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3 years ago

Find the equation of the line tangent to y = -3x2 + x - 5 at x = -1

Mathematics

1 answer:

SVEN [57.7K]3 years ago

6 0

$\boxed{y+9=7(x+1)}$

<h2>Explanation:</h2>

The Point-Slope form of the equation of a line is given by:

$y-y_{0}=m(x-x_{0}) \\ \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{0},y_{0}):A \ point$

To find the equation of the line tangent to $y=-3x^2+x-5 \ at \ x=-1$ , we need to take the derivative:

$\frac{dy}{dx}=-6x+ 1$

The slope of the line tangent to $y=-3x^2+x-5$ at $x=-1$ can be found evaluationg $x=1$ in the derivative:

$\frac{dy}{dx}\Bigr\rvert_{x=-1}=-6x+ 1 \\ \\ \\ \frac{dy}{dx}\Bigr\rvert_{x=-1}=-6(-1)+ 1 \\ \\ \\ m=\frac{dy}{dx}\Bigr\rvert_{x=-1}=7$

Finding the point:

$x_{0}=-1 \\ \\ Then: \\ \\ y_{0}=-3(-1)^2-1-5=-9 \\ \\ (x_{0},y_{0})=(-1,-9)$

Finally, our line is:

$y-(-9)=7(x-(-1)) \\ \\ \boxed{y+9=7(x+1)}$

The representation of this problem is shown below.

<h2>Learn more:</h2>

Derivative of functions: brainly.com/question/2142425

#LearnWithBrainly

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What is the diameter of a circle with the endpoints (4, 3) and (4, -3)?

Dahasolnce [82]

Given the endpoints of our diameter, we can use the distance formula to find the distance between the points.

Distance Formula:

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2$

( $x_2$ and $x_1$ are the x-values of the coordinates and $y_2$ and $y_1$ are the y-values of the coordinates)

Inserting our values into the distance formula we can find the length of the diameter:

$\sqrt{(4 - 4)^2 + (-3 - 3)^2}$

$\sqrt{(-6)^2}$

$\sqrt{36} = \boxed{6}$

The diameter of our circle is 6, or choice C.

3 0

3 years ago

9. If y varies directly with x and y = -3 when x = 6, find y when x = 14.

masya89 [10]

If y varies directly with x and y = -3 when x = 6, find y when x = 14.

We know if y varies directly with x, we get the equation

y ∝ x

y = kx

k = y/x

where k is called the constant of variation.

we are given y = -3 when x = 6

so substitute y = -3 and x = 6 to determine 'k'

k = y/x

k = -3/6 = -1/2

Now we have to find y when x = 14

so substituting x = 14 and k = -1/2 to find y

y = kx

y = -1/2 × 14 = -7

Therefore, the value of y = -7 when x = 14

10) If y is directly proportional to x and y = 4 when x = 3, find x when y = -12.

we are given y = 4 when x = 3

so substitute y = 4 and x = 3 to determine 'k'

k = y/x

k = 4/3

Now we have to find x when y = -12

so substituting y = -12 and k = 4/3 to find x

y = kx

x = y/k

x = [-12] / [4/3] = [-12×3] / [4]

x = -36/4

x = -9

Therefore, the value of x = -9 when x = 3

11)

If y varies directly with x and y = -6 when x = 2, find the constant of variation.

We are given

y = -6

x = 2

so substitute y = -6 and x = 2 in the equation

k = y/x

k = -6/2

k = -3

Therefore, the value of the constant of variation will be:

k = -3

7 0

3 years ago

Pythagorean theorem: find the perimeter

denis-greek [22]

The answer is 5
Explanation:
We need to use the Pythagorean,
a^2 + b^2 = c^2
Where c is the hypotenuse
We can fill in spots now 12^2 + b^2 = 13^2
And then we solve 144 + b^2 = 169
Next we get b^2 alone
169-144=25
So we get b^2=25
For the final step you have to find the square root of 25 to get b alone which is 5

3 0

3 years ago

The number of students who attended FPM in 2015 was 1380. In 2016, 1405 students attended FPM. what was the percent of change in

Fittoniya [83]

The percent of change in student enrollment is 1.81 % increase

Solution:

Given that, The number of students who attended FPM in 2015 was 1380

In 2016, 1405 students attended FPM

To find: Percent change

The percent change is given by formula:

$\text { percent change }=\frac{\text { final value - initial value}}{\text { initial value }} \times 100$

If the result is positive, it is percent increase

If the result is negative, it is percent decrease

From given,

Initial value in 2015 = 1380

Final value in 2016 = 1405

Substituting the values in formula, we get

$\text { percent change }=\frac{1405-1380}{1380} \times 100\\\\\text { percent change }=\frac{25}{1380} \times 100\\\\\text { percent change }= 0.01811 \times 100\\\\\text { percent change }= 1.81$

Thus percent of change in student enrollment is 1.81 % increase

6 0

3 years ago

2 Points

ch4aika [34]

I think the answer is b

5 0

3 years ago