Determine what type of transformation is represented.

Which correlation coefficient represents the strongest downward trend in a data set? -0.83 -0.23 0.12 0.92

klasskru [66]

Answer: -0.83

Step-by-step explanation:

A correlation coefficient(r) is used to determine the strength and direction of the relationship between two variables.

-1 ≤ r ≤1

For downward trend r is negative.

For strong correlation r should be closer to 1 or -1.

From the given correlation coefficients -0.83 is both negative and closer to -1.

Hence, a correlation coefficient represents the strongest downward trend in a data set = -0.83

3 0

3 years ago

Please help me answer this question

stealth61 [152]

The value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

<h3>Differentiation</h3>

From the question, we are to determine dy/dx for the given functions

(i) $x^{2} sin^{2}2x$

Let $u = x^{2}$

and

$v = sin^{2} 2x$

Also,

Let $w= sin2x$

∴ $v = w^{2}$

First, we will determine $\frac{dv}{dx}$

Using the Chain rule
$\frac{dv}{dx} = \frac{dv}{dw}.\frac{dw}{dx}$

$v = w^{2}$

∴ $\frac{dv}{dw} =2w$

Also,

$w= sin2x$

∴ $\frac{dw}{dx} =2cos2x$

Thus,

$\frac{dv}{dx} = 2w \times 2cos2x$

$\frac{dv}{dx} = 2sin2x \times 2cos2x$

$\frac{dv}{dx} = 4sin2x . cos2x$

Now, using the product rule

$\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$

From above

$u = x^{2}$

∴ $\frac{du}{dx}=2x$

Now,

$\frac{dy}{dx} = x^{2} (4sin2x.cos2x)+ sin^{2}2x (2x)$

$\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $xy^{2}+y^{2}x^{3} +2=0$

Then,

$x.2y\frac{dy}{dx}+ y^{2}(1)+y^{2}.3x^{2} + x^{3}.2y\frac{dy}{dx} +0=0$

$2xy\frac{dy}{dx}+ y^{2}+3x^{2}y^{2} + 2x^{3}y\frac{dy}{dx} =0$

$2xy\frac{dy}{dx}+2x^{3}y\frac{dy}{dx} =- y^{2}-3x^{2}y^{2}$

$\frac{dy}{dx} (2xy+2x^{3}y)=- y^{2}(1+3x^{2})$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy+2x^{3}y}$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy(1+x^{2}) }$

$\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Hence, the value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Learn more on Differentiation here: brainly.com/question/24024883

#SPJ1

8 0

2 years ago

What's the circumference of a<br> circle with a diameter of 9 inches?<br> Use 3.14 for n.

Rainbow [258]

Answer:

28.26 in

Step-by-step explanation:

Radius = (1/2) diameter

Radius = (1/2)(9)

Radius = 4.5 in

Circumference = 2πr

Circumference = 2(3.14)(4.5)

Circumference = 28.26 in

8 0

3 years ago

The Y-intercept (b0) represents the a. variation around the sample regression line. b. change in estimated Y per unit change in

inn [45]

Answer: I don’t honestly know. I just need points

Explanation:

3 0

3 years ago

Solve using derivatives.

Bond [772]

Answer:

Below in bold.

Step-by-step explanation:

The surface area of the box

= x^2 + 4hx where x = a side of the square base and h is the height.

So x^2 + 4hx = 8

The volume of the box

V = x^2h

From the first equation we solve for h

4hx = 8 - x^2

h = (8 - x^2) / 4x

Now we substitute for h in the formula for the volume:

V = x^2 * (8 - x^2) / 4x

V = 8x^2 - x^4 / 4x

V = 2x - 0.25x^3

Finding the derivative:

V' = 2 - 0.75x^2 = 0 for max/mimn values

x^2 = 2/ 0.75 = 2.667

x = 1.633.

So the length and width of the base is 1.633 m and the height

= ( 8 - 2.667) / (4*1.633)

= 0.816 m

The maximum volume = 0.816 * 2.667 = 2.177 m^2.

The answers are correct to the nearest thousandth.

7 0

3 years ago