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Zanzabum
3 years ago
15

When a = 6 and b = 22, c = 33. If c varies directly with b and inversely with a, which equation models the situation?

Mathematics
2 answers:
kogti [31]3 years ago
6 0

Answer:

c = 9b/c

Step-by-step explanation:

If c varies directly with b and inversely with a, then this may be written mathematically as;

c = kb/a

Therefore;

k = ac/b

Hence in this case;

k = (6 × 33)/22

   = k

Therefore; the equation connecting the variables is;

c = 9b/a

deff fn [24]3 years ago
4 0

Answer:

c= 9b/a

Step-by-step explanation:

The statement "y varies directly as x," means that when x increases, y increases by the same factor. The statement "y varies inversely as x means that when x increases, ydecreases by the same factor.

Then, we can say that:

c ∝ b, thus c= kb and c = k/a.

Using both equations we have that:

c= kb/a

Given that a=6, b=22 and c=33 we have that:

33 = 22k/6

Solving for k:

k=9.

Then the equation that models the situation is:

c= 9b/a

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A skier has decided that on each trip down a slope, she will do 3 more jumps than before. On her first trip she did 5 jumps. Der
taurus [48]
Since we are already given the amount of jumps from the first trial, and how much it should be increased by on each succeeding trial, we can already solve for the amount of jumps from the first through tenth trials. Starting from 5 and adding 3 each time, we get: 5 8 (11) 14 17 20 23 26 29 32, with 11 being the third trial.

Having been provided 2 different sigma notations, which I assume are choices to the question, we can substitute the initial value to see if it does match the result of the 3rd trial which we obtained by manual adding.

Let us try it below:

Sigma notation 1:

  10
<span>   Σ (2i + 3)
</span>i = 3

@ i = 3

2(3) + 3
12

The first sigma notation does not have the same result, so we move on to the next.

  10
<span>   Σ (3i + 2)
</span><span>i = 3
</span>
When i = 3; <span>3(3) + 2 = 11. (OK)
</span>
Since the 3rd trial is a match, we test it with the other values for the 4th through 10th trials.

When i = 4; <span>3(4) + 2 = 14. (OK)
</span>When i = 5; <span>3(5) + 2 = 17. (OK)
</span>When i = 6; <span>3(6) + 2 = 20. (OK)
</span>When i = 7; 3(7) + 2 = 23. (OK)
When i = 8; <span>3(8) + 2 = 26. (OK)
</span>When i = 9; <span>3(9) + 2 = 29. (OK)
</span>When i = 10; <span>3(10) + 2 = 32. (OK)

Adding the results from her 3rd through 10th trials: </span><span>11 + 14 + 17 + 20 + 23 + 26 + 29 + 32 = 172.
</span>
Therefore, the total jumps she had made from her third to tenth trips is 172.


3 0
3 years ago
Please answer this question now
Maurinko [17]

Answer:

1306.24 cm².

Step-by-step explanation:

From the diagram given above, we obtained the following information:

Radius (r) = 13 cm

Pi (π) = 3.14

Slant height (l) = 19 cm

Surface Area (SA) =.?

The surface area of the cone can be obtained as follow:

SA = πr² + πrl

SA = πr ( r + l)

SA = 3.14 × 13 ( 13 + 19)

SA = 40.82 (32)

SA= 1306.24 cm²

Therefore, the surface area of the cone is 1306.24 cm².

7 0
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Answer:

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