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RideAnS [48]
3 years ago
12

Look at the formula for the volume of a cylinder below.

Mathematics
1 answer:
scZoUnD [109]3 years ago
8 0
h = V / ( \pi r^2)

Okay, so we already have the volume equation for a cylinder here.
V = \pi r^2 h
Since we need to find the height(h), we need to basically isolate it in the equation. To do that we just have to divide both sides by (pi * r^2), where we end up with:
V / (\pi r^2) = h(\pi r^2) / (\pi r^2)
then
V / ( \pi  r^2) = h
h = V / ( \pi r^2)
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Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interes
Vsevolod [243]

Answer:

  • CDs — $10,000
  • bonds — $80,000
  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

  0.0275c +.045b +0.104s = 8555 . . . . . total income earned

  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

  b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b

  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

  2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify

  .0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn

  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

  s = 65000 -2c . . . . . . . expression we can substitute for s

  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

_____

Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

6 0
3 years ago
What is the answer and why is it true?
pashok25 [27]

Answer:

1.5 lbs b/c 2 block equal 3 vs 3 blocks equal 3

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
School a has 18 staff and 225 students.
Pavel [41]

Answer:

School A

Step-by-step explanation:

School A has a ratio of 18/225 = 2/25 staff to students
School B has a ratio of 23/322 = 2/28 = 1/14 staff to students
Assuming that a better ratio means more staff per students School A has a better ratio

6 0
3 years ago
Please answer this question, will give brainliest!
Ad libitum [116K]

Answer:

I dont really know the answer.. but ill try; if its wrong I am so sorry;

Step-by-step explanation:

First you must get the area of a circle, which is; A= pi r squared

and all you have to do is fill it in like this;

A= 3.14 x 2.0

           ^

    A= 6.28

5 0
3 years ago
4. A number m is such that when it is divided by 30, 36, and 45 the remainder is always 7,
Bezzdna [24]

Answer:

187

Step-by-step explanation:

A number m is such that when it is divided by 30, 36 and 45 the remainder is always 7.

We should first find the LCM of 30, 36 and 45

We get that the LCM of the three numbers is 280 (working attached).

So now;

\frac{180}{30} = 6

\frac{180}{36} = 5

\frac{180}{45} = 4

But we need a number that leaves a remainder of 7 so we add 7 to 180 to get; 180 + 7 = 187.

5 0
3 years ago
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