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Rom4ik [11]
2 years ago
9

Two piecewise functions are shown below. What is the value of

Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
3 0

Step-by-step explanation:

I am not sure what your problem here is.

you understand the inequality signs ?

anyway, to get

6×f(-2) + 3×g(1)

we can calculate every part of the expression separately, and then combine all the results into one final result.

f(-2)

we look at the definition.

into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?

is -2 < -2 ? no.

is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.

so, we have to use

1/3 x³

for x = -2 that is

1/3 × (-2)³ = 1/3 × -8 = -8/3

g(1)

again, we look at the definition.

into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?

is 1 > 2 ? no.

is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.

so we have to use

2×|x - 1| + 3

for x = 1 we get

2×0 + 3 = 3

6×f(-2) = 6 × -8/3 = 2× -8 = -16

3×g(1) = 3× 3 = 9

and so in total we get

6×f(-2) + 3×g(1) = -16 + 9 = -7

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Two rockets, A and B, are shot from two different launch pads. The path of rocket A can be represented by the quadratic function
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<span>A(t) = −(t − 8)2 + 535
You would like to find the maximum of this function:</span> −(t − 8)^2<span>This part is always negative or zero as a number squared cannot be negative and you multiply by -1:  Thus the maximum of this part MAX:</span>−(t − 8)^2=0  
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