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Murrr4er [49]
3 years ago
11

Find the length of KB¯¯¯¯¯¯¯¯+AK¯¯¯¯¯¯¯¯. A. 28 B. 33 C. 21 D. 35

Mathematics
1 answer:
Usimov [2.4K]3 years ago
8 0

Intersecting chord rule:

DK x KB = AK x CK

12 x 4x+1 = 14 x 3+3x

Simplify:

48x +12 = 42x +42

Subtract 12 from each side:

48x = 42x + 30

Subtract 42x from each side:

6x = 30

Divide both sides by 6:

x = 5

Now find the length of KB: 4x +1 = 4(5) +1 = 20 +1 = 21

Now add KB and AK:

21 + 14 = 35

The answer is D. 35

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Find a point on the curve x^3+y^3=11xy other than the origin at which the tangent line is horizontal.
attashe74 [19]

Compute the derivative dy/dx using the power, product, and chain rules. Given

x³ + y³ = 11xy

differentiate both sides with respect to x to get

3x² + 3y² dy/dx = 11y + 11x dy/dx

Solve for dy/dx :

(3y² - 11x) dy/dx = 11y - 3x²

dy/dx = (11y - 3x²)/(3y² - 11x)

The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when

11y - 3x² = 0

or

y = 3/11 x²

(provided that 3y² - 11x ≠ 0)

Substitute y into into the original equation:

x³ + (3/11 x²)³ = 11x (3/11 x²)

x³ + (3/11)³ x⁶ = 3x³

(3/11)³ x⁶ - 2x³ = 0

x³ ((3/11)³ x³ - 2) = 0

One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with

(3/11)³ x³ - 2 = 0

(3/11 x)³ - 2 = 0

(3/11 x)³ = 2

3/11 x = ³√2

x = (11•³√2)/3

Solving for y gives

y = 3/11 x²

y = 3/11 ((11•³√2)/3)²

y = (11•³√4)/3

So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).

3 0
2 years ago
The height and length of a right rectangular prism are each 12 cm. The surface area of the prism is
RideAnS [48]

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99

Step-by-step explanation:

8 0
3 years ago
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per mi
miss Akunina [59]

Answer:

Mean = 0, Standard deviation = 1

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 77.5 beats per minute

Standard Deviation, σ = 11.6 beats per minute

We are given that the distribution of pulse rates of women is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

Putting the values, we get,

z_{score} = \displaystyle\frac{x-77.5}{11.6}

After, the standardization, that is conversion of all pulse rates of women to z scores, the mean of the distribution is 0 and standard deviation is 1.

Mean = 0, Standard deviation = 1

7 0
3 years ago
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