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2 years ago

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Mathematics

1 answer:

Dovator [93]2 years ago

7 0

Answer:

Step-by-step explanation:

let the vertices on either side of the 0 be A and B

then let the vertex opposite of O be C

First, angle ACB will be equal to 90° as it is the angle that lies on the same arc as the diameter. From there you can find angle y with angle A+ angle B+ Angle C=180°

then you can find the angle complementary to x with the same formula then you can subtract that angle with 90° to get x.

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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:

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

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Step-by-step explanation:

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Answer:

y = -x+3

Step-by-step explanation:

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m =(y2-y1)/(x2-x1)

(1-2)/(2-1)

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y = mx+b where m is the slope and b is the y intercept

y = -x+b

Substitute a point into the equation to find b

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A Store owners offers a discount of 20% off the regular price of all jackets. Jessica has a coupon that gives her an additional

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Please help this question​

Please help this question