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timurjin [86]
3 years ago
9

A cylinder has a height of 13 millimeters and a radius of 15 millimeters. What is its volume? Use ​ ≈ 3.14 and round your answer

to the nearest hundredth.
Mathematics
1 answer:
Butoxors [25]3 years ago
5 0

Answer: The volume of the cylinder is 9,184.5 cubic millimeters.

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a cylinder (V) : π x radius ² x height

Replacing with the values given and solving for v (Volume)

V = 3.14 x 15² x 13

V = 9,184.5 mm3

In conclusion, the volume of the cylinder is 9,184.5 cubic millimeters.

Feel free to ask for more if needed or if you did not understand something  

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Please help! Its for my big test tomorrow!
Travka [436]

Answer:

# The solution x = -5

# The solution is x = 1

# The solution is x = 6.4

# The solution is x = 4

# The solution is 1.7427

# The solution is 0.190757

Step-by-step explanation:

* Lets revise some rules of the exponents and the logarithmic equation

# Exponent rules:

1- b^m  ×  b^n  =  b^(m + n) ⇒ in multiplication if they have same base

  we add  the power

2- b^m  ÷  b^n =  b^(m – n) ⇒  in division if they have same base we

   subtract  the power

3- (b^m)^n = b^(mn) ⇒ if we have power over power we multiply

   them

4- a^m × b^m = (ab)^m ⇒ if we multiply different bases with same  

   power then we multiply them ad put over the answer the power

5- b^(-m) = 1/(b^m)  (for all nonzero real numbers b) ⇒ If we have

   negative power we reciprocal the base to get positive power

6- If  a^m  =  a^n  ,  then  m  =  n ⇒ equal bases get equal powers

7- If  a^m  =  b^m  ,  then  a  =  b    or    m  =  0

# Logarithmic rules:

1- log_{a}b=n-----a^{n}=b

2- loga_{1}=0---log_{a}a=1---ln(e)=1

3- log_{a}q+log_{a}p=log_{a}qp

4- log_{a}q-log_{a}p=log_{a}\frac{q}{p}

5- log_{a}q^{n}=nlog_{a}q

* Now lets solve the problems

# 3^{x+1}=9^{x+3}

- Change the base 9 to 3²

∴ 9^{x+3}=3^{2(x+3)}=3^{2x+6}

∴ 3^{x+1}=3^{2x+6}

- Same bases have equal powers

∴ x + 1 = 2x + 6 ⇒ subtract x and 6 from both sides

∴ 1 - 6 = 2x - x

∴ -5 = x

* The solution x = -5

# ㏒(9x - 2) = ㏒(4x + 3)

- If ㏒(a) = ㏒(b), then a = b

∴ 9x - 2 = 4x + 3 ⇒ subtract 4x from both sides and add 2 to both sides

∴ 5x = 5 ⇒ divide both sides by 5

∴ x = 1

* The solution is x = 1

# log_{6}(5x+4)=2

- Use the 1st rule in the logarithmic equation

∴ 6² = 5x + 4

∴ 36 = 5x + 4 ⇒ subtract 4 from both sides

∴ 32 = 5x ⇒ divide both sides by 5

∴ 6.4 = x

* The solution is x = 6.4

# log_{2}x+log_{2}(x-3)=2

- Use the rule 3 in the logarithmic equation

∴ log_{2}x(x-3)=2

- Use the 1st rule in the logarithmic equation

∴ 2² = x(x - 3) ⇒ simplify

∴ 4 = x² - 3x ⇒ subtract 4 from both sides

∴ x² - 3x - 4 = 0 ⇒ factorize it into two brackets

∴ (x - 4)(x + 1) = 0 ⇒ equate each bract by 0

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

OR

∵ x + 1 = 0 ⇒ subtract 1 from both sides

∴ x = -1

- We will reject this answer because when we substitute the value

 of x in the given equation we will find log_{2}(-1) and this

 value is undefined, there is no logarithm for negative number

* The solution is x = 4

# log_{4}11.2=x

- You can use the calculator directly to find x

∴ x = 1.7427

* The solution is 1.7427

# 2e^{8x}=9.2 ⇒ divide the both sides by 2

∴ e^{8x}=4.6

- Insert ln for both sides

∴ lne^{8x}=ln(4.6)

- Use the rule ln(e^{n})=nln(e) ⇒ ln(e) = 1

∴ 8x = ln(4.6) ⇒ divide both sides by 8

∴ x = ln(4.6)/8 = 0.190757

* The solution is 0.190757

7 0
3 years ago
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Megan and her sister are planning their
Yuri [45]

Answer:  y = 12.50x + 45

Step-by-step explanation:

if x is the number of hours  and you pay $12.50 per hour then we can come up the expression 12.50x

You will be charge $45 as an initial fee so it will be 12.50x + 45 and that has to equal the total cost which is y.

y = 12.50x + 45

7 0
3 years ago
Which expression is equivalent to the given expression?
Studentka2010 [4]
Which expression is equivalent to the given expression?

15(12-x)

A. 15*12-x


hope this help
4 0
3 years ago
A square has an area of 49 in.² what is each side of the perimeter
ludmilkaskok [199]
I hope this helps you




square one side a



Area=a.a



49=a.a



7.7=a.a



a=7



Perimeter=4a=4.7=28
8 0
2 years ago
an ostrich egg weighs 2.9 pounds.The difference between the weight of this egg and the weight of an emu egg is 1.6 pounds.write
Alex73 [517]

Answer:

2.9-w=1.6

Step-by-step explanation:

Let w be weight of emu egg in pounds.

We have been given that an ostrich egg weighs 2.9 pounds.The difference between the weight of this egg and the weight of an emu egg is 1.6 pounds.

We can represent this information as:

2.9-w=1.6

Therefore, the equation 2.9-w=1.6 will give us the weight of the emu egg, w, in pounds.

8 0
3 years ago
Read 2 more answers
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