You are looking at your power bill for the month, you pay 12 cents per kilowatt-hour. Your power bill came out to $99.89 how many KWH of energy were used in your house this month?

[tex]\frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\[/tex]

====================================================

Proof:

Apply the derivative to choice A. The goal is to prove the derivative is equivalent to the given integrand.

[tex]y = \frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\\frac{dy}{dx} = \frac{4}{\pi}\left[\sin^{-1}(x)+\frac{x}{\sqrt{1-x^2}}-\frac{x}{\sqrt{1-x^2}}\right]-1\\\\\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-1\\\\[/tex]

It's far from obvious, but we can apply a bit of algebra like so

[tex]\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-1\\\\\frac{dy}{dx} = \frac{4}{\pi}\sin^{-1}(x)-\frac{\pi}{\pi}\\\\\frac{dy}{dx} = \frac{4\sin^{-1}(x)-\pi}{\pi}\\\\[/tex]

Next, we divide every term by 2. This is so we can replace the pi terms with pi/2

[tex]\frac{dy}{dx} = \frac{4\sin^{-1}(x)-\pi}{\pi}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\frac{\pi}{2}}{\frac{\pi}{2}}\\\\[/tex]

We do this to take advantage of the trig identity [tex]\sin^{-1}(x)+\cos^{-1}(x) = \frac{\pi}{2}[/tex]

So we'll be replacing every instance of "pi/2" with the left hand side of that equation just mentioned.

Therefore,

[tex]\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\frac{\pi}{2}}{\frac{\pi}{2}}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\left(\sin^{-1}(x)+\cos^{-1}(x)\right)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\frac{dy}{dx} = \frac{2\sin^{-1}(x)-\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\frac{dy}{dx} = \frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\[/tex]

This shows that differentiating the expression in choice A leads to the given integrand.

If we reverse all of the steps mentioned, then we can show that:

[tex]\displaystyle\frac{dy}{dx} = \frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}\\\\\\ \int\frac{dy}{dx}dx = \int\frac{\sin^{-1}(x)-\cos^{-1}(x)}{\sin^{-1}(x)+\cos^{-1}(x)}dx\\\\\\y = \frac{4}{\pi}\left[x*\sin^{-1}(x)+\sqrt{1-x^2}\right]-x+C\\\\[/tex]

since integrals and derivatives are tied together through inverse processes (one undoes the other more or less).

Answer:

=(-4+7)/2

=3/2

=1.5 answer

Answer:

141

2Step-by-step explanation:

Answer:

48 2/3

Step-by-step explanation:

Remember,

Absolute value of a +ve number = +ve

Absolute value of a -ve number = +ve

Absolute value of 48 2/3 = 48 2/3

Answer:

How many mg are there in a 5.00 grain aspirin tablet ? 1 grain = 0.00229 oz . there are 454 g/lb

Answer:

Step-by-step explanation:

Inverse variation equation:

We have:

Work out the value of k by substituting the values of x and y:

The equation is:

Answer:

y = -6/x

Step-by-step explanation:

y varies inversely as x

So, y = k/x, where k is the constant of proportionality.

If y = -1 when x = 6,

Then, -1 = k/6 ===> k = -6

Therefore, y = -6/x

Recall that

• tan(x) = sin(x) / cos(x)

• sin(x) sin(y) = - 1/2 (cos(x + y) - cos(x - y))

• cos(x) cos(y) = 1/2 (cos(x + y) + cos(x - y))

Then we can write

tan(6x) tan(7x) = (sin(6x) sin(7x)) / (cos(6x) cos(7x))

tan(6x) tan(7x) = - (cos(13x) - cos(x)) / (cos(13x) + cos(x))

Make this replacement in the original equation and simplify:

tan(6x) tan(7x) = -1

- (cos(13x) - cos(x)) / (cos(13x) + cos(x)) = -1

(cos(13x) - cos(x)) / (cos(13x) + cos(x)) = 1

cos(13x) - cos(x) = cos(13x) + cos(x)

2 cos(x) = 0

cos(x) = 0

Solving for x gives

x = π/2 + nπ = (2n + 1)π/2

where n is any integer. However, since 2n + 1 is odd, for any odd multiple of π/2, we would end up with

tan(6 (2n + 1)π/2) = tan((2n + 1)×3π) = tan(odd multple of π/2)

since odd×odd = odd, and cos(odd multiplie of π/2) = 0, which would make tan(6x) undefined.

Therefore there are no solutions to this equation.

Answer:

0.0089

Step-by-step explanation:

i dont know how to show my work i did it online, pls give me brainliest :(

Fun Fact: Octopuses lay 56,000 eggs at a time

Answer:

v=-155

Step-by-step explanation:

167 = 12 - v

subtract both sides by 12

155= -v

multiply both sides by -1

-155= v

Answer:

4800

Step-by-step explanation:

80 × 60 = 4800

Answer:

I hope this answer will help you

a)42+(-17) b)8-(-9) c)8(-9) d)-42+(-7)

=42-17 =8+9 =(-72) =-42-7

=25 =17 =-49

e)-2(-3)(-4) f)-18-7 g)(-5)^2 h)-5^2

=-2*12 =-25 =25 =25

=24

i)ans

7

Answer:30%

Step-by-step explanation:

GAIN = 156- 120=$ 36

% GAIN = [tex]\frac{gain}{old cost price } X 100%\\[/tex]

= [tex]\frac{36}{120} X 100%[/tex]

=30%

Answer:

< then >

Step-by-step explanation:

11 7/8 can be written as (11 + 7/8). If we find (11+7/8)², we know that √(11+7/8)² = (11+7/8), so we can compare (11+7/8)² with 129 and see which is bigger.

