What is 4/5×24/12 equal to and simplified

Use chain rule to find dw/dt w=ln(x^2 + y^2 + z^2)^(1/2) , x=sint, y=cost, z=tant

son4ous [18]

The chain rule states that

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

Since $\ln(x^2+y^2+z^2)^{1/2}=\dfrac12\ln(x^2+y^2+z^2)$ , you have

$\dfrac{\partial w}{\partial x}=\dfrac x{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial x}=\dfrac y{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac z{x^2+y^2+z^2}$

and

$\dfrac{\mathrm dx}{\mathrm dt}=\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=\sec^2t$

Also, since $x^2+y^2+z^2=\sin^2t+\cos^2t+\tan^2t=1+\tan^2t=\sec^2t$ , the derivative is

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\sin t\cos t}{\sec^2t}-\dfrac{\sin t\cos t}{\sec^2t}+\dfrac{\tan t\sec^2t}{\sec^2t}$
$\dfrac{\mathrm dw}{\mathrm dt}=\tan t$

4 0

3 years ago

Which of the following represents a weak positive correlation?a. -0.9b. 0c. +0.2d. +0.9

svetoff [14.1K]

Answer:

Option C) +0.2

Step-by-step explanation:

We are given the following information in the question:

Correlation:

Correlation is a technique that help us to find or define a relationship between two variables.

It is a measure of linear relationship between two quantities.

A positive correlation means that an increase in one quantity leads to an increase in another quantity

A negative correlation means with increase in one quantity the other quantity decreases.

+1 tells about a a perfect positive linear relationship and −1 indicates a perfect negative linear relationship.

Values between 0 and 0.3 tells about a weak positive linear relationship, values between 0.3 and 0.7 shows a moderate positive correlation and a correlation of 0.7 and 1.0 states a strong positive linear relationship.

Values between 0 and -0.3 tells about a weak negative linear relationship, values between -0.3 and -0.7 shows a moderate negative correlation and a correlation value of of -0.7 and -1.0 states a strong negative linear relationship.

Thus, a weak positive correlation is given by correlation coefficient of Option C) +0.2

3 0

3 years ago

Taletha is preparing for an exam in Algebra II. She knows she will be expected to determine if two functions are inverses of eac

seropon [69]

Answer:

f ○ g(x) = x and g ○ f(x) = x is the correct composition

Step-by-step explanation:

INVERSE FUNCTIONS: Two functions are said to be inverse of each other if for every y = f(x), there exists a function g(x),

such that x = $f^{-1} (y)$ = g(y)

Now, here if we need to show tha two functions f(x) and g(x) are inverse functions of each other , then show that for every x:

1. f o g(x) = f(g(x))= x

2. g o f(x) = g(f(x)) = x

If any two functions satisfy these two conditions, then they are inverse of each other.

5 0

4 years ago

The 9th and the 12th term of an arithmetic progression are 50 and 65 respectively. find the common difference

Rzqust [24]

The first term of the arithmetic progression exists at 10 and the common difference is 2.

<h3>How to estimate the common difference of an arithmetic progression?</h3>

let the nth term be named x, and the value of the term y, then there exists a function y = ax + b this formula exists also utilized for straight lines.

We just require a and b. we already got two data points. we can just plug the known x/y pairs into the formula

The 9th and the 12th term of an arithmetic progression exist at 50 and 65 respectively.

9th term = 50

a + 8d = 50 ...............(1)

12th term = 65

a + 11d = 65 ...............(2)

subtract them, (2) - (1), we get

3d = 15

d = 5

If a + 8d = 50 then substitute the value of d = 5, we get

a + 8 $*$ 5 = 50

a + 40 = 50

a = 50 - 40

a = 10.

Therefore, the first term is 10 and the common difference is 2.

To learn more about common differences refer to:

brainly.com/question/1486233

#SPJ4

4 0

2 years ago

PLEASE HELP.

Harrizon [31]

ANSWER

The maximum y-value is 0.

EXPLANATION

The domain of the given absolute value function is (-∞, ∞) .

This means the function is defined for all real values of x.

The range of the function is (-∞, 0].

This can be rewritten as

$y \leqslant 0$

This means that, the highest y-value on the gray of this absolute value function is 0.

Hence the maximum y-value of the function is 0.

3 0

3 years ago