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3 years ago

A rectangular box has a length of 9 inches, width of 5 inches, and hight of 1 foot. Find the volume of the box in cubic inches.

Mathematics

2 answers:

jarptica [38.1K]3 years ago

4 0

9x5x1 = 45^3 is the answer

Tems11 [23]3 years ago

3 0

Answer:

$45^{3}$ inches

Step-by-step explanation:

To calculate the volume of a rectangular prism(or in this case, the rectangular box), you need to multiply the length, width and height together.

length x width x height

9 x 5 x 1

= $45^{3}$ inches

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Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

3 years ago

Read 2 more answers

A music festival charges $54.95 per ticket sold on the day of the event. A ticket purchases before the festival costs only $39.9

Wewaii [24]

B=number of ticets sold before
a=number of tickets sold after

cost of a ticket=number of tickets times cost per ticket
beforecost=39.95b
aftercost=54.95a

total cost=925000
39.95b+54.95a=925000

total number tickets=20000
b+a=20000

we have

39.95b+54.95a=925000
b+a=20000
multiply second equation by -39.95 and add to first equatin
39.95b+54.95a=925000
<u>-39.95b-39.95a=-799000 +</u>
0b+15a=126000

15a=126000
divide bot sides by 15
a=8400

sub back
b+a=20000
b+8400=20000
minus 8400 both sides
b=11600

11,600 tickets sold before
8400 tickets sold after

7 0

3 years ago

HELP DUE IN 5 MINS!!!

UkoKoshka [18]

What are the units? Tell me the units so I can solve this please.

3 0

2 years ago

Read 2 more answers

Val needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 42-m-42-m squar

oee [108]

The area enclosed by the figure is 4533.48 square meters.

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

Side length of the square = 42m

The semicircle is attached to each side of the square. So the diameter of the semicircle is the length of the square.

Radius of the semicircle = 21m

Area of the square = 42 x 42 = 1764 square meters

Area of 1 semicircle = π(21 x 21) /2

= (3.14) (441) /2

= 1384.74/2

= 692.37 square meters

Area of 4 semicircle = 4 x 692.37

= 2769.48 square meters

Total area = 1764 + 2769.48

= 4533.48 square meters

The area enclosed by the figure is 4533.48 square meters.

7 0

3 years ago

20 points!! Solve this system of lineal equations.separate the x- and y- values with a comma

Zielflug [23.3K]

Solve the following system:{12 x = 54 - 6 y | (equation 1)-17 x = -6 y - 62 | (equation 2)
Express the system in standard form:{12 x + 6 y = 54 | (equation 1)-(17 x) + 6 y = -62 | (equation 2)
Swap equation 1 with equation 2:{-(17 x) + 6 y = -62 | (equation 1)12 x + 6 y = 54 | (equation 2)
Add 12/17 × (equation 1) to equation 2:{-(17 x) + 6 y = -62 | (equation 1)0 x+(174 y)/17 = 174/17 | (equation 2)
Multiply equation 2 by 17/174:{-(17 x) + 6 y = -62 | (equation 1)0 x+y = 1 | (equation 2)
Subtract 6 × (equation 2) from equation 1:{-(17 x)+0 y = -68 | (equation 1)0 x+y = 1 | (equation 2)
Divide equation 1 by -17:{x+0 y = 4 | (equation 1)0 x+y = 1 | (equation 2)
Collect results:Answer: {x = 4 {y = 1

Please note the { are supposed to span over both equations but it interfaces doesn't allow it. Please see attachment for clarification.

7 0

3 years ago