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3 years ago

What is the length of AB? A.2.59 B.9.66 C.10.35 D38.64

Mathematics

1 answer:

Jlenok [28]3 years ago

5 0

Answer:

what

Step-by-step explanation:

is the questionn

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The tangents to the curve with equation y = x^3-3x at the points A and B with x coordinates −1 and 4 respectively meet at the po

sladkih [1.3K]

Answer:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

Step-by-step explanation:

We need to find the equation of the tangent lines of Points A and B.

Differentiate the equation:

$\displaystyle \frac{dy}{dx}=3x^2-3$

Point A has an x-coordinate of -1. Hence, the slope of its tangent line is:

$\displaystyle \frac{dy}{dx}\Big|_{x=-1}=3(-1)^2-3=0$

Find the y-coordinate of Point A using the original equation:

$y(-1)=(-1)^3-3(-1)=2$

Hence, Point A is (-1, 2).

Thus, the tangent line at Point A is:

$y-2=0(x-(-1))$

Simplify:

$y=2$

Point B has an x-coordinate of 4. Hence, the slope of its tangent line is:

$\displaystyle \frac{dy}{dx}\Big|_{x=4}=3(4)^2-3=45$

Find the y-coordinate of Point B:

$y(4)=(4)^3-3(4)=52$

Thus, Point B is at (4, 52).

So, the tangent line at Point B is:

$y-52=45(x-4)$

Simplify:

$y=45x-128$

Point C occurs at the intersections of the tangent lines of Points A and B. Set the two equations equal to each other and solve for x:

$2=45x-128$

We acquire:

$\displaystyle x=\frac{26}{9}$

Since one of our equations is y = 2, the y-coordinate is 2.

Hence, Point C is:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

5 0

3 years ago

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Determine the slope between the points (-3, 0) and (0, 5) Thank you^^

liraira [26]

The slope is 5/3.hope this helps

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3 years ago

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Can somebody help me with this

denis-greek [22]

Answer:

Step-by-step explanation:

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3 years ago

Can someone please help me fill in the answer in the bottom.

Julli [10]

Answer:

Step-by-step explanation:

1) Initial water level = 30 feet

2) Rate of change = (30 - 25) / (0 - 1) = 5/(-1) = -5

5ft per hour

3) y-intercept = 30

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3 years ago

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A right rectangular pyramid is sliced vertically (down) by a plane passing

Anton [14]

A right rectangular pyramid when sliced vertically, the shape of the cross-section is known as Triangle.

<h3>What is A triangle?</h3>

This is known to be a kind of shape that is said to be in a closed form and it is also known to be a 2-dimensional shape that has 3 sides, 3 angles, and also 3 vertices.

Note that when the when the right rectangular pyramid is sliced vertically (down) by a plane passing through the of the pyramid, the new shape of the cross-section is a triangle.

See full question below

A right rectangular pyramid is sliced vertically (down) by a plane passing through the of the pyramid. What is the shape of the cross-section?

A. Rectangle

B. Pyramid

C. Triangle

D. Trapezoid

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Learn more about triangle from

brainly.com/question/17335144

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2 years ago