9. a. Maurice says that 1079 ÷ 62 is 16 with a remainder of 87. a. Without seeing his work, how can you tell Maurice divided inc
1 answer:
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Answer:
3.189 seconds
Step-by-step explanation:
You want f(t) = 0, so ...
0 = -16t^2 +13.4t +120
0 = t^2 -0.8375t -7.5 . . . . divide by -16
0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*
0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square
√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root
t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875
It will take the rock about 3.189 seconds to hit the ground.
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* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...
(t^2 -2at +a^2) = (t -a)^2
Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.
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<em>Comment on the question</em>
We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...
Answer:
Side length and perimeter of 1 face
Area of 1 face and surface area
Step-by-step explanation:
Suppose you are given cube with side length of x units.
Then
Side length = x units
Perimeter = 4x units
Area of 1 face square units
Surface area square units
Volume cubic units
A linear relationship is any equation that, when graphed, gives you a straight line.
Consider all options:
A. Side length and perimeter of 1 face is a linear relationship, because the graph of the function is a straight line.
B. Perimeter of 1 face and area of 1 face is not a linear relationship, because the graph of this relationship is a quadratic parabola with equation .
C. Surface area and volume is not a linear relationship, because the graph of this relationship is a curve with equation .
D. Area of 1 face and surface area is a linear relationship, because the graph of the function is a straight line.
E. Side length and volume is not a linear relationship, because the graph of this relationship is a cubic parabola with equation .