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son4ous [18]
3 years ago
10

The width of a swimming pool is 12 feet less than the pool's length. The area of the pool is 540 square feet. What are the dimen

sions of the pool?
Mathematics
1 answer:
fredd [130]3 years ago
8 0
100ft long and 42 wide
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A cone has a volume of 108 pi and a base diameter of 12. What is the height of the cone?
serious [3.7K]

Answer:

h  = 9 units of length

Step-by-step explanation:

Volume of a circular right cone is:

V(c)  = (1/3)*Area of the circular base * h

Where h is the height of the cone, then

V(c)  =  (1/3) * π * r² * h

And  we have that  V(c) = 108*π

Then:

108 * π  =  (1/3) * π * r² * h                  (1)

We know diameter of the circular base is 12 units, according to that

r =  d/2     ⇒  r = 12/2     r = 6 units

Then:

108 * π  [ cubic units ]  =  (1/3) * π * (6)² * h  [square units] [ units of length]

When simplifying we have to take into account that in order to keep last equation h needs to have units of length  

Therefore:

108  =  (1/3) * 36 * h

h = ( 108* 3 )/ 36

h  = 9 units of length

7 0
3 years ago
Find the maturity value of a loan of $2500 at simple interest that is to be repaid in 8 months. The interest rate is 4. 3%. A) $
Oksanka [162]

The maturity value of a loan of $2500 at the simple interest rate of 4.3% that is needed to be repaid in 8 months is $2607.50.

<h3>What is simple interest?</h3>

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = \dfrac{P\times R\times T}{100}

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

As it is given the principal amount of the loan is $2500, while the interest rate is 4.3%, therefore, after a period the interest on the loan will be,

SI = \dfrac{P\times R\times T}{100}\\\\SI = \dfrac{2500 \times 4.3 \times 1}{100}\\\\SI =107.5

Thus, the interest amount on the loan of $2500, is $107.5.

Now, in order to find the value of the loan we need to add the interest and the principal amount of the loan together. Therefore, the value of the loan can be written as,

The value of the loan = Principal Amount + Interest rate

                                    = $2500 + $107.5

                                    = $2607.50

Hence, the maturity value of a loan of $2500 at the simple interest rate of 4.3% that is needed to be repaid in 8 months is $2607.50.

Learn more about Simple Interest:

brainly.com/question/2793278

8 0
2 years ago
Y-x-3=0 rewrite as a linear equation
Delvig [45]
Solving to y gives you:y=x+3
4 0
3 years ago
Which values are solutions to the inequality below? <br><br>Check all that apply.<br><br>x2 &lt; 81
11111nata11111 [884]
A(6) and D(-4) are solutions to the equations

(6)^2 < 81  |  36 < 81

(-4)^2 < 81  |  16 < 81
5 0
2 years ago
Read 2 more answers
Write the quadratic function in the form f (x) = a (x - h)? +k
seraphim [82]

Answer:

f(x) = -3(x - 5)^2 + 4

vertex (5,4)

Step-by-step explanation:

f(x) = -3x² +30x - 71

f(x) = -3(x² +-10x) - 71

f(x) = -3(x² +-10x+5^2-5^2) - 71

f(x) = -3(x² +-10x+5^2) -3(-5^2) - 71

f(x) = -3(x² +-10x+5^2) + 4

f(x) = -3(x - 5)^2 + 4

vertex (5,4)

5 0
2 years ago
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