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. Derive the sigma notation that shows how many total jumps she attempts from her third trip down the hill through her tenth trip. Then solve for the number of total jumps from her third to tenth trips.
Answers
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
Σ (2i + 3)
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
Σ (3i + 2)
i = 3
When i = 3; 3(3) + 2 = 11. (OK)
Since the 3rd trial is a match, we test it with the other values for the 4th through 10th trials.
When i = 4; 3(4) + 2 = 14. (OK)
When i = 5; 3(5) + 2 = 17. (OK)
When i = 6; 3(6) + 2 = 20. (OK)
When i = 7; 3(7) + 2 = 23. (OK)
When i = 8; 3(8) + 2 = 26. (OK)
When i = 9; 3(9) + 2 = 29. (OK)
When i = 10; 3(10) + 2 = 32. (OK)
Adding the results from her 3rd through 10th trials: 11 + 14 + 17 + 20 + 23 + 26 + 29 + 32 = 172.
Therefore, the total jumps she had made from her third to tenth trips is 172.
Answer:d
Step-by-step explanation:test
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In a rectangle, opposite sides are equal in length. Therefore, in rectangle CALM, CL is equal to AD, the diagonal of the rectangle.
Since LD is given as 15 cm, and LD is the same as AD, the length of diagonal CL is also 15 cm.
So, the correct answer is:
A. 15 cm
Final answer:
The length of diagonal CL in rectangle CALM, with LD=15cm, was calculated on the assumption that CALM is a square. Using the Pythagorean theorem, we derived approximately 21.21cm for the diagonal length, although none of the provided alternatives matched this result.
Explanation:
In rectangle CALM, if LD is 15 cm, we can solve for the length of diagonal CL using the Pythagorean theorem. The theorem relates the lengths of the sides and diagonal (hypotenuse) of a right triangle, which is formed by the diagonal and two sides of the rectangle. In this case, if LD is 15 cm and assuming that the rectangle is a square (both sides equal), we would have a right triangle with two sides of 15 cm.
Using the Pythagorean theorem, we can calculate the diagonal: a² + a² = d², where a represent the length of the sides and d stands for the diagonal. Using the equation, we get 15^2 + 15^2 = d^2, after solving it we get d=approximately 21.21.
However, none of the provided alternatives (15cm, 20cm, 25cm, 30cm) match this result, indicating that the rectangle may not be a square or that a different side (not LD) might define the diagonal length. It is crucial to have all required measurements to accurately solve the problem.
Learn more about Pythagorean theorem here:
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Answers
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.
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2x*(2x + 8) + 26*(2x + 8 ) = 1008
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Multiply first and last coefficients: 1*-200 = -200
We look for two numbers that multiply to give -200, and add to give +17
Those two numbers are 25 and -8.
Check: 25*-8 = -200 25 + -8 = 17
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Answers
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b
Step-by-step explanation:
Sphere V= 3
2. Substitute the radius into the formula:
V = 4659
2. Evaluate the power
V = 4(125)
3 Simplify:
VE
It in