16 inches).

2. Substitute values:

$SA1=2[(20in)(42in)+(20in)(16in)+(16in)(42in)]=3,664in^{2$

3. The surface area of the other gifts can be calculated with the formula for calculate the surface area of a cube:

$SA=6s^{2}$

Where $s$ is the side.

4. The surface area of the bigger cube is:

$SA2=6(15in^{2})=1,350in^{2}$

5. The surface area of the smaller cube is:

$SA3=6(10in^{2})=600in^{2}$

6. The total surface area (the combined surface area of the three gifts) is:

$SAt=SA1+SA2+SA3\\SAt=3,664in^{2}+1,350in^{2}+600in^{2}\\SAt=5,614in^{2}$

7 0

3 years ago