(11+7/8)² = (11+7/8) * (11+7/8)

= 121 + 7/8 * 11 + 7/8 * 11 + (7/8)²

= 121 + 77/8 + 77/8 + (7/8)²

77/8 is greater than 9 (8*9 = 72) but less than 10 (8*10=80). Rounding down to 7, we have

121 + 7 + 7 + (7/8)²

= 135 + (7/8)²

Even when rounding down, (11+7/8)² is greater than 129. Therefore,

129 < (11+7/8)²

square root both sides

√129 < (11+7/8)

We can apply a similar process for the next one.

(3+5/6)² = (3+5/6) * (3+5/6)

= 9 + 5/6 * 3 + 5/6 * 3 + (5/6)²

= 9 + 15/6 + 15/6 + (5/6)²

15/6 is less than 3 (6*3 = 18) but greater than 2 (6*2 = 12). Rounding down to 2, we have

9 + 2 + 2 + (5/6)²

= 13 + (5/6)² > 10

Even when rounding down, (3+5/6)² is greater than 10

(3+5/6)² > 10

square root both sides

(3+5/6) > √10

The best unit for measuring the distance between two cities is kilometer.

Answer:

y-intercept is (0, -8)

Step-by-step explanation:

[tex]y = {x}^{2} + 2x - 8[/tex]

At y-intercept, x is zero

substitute x as zero:

[tex]y = {(0)}^{2} + 2(0) - 8 \\ y = 0 + 0 - 8 \\ y = - 8[/tex]

Law of Exponent

[tex] \displaystyle \large{( \frac{a}{b} )^{n} = \frac{ {a}^{n} }{ {b}^{n} } }[/tex]

From the expression.

[tex] \displaystyle \large{( \frac{2}{3} )^{2} = \frac{ {2}^{2} }{ {3}^{2} } = \boxed{\frac{4}{9} } }[/tex]

Jerome's mistake is that Jerome forgot to evaluate 2^2 or forgot to add 2^2. The denominator is correct but the numerator is wrong.

Answer: A

Step-by-step explanation:

[tex]x^2+2x+1-y^2\\\\=(x+1)^2-y^2\\\\=((x+1)-y)((x+1)+y)\\\\=(x+1-y)(x+1+y)\\\\Answer\ A\\[/tex]

Answer:

It’s 48 just do 8*6=48 I don’t know how I got that answer but Ik it’s right lol

Answer:

soln

Step-by-step explanation:

a=7

b=-2

5a-3b

5×7-3×-2

35+6(because - and - becomes+

41ans

Answer:

5a-3b

5×7-3×-2

35-6

29

I think soo

Answer:

z = -3

Step-by-step explanation:

42 = -7 ( z-3)

42 = -7z + 21

21 = -7z

z = -3

Answer and Step-by-step explanation:

We have to solve for z. That means everything that is next to z has to move to the other side of the equation.

First, divide -7 from both sides of the equation.

-6 = z - 3

Now add 3 to both sides of the equation.

-3 = z

z is equal to -3.

#teamtrees #PAW (Plant And Water)

I hope this helps!

Answer: -13 + 10i

Step-by-step explanation: ((-6) + (2 * i)) - (7 - (8 * i)) = -13+10i

Explanation:

Think of the problem as x-3 = 2 where x is the blank that we need to fill in.

Adding on -3 is the same as subtracting 3, so that's why x+(-3) is the same as x-3.

To solve x-3 = 2, we add 3 to both sides and we'll get x = 5

Then note how 5-3 = 2 to help confirm the answer.

Answer:

5

Step-by-step explanation:

5 + (-3) = 5 - 3

Answer:

no solutions

Step-by-step explanation:

2x-4=2x-7 (subtract 2x by the 2x on the other side)

-4 = -7 ( add 4 to negative 4 and add 4 to negative 7)

0 ≠ -3 (0 zero does not equal -3, if the solution had one solution then you would find x. if the solution had infinitely solutions then the numbers would be equal [like -3 = -3])

Since the equation ended with an invalid answer ( 0 ≠ -3) it has no solutions. hope this helps!

Hope this help! Everything is in the picture!

Answer:

$471.60

Step-by-step explanation:

The double time rate is not specified in the question. But I will assume it's 2 times the normal rate. Therefore...

13.10 x 20 + 8 x (13.10 x 2)

Answer = $471.60

Hey there! I'm happy to help!

We see that this is an isosceles triangle. This means that two sides are the same length. . We can see that the sides DE and EF are marked with two orange lines, which shows that they are congruent.

We want to find the measure of angle D. We see that our two lines of equal length both create an angle with the hypotenuse DF. Since these lines are the exact same length, they are going to have to create the same angle. Even if you just eyeball it, the angles look to be the same.

So, our measure of angle D is going to be the same as angle F. Let's call this measure m and put it into an equation.

2m+92=180 (sum of all angle measures in a triangle is 180)

Subtract 92 from both sides.

2m=88

Divide both sides by 2

m=44

So, the measure of angle D is B. 44°.

Have a wonderful day and keep on learning! :D

Hello ;)

We have :

Claude's net pay → $985.50

Claude's gross pay → $1350.00

We know that the gross pay represents 100 % of the salary.

So :

$1350.00 ⇔ 100 %

$985.50 ⇔ ? %

? = 985.5 × 100 ÷ 1350 = 73 %

Claude's net pay is 73 % of the gross pay.

:-)

Based on his net pay being $985.50 and his gross pay being $1,350.00, the net pay is 73% of the gross pay.

To find out how much of the percentage of something a variable is, you make the variable the numerator and the other measure the denominator.

In this instance that would be:

= Net pay / Gross pay x 100%

= 985.50 / 1,350 x 100%

= 73%

In conclusion, the net pay is 73% of the gross pay.

Find out more at https://brainly.com/question/8568211.