Please help. I need an explanation with the answer in the pictures is the question.
1 answer:
Answer:
4, 1, 6, 2, 3, 5
Step-by-step explanation:
When you have so many to do, it is convenient to let a calculator or spreadsheet do the math for you. The attached calculated the sums. Then the magnitudes needed to be calculated from those.
The numbers listed in the answer section are the order in which the resultant vectors appear in the ascending order list. That is, (u+2v-w)/6 appears first in the list.
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Each resultant is found by adding the given vectors with the given coefficients. For example, consider the first one on the list:
... -1/2u +5v = (-1/2)(9, -2) + 5(-1, 7)
... = (-9/2 -5, +1 +35) = (-19/2, 36)
Then the magnitude of it is found by adding the components according to the Pythagorean theorem. For the resultant just computed, the magnitude is ...
... √((-19/2)² +36²) = √(90.25 +1296) = √1386.25 ≈ 37.23
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In the attached, matrix multiplication is used to compute all 6 resultants at once. The 6 resultant vectors are the answer to that multiplication. The magnitudes are computed from these results as above.
I get the magnitudes of the resultants (to 2 decimal places) to be ...
37.23, 3.89, 42.04, 28.50, 32.04, 41.10
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Answer: first choice, exponential, because there is a relatively consistent multiplicative rate of change.
Explanation:
1) I have attached the figure with the data table that represents the temperature of a cup of coffee over time.
These are the data:
Time (min) ------ Temperature (°F)
0 ----------------------- 200
10 ---------------------- 180
20 --------------------- 163
30 --------------------- 146
40 ---------------------131
50 -------------------- 118
60 -------------------- 107
2) Since, the increase in time is constant, while the decrease in temperaute is not, you know that it is not linear.
3) The other two options involve exponential models.
The exponential models have a constant multiplicative rate of change, not additive. Therefore, the only feasible choice is the first one: temperature of a cup of coffee over time.
4) You can prove it:
i) Exponential models have the general form y = A [r]ˣ, where B is r is the multiplicative rate of change: any value is equal to the prior value multiplied by r:
y₁ = A [r]¹
y₂ = A[r]²
y₂ / y1 = r ← as you see this is the constant multiplicative rate of change.
ii) Test some data:
180 / 200 = 0.9
163 / 180 ≈ 0.906 ≈ 0.9
146 / 163 ≈ 0.896 ≈ 0.9
131 / 146 ≈ 0.897 ≈ 0.9
118 / 131 ≈ 0.901 ≈ 0.9
107 / 118 ≈ 0.907 ≈ 0.9
As you see all the data of the table have a relatively consistent multiplicative rate of change, which proves that the temperature follows an exponential decay; so the right choice is the first one.
