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3 years ago

How are discontinuities and zeros created in rational expressions, and in what ways can they be accounted for graphically?

1 answer:

8 0

Discontinuities can be recognized by observing at asymptotes. An asymptote is a line where the space between the curve and the line go to zero as single or both of the x or y coordinates inclines to infinity. Graphically, they're holes in the graph. Zeroes are points wherever the graph hits the x axis.

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PLS PLS PLS HELP!!!!!!!!!!

posledela

The absolute value is c.8

absolute value is always positive the answer is never negative. mark me as brainliest:)

7 0

3 years ago

M=2 and containing the point (7,6)

Law Incorporation [45]

Answer:

$the \: equation \: of \: the \: line \: is \to \\ \boxed{ \underline{y = 2x - 8 }}$

Step-by-step explanation:

$according \: to \: the \: provided \: info : \\ the \: equation \: of \: the \: line \: is \to \\ y - y_{1} = m(x - x_{1}) \\ y - 6 = 2(x -7) \\ y = 2x - 14 + 6 \\ \underline{y = 2x - 8 }$

7 0

3 years ago

Read 2 more answers

A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i

sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0

3 years ago

A tent forms an equilateral triangular prism, with both triangular faces exposed. each side of the triangular face has a length

Soloha48 [4]

Given:
Equilateral Triangular Prism
Each side of the triangular face has a length of 196cm
The tent is 250cm long

I have attached an image of the tent. Since the height of the tent is also the height of the triangle, I will solve for the height of the triangle using Pythagorean theorem.

I divided the equilateral triangle into 2 right triangle. The height then becomes the long leg of the triangle. The hypotenuse is 196cm and the short leg is 98cm, half of one side of the triangle.

a² + b² = c²
a² = c² - b²
a² = (196cm)² - (98cm)²
a² = 38,416cm² - 9,604cm²
a² = 28,812cm²
a = √28,812cm²
a = 169.74cm

The height of the tent is 169.74 centimeters.