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3 years ago

I need help please :)

Mathematics

1 answer:

emmasim [6.3K]3 years ago

6 0

Answer:

4th option

10x + 32 / x(x+8)

Step-by-step explanation:

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Find the derivative of the function at P 0 in the direction of A. f(x,y,z) = 3 e^x cos(yz), P0 (0, 0, 0), A = - i + 2 j + 3k

Alik [6]

The derivative of $f(x,y,z)$ at a point $p_0=(x_0,y_0,z_0)$ in the direction of a vector $\vec a=a_x\,\vec\imath+a_y\,\vec\jmath+a_z\,\vec k$ is

$\nabla f(x_0,y_0,z_0)\cdot\dfrac{\vec a}{\|\vec a\|}$

We have

$f(x,y,z)=3e^x\cos(yz)\implies\nabla f(x,y,z)=3e^x\cos(yz)\,\vec\imath-3ze^x\sin(yz)\,\vec\jmath-3ye^x\sin(yz)\,\vec k$

and

$\vec a=-\vec\imath+2\,\vec\jmath+3\,\vec k\implies\|\vec a\|=\sqrt{(-1)^2+2^2+3^2}=\sqrt{14}$

Then the derivative at $p_0$ in the direction of $\vec a$ is

$3\,\vec\imath\cdot\dfrac{-\vec\imath+2\,\vec\jmath+3\,\vec k}{\sqrt{14}}=-\dfrac3{\sqrt{14}}$

3 0

4 years ago

Find the surface area of the cylinder. Round to the nearest tenth.

OleMash [197]

Hello!

To find the surface area of the given cylinder, we need to use the formula of the surface area of a cylinder.

The formula for the surface area of a cylinder is SA = 2πrh + 2πr².

In this formula, r is the radius and h is the height.

In the given diagram, we see that the height is 6 meters, and the radius 9 meters. With those values, we can substitute them into our formula and solve for the surface area.

In some cases, you are given the diameter. To find the radius, you would need to divide the diameter by two.

SA = 2π(9)(6) + 2π(9)²

SA = 54(2π) + 2(81π)

SA = 108π + 162π

SA = 270π

SA ≈ 848.2 m²

Therefore, the surface area of the given cylinder is choice A, 848.2 m².

5 0

3 years ago

Which equation is equivalent to 16^2p=32^p+3?

Serggg [28]

Answer:

C. 2^8p=2^5p+15

7 0

3 years ago

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5

Anuta_ua [19.1K]

Answer:

$y = \frac{3}{2} x-11$

Step-by-step explanation:

We are to find the equation a line that passes through the point (8, 1) and which is perpendicular to a line whose equation is $y = - \frac{2}{3} x+5$ .

We know that the slope of line which is perpendicular to another line is the negative reciprocal of the slope of the other line so it will be $\frac{3}{2}$ .

Then, we will find the y-intercept of the line using the standard equation of a line:

$y=mx+c$

$1=\frac{3}{2} (8)+c$

$c=-11$

Therefore, the equation of the line will be $y = \frac{3}{2} x-11$ .

7 0

3 years ago

Read 2 more answers

I am still lost.....

exis [7]

-3(-15w+2)
You have to use the distributive property to simplify this expression.
-3 times -15w is 45w.
-3 times 2 is -6.

-3(-15w+2)
45w-6 is the answer

4 0

3 years ago