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MatroZZZ [7]
3 years ago
7

Given that f(x)=5x^3+ax^2-4x-2 and that (x-1) is a factor of f(x), find a.

Mathematics
1 answer:
stepladder [879]3 years ago
5 0

Answer:

a=1

Step-by-step explanation:

Because x-1 is factor of f(x)

for x1=1, f(1)=0, then

f(1)=5*1^3+a*1^2-4*1-2=0

5*1+a*1-4-2=0

5+a-6=0

a-1=0

a=1

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An object is launched from ground level with an initial velocity of 120 meters per second. For how long is the object at or abov
babunello [35]

Answer:

D) 14 seconds

Step-by-step explanation:

First we will plug 500 in for y:

500 = -4.9t² + 120t

We want to set this equal to 0 in order to solve it; to do this, subtract 500 from each side:

500-500 = -4.9t² + 120t - 500

0 = -4.9t²+120t-500

Our values for a, b and c are:

a = -4.9; b = 120; c = -500

We will use the quadratic formula to solve this.  This will give us the two times that the object is at exactly 500 meters.  The difference between these two times will tell us when the object is at or above 500 meters.

The quadratic formula is:

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Using our values for a, b and c,

x=\frac{-120\pm \sqrt{120^2-4(-4.9)(-500)}}{2(-4.9)}\\\\=\frac{-120\pm \sqrt{14400-9800}}{-9.8}\\\\=\frac{-120\pm \sqrt{4600}}{-9.8}\\\\=\frac{-120\pm 67.8233}{-9.8}\\\\=\frac{-120+67.8233}{-9.8}\text{ or }\frac{-120-67.8233}{-9.8}\\\\=\frac{-57.1767}{-9.8}\text{ or }\frac{-187.8233}{-9.8}\\\\=5.3242\text{ or }19.1656

The two times the object is at exactly 500 meters above the ground are at 5 seconds and 19 seconds.  This means the amount of time it is at or above 500 meters is

19-5 = 14 seconds.

6 0
3 years ago
Is this the answer someone help plz
ivann1987 [24]

You're right.

Since the output has different number of jumps from one number to another.

7 0
3 years ago
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What is 4 wholes and 2 3rds divided my 1 whole and w ninths
ira [324]

Answer:

Step-by-step explanation:

7 0
3 years ago
Find each unknown side length <br> X=<br> Y=
WARRIOR [948]

Answer:

7 i think not sure

Step-by-step explanation:

3 0
2 years ago
If 3 workers can paint a room in 2 hours, then approximately how long does it take 4 workers to paint the same room? Assume the
Olin [163]

It takes 1.5 hours for 4 workers to paint the same room

<em><u>Solution:</u></em>

Given that 3 workers can paint a room in 2 hours

To find: Time taken for 4 workers to paint the same room

Assume the time needed to paint the room is inversely proportional to the number of worker

time $ \propto \frac{1}{\text { number of workers }}\\\\time =k \times \frac{1}{\text { number of workers }}

Where, "k" is the constant of proportionality

<em><u>3 workers can paint a room in 2 hours</u></em>

Substitute number of workers = 3 and time = 2 hours

time =k \times \frac{1}{\text { number of workers }}\\\\2 = k \times \frac{1}{3}\\\\k = 6

Therefore,

\text {time}=6 \times \frac{1}{\text { number of workers }}

To find time taken for 4 workers to paint the same room, substitute number of workers = 4 in above expression

time = 6 \times \frac{1}{4} = 1.5

Thus it takes 1.5 hours for 4 workers to paint the same room

6 0
3 years ago
Read 2 more answers
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