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3 years ago

8

ou are having a meeting with the CEO of a technology company. You have interpreted the number of laptops produced versus profit

as the function P(x) = x4 − 3x3 − 8x2 + 12x + 16. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

1 answer:

Mama L [17]3 years ago

4 0

Answer: We can plot the graph with help of below explanation.

Step-by-step explanation:

Since, given equation of polynomial,

$P(x) = x^4 - 3x^3 - 8x^2 + 12x + 16$

End behavior : Since, the leading coefficient of the polynomial is positive and even.

Therefore, the end behavior of the polynomial is,

$f(x)\rightarrow -\infty$ as $x\rightarrow -\infty$

And, $f(x)\rightarrow +\infty$ as $x\rightarrow +\infty$

Points of the curve : since, P(4) = 0

Therefore, (x-4) is the multiple of P(x),

And we can write, $x^4 - 3x^3 - 8x^2 + 12x + 16= (x-4)(x^3+x^2-4x-4)$

$x^4 - 3x^3 - 8x^2 + 12x + 16=(x-4)(x+1)(x^2-4)$

$x^4 - 3x^3 - 8x^2 + 12x + 16= (x-4)(x+1)(x+2)(x-2)$

Thus, the roots of equation are 4, 2, -1 and -2.

Therefore, x-intercepts of the polynomial are (4,0) (2,0) (-1,0) and (-2,0)

Also, the y-intercept of the polynomial is ( 0,16)

Thus, we can plot the graph with help of the above information.

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Which linear inequality is represented by the graph?

laiz [17]

<h2>Answer</h2>

$y\leq \frac{1}{2} x+3$

<h2>Explanation </h2>

First we are going to find the equation of the solid line passing trough the points (0, 3) and (2, 4).

Using the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{4-3}{2-0}$

$m=\frac{1}{2}$

Now we can use the point slope formula to complete the line equation:

$y-y_{1}=m(x-x_{1})$

$y-3=\frac{1}{2} (x-0)$

$y-3=\frac{1}{2}x$

$y=\frac{1}{2}x+3$

Since the shaded region is bellow the line $y=\frac{1}{2}x+3$ , the inequality represented in the graph is $y\leq \frac{1}{2} x+3$ .

5 0

3 years ago

Read 2 more answers

If y=3x and 2x-4y=3, then x=?

Allushta [10]

Answer:

y=x/2-3/4

y=3x

Step-by-step explanation:

7 0

3 years ago

An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the

lora16 [44]

Answer:

Expected benefit under this policy = $ 2694

Step-by-step explanation:

Given - An insurance policy on an electrical device pays a benefit of

4000 if the device fails during the first year. The amount of the

benefit decreases by 1000 each successive year until it reaches 0.

If the device has not failed by the beginning of any given year, the

probability of failure during that year is 0.4.

To find - What is the expected benefit under this policy ?

Proof -

Let us suppose that,

The benefit = y

Given that, the probability of failure during that year is 0.4

⇒Probability of non-failure = 1 - 0.4 = 0.6

Now,

If the device fail in second year , then

Probability = 0.6×0.4

If the device fail in third year, then

Probability = 0.6×0.6×0.4 = 0.6² × 0.4

Going on like this , we get

If the device is failed in n year, then

Probability = 0.6ⁿ⁻¹ × 0.4

Now,

The probability distribution is-

Benefit , x 4000 3000 2000 1000 0

P(x) 0.4 0.6×0.4 0.6² × 0.4 0.6³ × 0.4 1 - 0.8704

(0.4) (0.24) (0.144) (0.0864) (0.1296)

At last year, the probability = 1 - (0.4+ 0.24+ 0.144+ 0.0864) = 1 - 0.8704

Now,

We know that,

Expected value ,

E(x) = ∑x p(x)

= 4000(0.4) + 3000(0.24) + 2000(0.144) + 1000(0.0864) + 0(0.1296)

= 1600 + 720 + 288 + 86.4 + 0

= 2694.4

⇒E(x) = 2694.4 ≈ 2694

∴ we get

Expected benefit under this policy = $ 2694

5 0

3 years ago

Work out the percentage change to 2 decimal places when a price of £60 is increased to £89.99

givi [52]

Answer:

that is the solution to the question

3 0

3 years ago

Terrance claims that for the input coordinates (x, y), a rotation of 180° clockwise about the origin, followed by a reflection o

vodka [1.7K]

Answer:

Terrance is incorect.

Correct output coordinates (-y,-x)

Step-by-step explanation:

Let $(x,y)$ be the input coordinates.

First translation is a rotation of 180° clockwise about the origin. This translation has a rule

$(x,y)\rightarrow (-x,-y)$

Second translation is a reflection over the line y = x. The general rule for the reflection across the line y=x has the rule

$(a,b)\rightarrow (b,a)$

When a sequence of two translations are applied to the initial input coordinates, then

$(x,y)\rightarrow (-x,-y)\rightarrow (-y,-x)$

As you can see Terrance made a mistake and these two transformations do not cancel themselves out.

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3 years ago