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2 years ago

What are the zeros of this polynomial and state their multiplicity at each y=(x-5)(x+2)^2

Mathematics

1 answer:

N76 [4]2 years ago

7 0

Answer:

Step-by-step explanation:

The zeros of a polynomial are the x-intercepts of the function. To find them, we factor the polynomial and set each factor equal to 0.

This polynomial is already factored so set each to 0 and solve for x.

$x-5=0\\x=5\\(x+2)^{2}=0 \\(x+2)=0\\x=-2$

This means x=-2, 5. Each zero or root has a multiplicity - the number of times the factor occurs. This is also known as the exponent of the factor expression.

(x+5) occurs once since it has exponent 1.

$(x+2)^{2}$ occurs twoce since it has exponent 2.

x=5 mult. 1, x=-2 mult. 2

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What is the value of c such that the line y=2x+3 is tangent to the parabola y=cx^2

satela [25.4K]

The value of $c$ such that the line $y = 2\cdot x + 3$ is tangent to the parabola $y = c\cdot x^{2}$ is $-\frac{1}{3}$ .

If $y = 2\cdot x + 3$ is a line tangent to the parabola $y = c\cdot x^{2}$ , then we must observe the following condition, that is, the slope of the line is equal to the first derivative of the parabola:

$2\cdot c \cdot x = 2$ (1)

Then, we have the following system of equations:

$y = 2\cdot x + 3$ (1)

$y = c\cdot x^{2}$ (2)

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Whose solution is shown below:

By (3):

$c =\frac{1}{x}$

(3) in (2):

$y = x$ (4)

(4) in (1):

$y = -3$

$x = -3$

$c = -\frac{1}{3}$

The value of $c$ such that the line $y = 2\cdot x + 3$ is tangent to the parabola $y = c\cdot x^{2}$ is $-\frac{1}{3}$ .

We kindly invite to check this question on tangent lines: brainly.com/question/13424370

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1 year ago

Driving to your friend's house, you travel at an average rate of 35 miles per hour. On your

Mamont248 [21]

Answer:

14 miles.

Step-by-step explanation:

Let the distance traveled from home to destination = x miles.

Speed while going to friend's house = 35 miles per hour.

Speed while coming back = 40 miles per hour.

Total Time taken for the journey = 45 minutes = 0.75 hours.

Let the time taken while going to friend's house = y hours.

Therefore, the time taken while going to friend's house = (0.75 - y) hours.

To find x and y, model the speeds of both the journeys.

Speed while going to friend's house = Distance/Time.

35 = x/y.

x = 35y (Equation 1).

Speed while coming back = Distance/Time.

40 = x/(0.75 - y).

x = 40(0.75 - y) (Equation 2).

Since x = x, therefore:

35y = 30 - 40y.

75y = 30.

y = 30/75.

y = 0.4 hours.

Put y = 0.4 hours in Equation 1:

x = 35y.

x = 35(0.4).

x = 14.

Therefore, the distance between my friend's house and my house is 14 miles!!!

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2 years ago

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Hello,

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FinnZ [79.3K]

Answer:

The speed of the private airplane is 770 mph, the speed of the commercial airplane is 980 mph.

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2 years ago

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