Deviation from the mean for 173

WILL MARK THE BRAINIEST!!! LOTS OF POINTS!! HELP NOW

ElenaW [278]

cos (arctan (1))=

arctan (1) = 45 take it to the third quadrant = add 180 = 225

cos (225) = -1 / sqrt(2)

never leave a sqrt in the denominator

= -1 /sqrt(2) * sqrt(2)/sqrt(2)

= -sqrt(2)/2

sin (arccos (1/2)

arccos (1/2) = 60 take it to the 4th quadrant -60 degrees

sin (-60)

- sin 60

- sqrt(3)/2

3 0

3 years ago

Consider the surface defined by the equation x3 + y3 + z3 = 3xyz. Use implicit differ- ∂z entiation to find ∂x. (Note z is not a

Aloiza [94]

Answer:

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

Step-by-step explanation:

Given equation is $x^{3}+y^{3}+z^{3}=3xyz$ ………………(1)

we use derivative formula $\frac{d}{dx}(x^{n}) = n x^{n-1}$

$\frac{d}{dx}(x^{3)} = 3 x^{2}$

$\frac{d}{dx}(z^{3)} = 3 z^{2}$

And also apply 'u v' formula

$\frac{d}{dx}(uv}) = u\frac{d}{dx}(v)+v\frac{d}{dx}(u)$

Differentiating equation (1) partially with respective to 'x' , we treated 'y' as constant.

$(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =3y(x\frac{∂z}{∂x}+z(1))$ ( here y treated as constant so the derivative of constant function is zero in addition but in multiplication the constant is keep as like 'y').

on simplification , we get

$(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =(3yx\frac{∂z}{∂x}+3yz)$

again simplification, we get

$3z^{2}\frac{∂z}{∂x}- 3yx\frac{∂z}{∂x}=3yz-3x^{2}$

taking common ' $\frac{∂z}{∂x}$ on left on side , we get

$(3z^{2}- 3yx)\frac{∂z}{∂x}=3yz-3x^{2}$

dividing ' $(3z^{2}- 3yx)$ on both sides, we get

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

<u>Final answer</u>:-

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

6 0

3 years ago

Last Thursday was costume day at Wayne's school. 20 out of the 100 students at the school wore a costume. What percentage of the

Paraphin [41]

Answer:

20 percent or 2/10

Step-by-step explanation:

to make into a percentage it would be easy because of it being out of 100 so make the 100 a percentage and then see how much the 20 would be it would be the same 20/100 only in percentage form so 20 percent

8 0

3 years ago

alec is climbing a 14 foot ladder where the rungs are 3/4 of a foot apart. there is one foot of space on each end of the ladder

Aleks [24]

Answer:

Alec is climbing 17 rungs on the ladder of 14 feet ( including first and last rung ) .

Step-by-step explanation:

Given:

Length of the ladder = 14 foot

Distance between Rungs in ladder = $\frac{3}{4}$

There is one foot of space on each end of the ladder before the first and last rung .

To Find:

Number of rungs are on the ladder =?

Solution:

Let us assume there are 3 rungs. Between 3 rungs there will be two spaces. between four rungs there will be 3 spaces , so between n + 1 rungs there will be n spaces.

Given that length of the ladder = 14 feet

There is one foot of space on each end before the first and last rung.

So length of the ladder between first and last rung = 14 – 2 ( 1 foot of each side) = 12 feet

As distance between each rung = $\frac{3}{4}$

Number of $\frac{3}{4}$ spaces in ladder of 12 feet = $\frac{( 12)}{\frac{3}{4}}$

Number of $\frac{3}{4}$ spaces in ladder of 12 feet= $\frac{(12\times4)}{3}$

Number of $\frac{3}{4}$ spaces in ladder of 12 feet= $\frac{(48)}{3}$

Number of $\frac{3}{4}$ spaces in ladder of 12 feet =16

And as for n spaces there will be n + 1 rungs, so for 16 spaces there will be 16 + 1 = 17 rungs.

6 0

3 years ago

In this figure, angle 3 = (2x+15) and angle 6 = (3x+10)<br><br> What value of x makes a || b?

zvonat [6]

$\angle3+\angle6=180^o\\\\\text{substitute}\\\\(2x+15)+(3x+10)=180\\\\2x+15+3x+10=180\\\\5x+25=180\ \ \ |-25\\\\5x=155\ \ \ |:5\\\\\boxed{x=31}$

4 0

4 years ago