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Vesnalui [34]
3 years ago
14

The volume of a cylinder is 441π cubic centimeters and its radius is 7 centimeters. What is the height of the cylinder?

Mathematics
2 answers:
Sergio039 [100]3 years ago
8 0

Answer:

height =  9cm

Step-by-step explanation:

The volume of a cylinder is given as 441π cubic centimeters and it radius is 7 centimeter . The height can be computed as follows;

volume of a cylinder = πr²h

volume of the cylinder = 441π

where r = 7 cm

Therefore,

πr²h = 441π

π × 7² × h = 441π

49πh = 441π

divide both sides by π

49h = 441

divide both sides by 49

h = 441/49

h = 9cm

kvasek [131]3 years ago
7 0
The answer is:
h<span>≈2.86</span>
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Vinvika [58]

We have been given angle A as 75 degrees and sides a = 2 and b = 3.

Using Sine rule, we can set up:

\frac{Sin(A)}{a}=\frac{Sin(B)}{b}

Upon substituting the given values of angle A, and sides a and b, we get:

\frac{Sin(75)}{2}=\frac{Sin(B)}{3}

Upon solving this equation for B, we get:

\Rightarrow 3Sin(75)=2Sin(B)\\  \Rightarrow Sin(B)=\frac{3Sin(75)}{2}\\  \Rightarrow Sin(B)=1.4488\\

Since we know that value of Sine cannot be more than 1. Hence there are no values possible for B.

Hence, the triangle is not possible. Therefore, first choice is correct.

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2 years ago
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Is 2 a solution to the equation 1/2x-4=5?​
dusya [7]

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Answer:

  no

Step-by-step explanation:

Put 2 where x is and see if you get a true statement.

  1/2(2) -4 = 5

  1 -4 = 5

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2 years ago
Find f(4) when f(x)=4x^2 - 2 x - 4
prisoha [69]

Answer:

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Step-by-step explanation:

f(x)=4x^2-2x-4

f(4)=4(4)^2-2(4)-4 (I replaced x with (4) since we are to find f(4).)

f(4)=4(16)-2(4)-4    (By the order of operations, we take care of the exponents before whatever else we have here.)

f(4)=64-8-4           (By the order of operations, we take care of the multiplication as we see if left to right.)

f(4)=56-4              (By the order of operations, we perform addition/subtraction as we see it left to right.)

f(4)=52                 (This completes the simplification.)

We could have also put this in our calculator as:

4(4)^2 -  2(4)  -  4

This would have returned 52.

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3 years ago
Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for reg
Contact [7]

Answer:

a) MAX--> PC (R,P) = 0,3R+ 0,5P

b) <u>Optimal solution</u>: 40.000 units of R and 10.000 of PC = $17.000

c) <u>Slack variables</u>: S3=1000, is the unattended demand of P, the others are 0, that means the restrictions are at the limit.

d) <u>Binding Constaints</u>:

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

Step-by-step explanation:

I will solve it using the graphic method:

First, we have to define the variables:

R : Regular Gasoline

P: Premium Gasoline

We also call:

PC: Profit contributions

A: Grade A crude oil

• R--> PC: $0,3 --> 0,3 A

• P--> PC: $0,5 --> 0,6 A

So the ecuation to maximize is:

MAX--> PC (R,P) = 0,3R+ 0,5P

The restrictions would be:

1. 18.000 A availabe (R=0,3 A ; P 0,6 A)

2. 50.000 capacity

3. Demand of P: No more than 20.000

4. Both P and R 0 or more.

Translated to formulas:

Answer d)

1. 0.3 R+0.6 P ≤ 18.000

2. R+P ≤ 50.000

3. P ≤ 20.000

4. R ≥ 0

5. P ≥ 0

To know the optimal solution it is better to graph all the restrictions, once you have the graphic, the theory says that the solution is on one of the vertices.

So we define the vertices: (you can see on the graphic, or calculate them with the intersection of the ecuations)

V:(R;P)

• V1: (0;0)

• V2: (0; 20.000)

• V3: (20.000;20.000)

• V4: (40.000; 10.000)

• V5:(50.000;0)

We check each one in the profit ecuation:

MAX--> PC (R,P) = 0,3R+ 0,5P

• V1: 0

• V2: 10.000

• V3: 16.000

• V4: 17.000

• V5: 15.000

As we can see, the optimal solution is  

V4: 40.000 units of regular and 10.000 of premium.

To have the slack variables you have to check in each restriction how much you have to add (or substract) to get to de exact (=) result.  

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