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nadezda [96]
3 years ago
15

If h(x)=6-x what is the value of (hxh)(10)?

Mathematics
2 answers:
Elanso [62]3 years ago
7 0

For this case we have by definition, that given two functions, then:

(f * g) (x) = f (x) + g (x)

Here, we want to find ((h * h) (x):

(h * h) (x) = (6-x) (6-x)\\(h * h) (x) = 36-6x-6x + x ^ 2\\(h * h) (x) = 36-12x + x ^ 2

We want to find the value of the function when x = 10.

(h * h) (10) = 36-12 (10) + (10) ^ 2\\(h * h) (10) = 36-120 + 100\\(h * h) (x) = 16

Answer:

(h * h) (x) = 16

Ghella [55]3 years ago
5 0

Answer:

16

Step-by-step explanation:

h(x) × h(x) = (6 - x)²

(h × h)(10) = (6 - 10)² = (- 4)² = 16

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Answer: -10

Step-by-step explanation:

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1
charle [14.2K]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t   (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ \frac{dx}{dt} = -\sin t

  \frac{dy}{dt} = 2 \cos t

  \frac{dz}{dt} = \sin t-2cos t

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}

=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}

=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)

Now evaluating the integral using calculator,

=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t) = 13.5191




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vekshin1
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