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Sonja [21]
3 years ago
5

A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. Su

ppose water is pumped out of the pool at a rate of 216ft3 per hour. If the pool starts completely full, how many hours does it take to empty the pool?
Mathematics
1 answer:
Gala2k [10]3 years ago
8 0

Answer: it will take 9 hours to empty the pool.

Step-by-step explanation:

The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is

30 × 18 × 4 = 2160 ft³

If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence(initial amount of water in the pool when completely full).

d represents the common difference(rate at which it is being pumped out)

n represents the number of terms(hours) in the sequence.

From the information given,

a = 2160 degrees

d = - 216 ft3

Tn = 0(the final volume would be zero)

We want to determine the number of terms(hours) for which Tn would be zero. Therefore,

0 = 2160 - 216 (n - 1)

2160 = 216(n - 1) = 216n + 216

216n = 2160 - 216

216n = 1944

n = 1944/216

n = 9

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Y=-3/2L -2. At the Y axis, line L is at -2, so we add that as B or the Y intercept. We can see that the graph goes 2 over to the right and down three, which makes the slope negative and 3/2 (rise/run)
5 0
3 years ago
Curtis plays a trivia game he earns 2 points for each correct answer and loses 0.25 points for each incorrect answer he get 21 c
Maslowich

Answer:

41

Step-by-step explanation:

Curtis is playing a trivia game.

Number of points earned for each correct answer = 2

Number of points lost for each correct answer = 0.25

Given that:

Number of correct answers given by Curtis = 21

Number of wrong answers given by Curtis = 4

To find:

Total score of the game by Curtis?

Solution:

First of all, let us find the points earned by correct answers.

Points earned by correct answers = Number of correct answers multiplied by Points earned on one correct answer.

Points earned by correct answers = 21 \times 2 = 42

Now, let us find the points to be lost by wrong answers.

Points lost by wrong answers = Number of wrong answers multiplied by Points lost on one correct answer.

Points lost by wrong answers = 4 \times 0.25 = 1

The score of the game can be calculated by subtracting the points lost from the points earned.

Score = 42 - 1 = <em>41</em>

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2 years ago
Grade 8 Math
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7 0
3 years ago
Solve 7/8c-3(1/8c-7)=-6
Sergeu [11.5K]

Answer:

c = -54

Step-by-step explanation:

Solve for c:

(7 c)/8 - 3 (c/8 - 7) = -6

Put each term in c/8 - 7 over the common denominator 8: c/8 - 7 = c/8 - 56/8:

(7 c)/8 - 3 c/8 - 56/8 = -6

c/8 - 56/8 = (c - 56)/8:

(7 c)/8 - 3(c - 56)/8 = -6

(7 c)/8 - (3 (c - 56))/8 = (7 c - 3 (c - 56))/8:

(7 c - 3 (c - 56))/8 = -6

-3 (c - 56) = 168 - 3 c:

(7 c + 168 - 3 c)/8 = -6

7 c - 3 c = 4 c:

(4 c + 168)/8 = -6

Multiply both sides of (4 c + 168)/8 = -6 by 8:

(8 (4 c + 168))/8 = -6×8

(8 (4 c + 168))/8 = 8/8×(4 c + 168) = 4 c + 168:

4 c + 168 = -6×8

8 (-6) = -48:

4 c + 168 = -48

Subtract 168 from both sides:

4 c + (168 - 168) = -168 - 48

168 - 168 = 0:

4 c = -168 - 48

-168 - 48 = -216:

4 c = -216

Divide both sides of 4 c = -216 by 4:

(4 c)/4 = (-216)/4

4/4 = 1:

c = (-216)/4

The gcd of -216 and 4 is 4, so (-216)/4 = (4 (-54))/(4×1) = 4/4×-54 = -54:

Answer: c = -54

4 0
3 years ago
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Allushta [10]

Answer:

Descarte's rule says that the polynomial will have the number of zeroes equal to the number of times  the sign off the coefficient changes.

For positive real roots:

P(x)=9x^3-4x^2+10

The coefficient of polynomial is:

+9 -4 +10

There is 2 time sign in changing in 1st and 2nd term and then in 2nd and 3rd term.

So,there will be 2 positive  real roots or less but even.

For negative real roots  find P(-x)

P(-x)=-(9x^3-4x^2+10)

P(-x)=-9x^3+4x^2-10

So, coefficient of above polynomial is:

-9 +4 -10

There is 2 time sign in changing in 1st and 2nd term and then in 2nd and 3rd term.

So,there will be 2 negative real roots or less but even.

7 0
3 years ago
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