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DerKrebs
3 months 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:
AnnZ [12.3K]3 months ago
7 0
For this scenario, we start with the function:
 <span>w (x) = - 5 (x-8) (x + 4)
 </span><span>Reorganizing yields:
 </span><span>w (x) = - 5 (x² + 4x - 8x - 32)
 </span><span>w (x) = - 5x² - 20x + 40x + 160
 </span><span>w (x) = - 5x² + 20x + 160
 </span><span>Next, we take the derivative:
 </span><span>w '(x) = - 10x + 20
 </span><span>Setting this to zero and solving for x:
 </span><span>0 = -10x + 20
 </span><span>10x = 20
 </span><span>x = 20/10
 </span><span>x = 2 seconds
 </span><span>Substituting back:
 </span><span>w (2) = - 5 (2-8) (2 + 4)
 </span><span>w (2) = - 5 (-6) (6)
 </span><span>w (2) = 180 meters
 </span>Conclusion:
 
The peak height attained by the stone is:
 
w (2) = 180 meters
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Which shows the factored form of x2 – 12x – 45?
AnnZ [12381]
Hello!

(x+a)·(x+b) equals x²+xa+xb+ab which simplifies to x²-12x-45

x² equals x²
xa+xb can be expressed as (a+b)x = -12x thus, (a+b) = -12
ab equals -45

Under what conditions do (a+b) equal -12 and ab equal -45?

+3-15 results in -12 while (+3)(-15) gives -45
-3-15 yields -18 and (-3)(-15) results in +45
+3+15 produces +18 and (+3)(+15) also equal to +45
-3+15 equals +12 and (-3+15) results in -45

Conclusion:

(x+3)(x-15) 



6 0
2 months ago
Read 2 more answers
Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%. During the first month, Tran c
babunello [11817]

Detailed explanation:

Information provided:

Tran possesses a credit card that allows up to $2000 in spending with an APR of 12%.

In the initial month, Tran incurred charges of $450 and settled $150 within that billing period.

The formula to determine the interest that will accrue for Tran in the first month is (0.012)(300)

Here, 0.01 signifies the monthly interest rate.

The 300 reflects the outstanding balance, as Tran charged $450 but only paid back $150.

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2 months ago
The pilot of a plane wants to fly 800 miles east and 155 miles north of the airport. To the nearest degree, in what direction sh
babunello [11817]
It's b, you're welcome, I hope this is helpful.
6 0
1 month ago
At what rate would you need to invest $12000 and make $2880 after 8 years?
PIT_PIT [12445]

Answer:

3\%

Step-by-step explanation:

We start with the fact that

The formula for simple interest is represented by

I=P(rt)

where:

I denotes the Final Interest Value

P indicates the Principal amount to be invested

r specifies the interest rate

t refers to the Number of Time Periods

For this scenario, we have

t=8\ years\\ P=\$12,000\\I=\$2,880\\r=?

We can substitute these values into the formula mentioned above

2,880=12,000(8r)

Next, we solve for t

2,880=96,000(r)

r=2,880/96,000

r=0.03

Convert to a percentage format

0.03*100=3\%

4 0
3 months ago
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