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2 years ago

Which graph represents the function f(x)=x4+8x3+6x2−40x+25?

Mathematics

2 answers:

dimulka [17.4K]2 years ago

8 0

Answer:

Graphic A. (Upper left graphic)

Step-by-step explanation:

The roots of the fourth-order polynomial are, that is the values of x which make polynomial equal to zero:

$x = 1$ and $x = -5$

By comparing the results with each graphic, it is evident that option A corresponds with the function. (Upper left graphic)

son4ous [18]2 years ago

6 0

Answer:

In the picture below.

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The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillat

Greeley [361]

Answer:

1) $L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

2) $T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

3) $T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

Step-by-step explanation:

Part 1

For this case we know the following info: The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillation), T seconds.

$L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

Part 2

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

Part 3

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

Replacing we got:

$T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

8 0

2 years ago

Henri bought a swimsuit at a cost of $8. Which statements are true regarding the cost of the suit? Select three options.

lora16 [44]

Answer:

The first, second to last and last stements are true

Step-by-step explanation:

You times 8 by the percentage as

e.g 8 x 1.50 = 12 is the same as marked up by 50%

e.g 8 x 1.70 =13.6 is the same as marked up by 70%

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2 years ago

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A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

den301095 [7]

Answer:

The maximum height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> the height of the prism

we know that

the area of the rectangular base of the prism is equal to

$A=L*W$

$A\leq 27\ m^{2}$

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Substitute equation B in equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substitute equation B and equation D in the inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The solution for x is the interval----------> $[0,12]$

see the attached figure

but remember that

The width of the base must be $9$ meters less than the height of the prism

the solution for x is the interval ------> $(9,12]$

The maximum height of the prism is $12\ m$

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2 years ago

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The random variable x is said to have the yule simon distribution if

balu736 [363]

The Yule-Simon distribution is a discrete probability distribution. It is named after Udny Yule and Herbert A. Simon.

The Yule–Simon distribution was originally created by Yule as a limiting distribution model for a particular stochastic process, called the "Yule process" or the "preferential attachment process," in his study of the distribution of biological taxa and subtaxa.

The random variable X is said to have the Yule-Simon distribution if

P (X=k) = <u> 4 </u> where k = 1,2,...<u>
</u> k (k+1)(k+2)

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2 years ago

A man purchased 6 fruits at Rs 10 How many fruits will he sell at Rs 9 so that he may make an overall profit of 8%

Agata [3.3K]

Answer:

Step-by-step explanation:

P(x)=S(x)-C(x)

0.8=9-C(x)

C(x)=9 -0.08

C(x)=8.92

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2 years ago