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zimovet [89]
3 years ago
9

Ricardo throws a stone off a bridge into a river below. The stone's height (in meters above the water), xxx seconds after Ricard

o threw it, is modeled by w(x)=-5(x-8)(x+4)w(x)=−5(x−8)(x+4)w, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, minus, 8, right parenthesis, left parenthesis, x, plus, 4, right parenthesis What is the maximum height that the stone will reach?
Mathematics
1 answer:
Dominik [7]3 years ago
7 0
For this case we have the following function:
 <span>w (x) = - 5 (x-8) (x + 4)
 </span><span>Rewriting we have:
 </span><span>w (x) = - 5 (x ^ 2 + 4x - 8x - 32)
 </span><span>w (x) = - 5x ^ 2 - 20x + 40x + 160
 </span><span>w (x) = - 5x ^ 2 + 20x + 160
 </span><span>Then, deriving we have:
 </span><span>w '(x) = - 10x + 20
 </span><span>We equal zero and clear x:
 </span><span>0 = -10x + 20
 </span><span>10x = 20
 </span><span>x = 20/10
 </span><span>x = 2 seconds
 </span><span>Substituting values:
 </span><span>w (2) = - 5 (2-8) (2 + 4)
 </span><span>w (2) = - 5 (-6) (6)
 </span><span>w (2) = 180 meters
 </span>Answer:
 
The maximum height that the stone will reach is:
 
w (2) = 180 meters
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In Δ A B C, the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 mo
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Answer:

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Step-by-step explanation:

Let the measure of the largest angle be x

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smallest angle be z

Since the sum of angle in a triangle is 180 degrees, hence;

x + y + z = 180 .... 1

If the measure of the largest angle is 32 less than 3 times the smallest angle, then;

x = 3z - 32

3z = x+ 32

z = x+32/3 ..... 2

If he measure of the middle angle is 8 more than half the measure of the largest angle, then;

y = x/2 + 8 .... 3

Substitute 2 and 3 into 1;

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multiply through by 6

6x + 3x + 48 + 2(x+32) = 1080

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11x + 112 = 1080

11x = 1080-112

11x = 968

x = 968/11

x = 88 degrees

Get the middle angle y;

Since y = x/2 + 8

y = 88/2 + 8

y = 44 + 8

y = 52 degrees

Hence the measure of the middle angle is 52degrees

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