Answer:
k = - 89
Step-by-step explanation:
To calculate the output, substitute t = - 7 into the equation for output, that is
k = 10(- 7) - 19 = - 70 - 19 = - 89
Factor by grouping. Group up the terms into pairs, factor each pair, then factor out the overall GCF.
x^3 + 2x^2 - 16x - 32
(x^3 + 2x^2) + (-16x-32) ... pair up terms
x^2(x + 2) + (-16x - 32) ... factor x^2 from the first group
x^2(x + 2) - 16(x + 2) ... factor -16 from the second group
(x^2 - 16)(x + 2) .... factor out (x+2)
(x - 4)(x + 4)(x + 2) .... Use the difference of squares to factor x^2-16
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The original expression completely factors to (x - 4)(x + 4)(x + 2)
The three factors are x - 4 and x + 4 and x + 2
Well, Brainly really doesn't like questions that are lifted straight out of exams, tests, or quizzes, so there's only so much I can say.
... You've GOT the formula for the height h at any time t .
... It TELLS you to find t when h=0.
... So write the equation
-16 t^2 + 32 t = 0
and then solve the equation to find t .
You'll find two solutions for t .
One of them is. t=0 .
This reveals the mind-blowing fact that the instant before the rocket was launched, at t=0, the rocket was on the ground.
The other solution for t will tell you how many seconds after launch the rocket is back on the ground.
