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Lana71 [14]
3 years ago
9

A trough is 14 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1

ft. If the trough is being filled with water at a rate of 15 ft3/min, how fast is the water level rising when the water is 4 inches deep?

Mathematics
1 answer:
jeka57 [31]3 years ago
8 0

Step-by-step explanation:

Using similar triangles, the height and width of the water is proportional to the height and width of the trough.

w / h = 5 / 1

w = 5h

The volume of the water is:

V = AL

V = (½ wh) (14)

V = 7wh

Substituting:

V = 7(5h)h

V = 35h²

Take derivative with respect to time:

dV/dt = 70h dh/dt

Given that dV/dt = 15 and h = ⅓:

15 = 70 (⅓) dh/dt

dh/dt = 9/14

dh/dt ≈ 0.643 ft/min

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Two cars start from the same point driving in opposite directions. Both cars drive 6miles. One car stops, the other car makes a
dimaraw [331]

Answer:

  • <u>14.4 mile</u>²

Explanation:

1. By driving 6 miles each, the cars will be 6 miles + 6 miles = 12 miles appart.

2. When one car stops and the other car makes a 90° left-hand turn and drive 8 miles, you can model the situation with a right triangle, where one leg is 12 miles, the other leg is 8 miles, and the hypotenuse is the distance that separates the cars.

Hence, you must use Pythagoras to find that distance.

3. Pythagoras

  • hypotenuse² = leg₁² + leg₂²

  • hypotenuse = (12 mile)² + (8 mile)² = 144 mile² + 64 mile² = 208 mile²

  • hypotenuse=\sqrt{208mile^2}=14.4mile^2, which is rounded to the neartest tenth of a mile.
8 0
3 years ago
Cada uno de los 28 estudiantes en la clase de Romi recaudó al menos $ 25 durante el jump-a-thon. ¿Cuál es la menor cantidad de d
Crank

Answer:

$700.00 porque si cada uno recaudo por lo menos $25.00 entonces multiplicas 28 por los estudiantes y $25.00 por la cantidad menos recaudada equivalente a $700.00

Step-by-step explanation:


7 0
2 years ago
American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 50.4% of American
OLga [1]

The variance of the binomial distribution of the number of households with landline service is 2.

<h3>What is the binomial probability distribution?</h3>

It is the probability of <u>exactly x successes on n repeated trials, with p probability</u> of a success on each trial.

The variance of the distribution is given by:

V(X) = np(1 - p)

In this problem, the parameters are given as follows:

n = 8, p = 0.504.

Hence the variance is given by:

V(X) = 8 x 0.504 x 0.496 = 2.

More can be learned about the binomial distribution at brainly.com/question/24863377

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5 0
1 year ago
Choose the improper fraction that is equivalent to the mixed number 2 17/24
Alborosie

Answer:

31/24

Step-by-step explanation:

multiple 2 by 24, then add 17, which you get 31, and put it over 24

31/24

8 0
2 years ago
Read 2 more answers
A particle moves along a line so that its position at any time t &gt; 0 is given by the function s(t) = - t3 + 7t2 - 14t +8 wher
eimsori [14]

Answer:

s(5) = -12

Step-by-step explanation:

s(t) = - t³ + 7t² - 14t +8

Find the displacement during the first 5 seconds.

When t = 5

s(t) = - t³ + 7t² - 14t +8

s(5) = -5³ + 7(5)² - 14(5) + 8

= -125 + 7(25) - 70 + 8

= -125 + 175 - 70 + 8

= -12

s(5) = -12

4 0
3 years ago
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