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2 years ago

The volume of this rectangular prism is 108 cubic feet.

Mathematics

2 answers:

Reil [10]2 years ago

7 0

Answer:

8 feet.

Step-by-step explanation:

We have been given that the volume of this rectangular prism is 108 cubic feet. Width are height are 4.5 feet and 3 feet. We are asked to find the length of the prism.

We know that volume of rectangular prism is product of length, height and width of prism.

$V=lwh$

Upon substituting our given values in volume formula, we will get:

$108\text{ ft}^3=l(4.5\text{ ft})(3\text{ ft})$

$108\text{ ft}^3=l(13.5\text{ ft}^2)$

$l(13.5\text{ ft}^2)=108\text{ ft}^3$

$\frac{l(13.5\text{ ft}^2)}{13.5\text{ ft}^2}=\frac{108\text{ ft}^3}{13.5\text{ ft}^2}$

$l=8\text{ ft}$

Therefore, the length d the prism is 8 feet.

aleksley [76]2 years ago

3 0

Answer:

8 feet

Step-by-step explanation:

4.5 times 3 is 13.5 and 108 divided by 13.5 is 8

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The population can be modeled by P(t) = 82.5 − 67.5cos⎡ ⎣(π/6)t ⎤ ⎦, where t is time in months (t = 0 represents January 1) and

Fed [463]

Answer:

The intervals in which the population is less than 20,000 include

(0 ≤ t < 0.74) and (11.26 < t ≤ 12)

Step-by-step explanation:

P(t) = 82.5 - 67.5 cos [(π/6)t]

where

P = population in thousands.

t = time in months.

During a year, in what intervals is the population less than 20,000?

That is, during (0 ≤ t ≤ 12), when is (P < 20)

82.5 - 67.5 cos [(π/6)t] < 20

- 67.5 cos [(π/6)t] < 20 - 82.5

-67.5 cos [(π/6)t] < -62.5

Dividing both sides by (-67.5) changes the inequality sign

cos [(π/6)t] > (62.5/67.5)

Cos [(π/6)t] > 0.9259

Note: cos 22.2° = 0.9259 = cos (0.1233π) or cos 337.8° = cos (1.8767π) = 0.9259

If cos (0.1233π) = 0.9259

Cos [(π/6)t] > cos (0.1233π)

Since (cos θ) is a decreasing function, as θ increases in the first quadrant

(π/6)t < 0.1233π

(t/6) < 0.1233

t < 6×0.1233

t < 0.74 months

If cos (1.8767π) = 0.9259

Cos [(π/6)t] > cos (1.8767π)

cos θ is an increasing function, as θ increases in the 4th quadrant,

[(π/6)t] > 1.8767π (as long as (π/6)t < 2π, that is t ≤ 12)

(t/6) > 1.8767

t > 6 × 1.8767

t > 11.26

Second interval is 11.26 < t ≤ 12.

Hope this Helps!!!

3 0

2 years ago

Which of the following functions gives the radius, r(v), of a conical artifact that is 20 inches tall as a function of its volum

irinina [24]

<h3>Radius as function of volume is:</h3>

$r(v) = \sqrt{\frac{3v}{20 \pi }}\ inches$

Solution:

The volume of cone is given as:

$v = \frac{1}{3}\pi r^{2} h$

Where,

r is the radius

h is the height

From given,

height = 20 inches

From formula,

$v = \frac{1}{3}\pi r^{2} h$

Rearrange , so that r is alone in left side of equation

$3v = \pi r^2 h\\\\\pi r^2 h = 3v\\\\r^2 = \frac{3v}{\pi h}\\\\Take\ square\ root\ on\ both\ sides\\\\r = \sqrt{\frac{3v}{\pi h}}$

Substitute h = 20

$r = \sqrt{\frac{3v}{20 \pi }}$

Thus, radius as function of volume is:

$r(v) = \sqrt{\frac{3v}{20 \pi }}\ inches$

4 0

2 years ago

Nadia is mountain climbing. She started at an altitude of 19.26 feet below sea level and then changed her altitude by climbing a

lesya692 [45]

Answer:

5,418.2 feet

Step-by-step explanation:

Nadia is carrying out mountain climbing.

She started climbing the mountain at an altitude of 19.26 feet below the sea level.

Nadia changed her altitude by climbing a total of 5,437.8 feet from her starting position.

Therefore, Nadia's altitude at the end of her climb can be calculated as follows

= 5,437.8-19.6

= 5,418.2

Hence Maria's altitude at the end of her climb is 5,418.2 feet

3 0

2 years ago

A maple syrup company is making a new label for its barrels of syrup. If the barrels are 5 feet tall and have a radius of 2 feet

Elanso [62]

Answer:

(A)62.8 square feet

Step-by-step explanation:

Height of the barrels = 5 feet

Radius of the barrels= 2 feet

$\pi$ =3.14

The barrel is in the shape of a cylinder and the area of the label the company needs is that of the round sides(curved surface area) of the cylinder.

Curved Surface Area of a Cylinder= $2\pi rh$

=2X3.14X2X5

=62.8 square feet

The company need 62.8 square feet of label.

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2 years ago

A rectangle and a triangle have the same area.

Ivanshal [37]

Area of a rectangle is length times width. Area of a triangle is one-half base times height. Now just plug in everything we know and set the equations equal to each other.

(6)(8) = 0.5(8)(h)

Solve for height

48 = 4h

h = 12 m

7 0

2 years ago