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2 years ago

Find the value of c so that the polynomial p is divisible by (x+2)

Mathematics

1 answer:

alexandr1967 [171]2 years ago

3 0

Answer:

The value of c is 8.

Step-by-step explanation:

When a function is divisible by a factor, it will get 0 value. So, you have to substitute x = -2 into p(x) and equals to 0 :

$p(x) = 4 {x}^{3} + c {x}^{2} + x + 2$

$p( - 2) = 4 {( - 2)}^{3} + c {( - 2)}^{2} + ( - 2) + 2$

$4( - 8) + 4c - 2 + 2 = 0$

$- 32 + 4c = 0$

$4c = 32$

$c = 32 \div 4$

$c = 8$

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Find the volume of the rectangular

Kobotan [32]

Answer:

Hope this will help you

Step-by-step explanation:

$volume \: of \: rectangular \: prism = l \times b \times h \\ = 0.6 ft\times 0.8 ft\times 3.8ft \\ = 1.824 {ft}^{3}$

4 0

1 year ago

Solve for x.<br> Your answer must be simplified.<br> 17r > -17

Snowcat [4.5K]

Hello :D

Answer:

$\boxed{R>-1}$

The answer should have a negative sign.

Step-by-step explanation:

First, you do is divide by 17 from both sides of an equation.

$\frac{17r}{17}>\frac{-17}{17}$

Then, you simplify and solve to find the answer.

$-17\div17=-1$

$\boxed{R>-1}$ , which is our answer.

I hope this helps you!

Have a great day! :D

4 0

2 years ago

Read 2 more answers

Talulah is an ecologist who studies the change in the penguin population of Antarctica over time. She observed that the populati

Oksana_A [137]

Answer:

P(t) = 27000 * (1/9)^(t/4)

Step-by-step explanation:

This problem can me modelled with an exponencial formula:

P = Po * (1+r)^t

Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.

In this problem, we have that the inicial population/value is 27000, the rate is -8/9 (negative because the population decays), and the time t is in months, so as the rate is for every 4 months, we use the value (t/4) in the exponencial.

So, our function will be:

P(t) = 27000 * (1-8/9)^(t/4)

P(t) = 27000 * (1/9)^(t/4)

8 0

2 years ago

Read 2 more answers

Solve the system by substitution.<br> 10x + 5y = -50<br> y = -x

Pie

Answer:

(1,-12)

Step-by-step explanation:

-10+5y=-50

5y=-60

y=-12

10x-60=-50

10x=10

x=1

8 0

2 years ago

A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is f

jonny [76]

Answer:

2580 ft-lb

Step-by-step explanation:

Water leaks out of the bucket at a rate of $\frac{0.15 \mathrm{lb} / \mathrm{s}}{1.5 \mathrm{ft} / \mathrm{s}}=0.1 \mathrm{lb} / \mathrm{ft}$

Work done required to pull the bucket to the top of the well is given by integral

$W=\int_{a}^{b} F(x) dx$

Here, function $F(x)$ is the total weight of the bucket and water $x$ feet above the bottom of the well. That is,

$F(x)=4+(42-0.1 x)$

$=46-0.1x$

$a$ is the initial height and $b$ is the maximum height of well. That is,

$a=0 \text { and } b=60$

Find the work done as,

$W=\int_{a}^{b} F(x) d x$

$=\int_{0}^{60}(46-0.1 x) dx$

$&\left.=46x-0.05 x^{2}\right]_{0}^{60}$

$=(2760-180)-0[$

$=2580 \mathrm{ft}-\mathrm{lb}
$

Hence, the work done required to pull the bucket to the top of the well is $2580 \mathrm{ft}- \mathrm{lb}$

4 0

2 years ago