This is midpoint please help.

Answer:

The average hourly number of inches that the water level changes per day is about 0.0231 inches per hour.

Step-by-step explanation:

The water level of a certain body of water is changing at a rate represented by the function:

[tex]\displaystyle W(t) = \frac{1}{2}\cos \left( 3- \frac{t}{2}\right)[/tex]

Where W is measured in inches per hour and t represents hours since 12 A.M.

And we want to determine the average hourly number of inches that the water level changes for the lake in one day.

Recall that the average value of a function is given by:

[tex]\displaystyle f_\text{avg} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx[/tex]

Hence, the find the average hourly number of inches that the water level changes in one day, we simply need to find the average value of W from t = 0 to t = 24.

Substitute:

[tex]\displaystyle W(t)_{\text{avg}} = \frac{1}{(24)-(0)} \int_{0}^{24} \frac{1}{2}\cos \left(3 - \frac{t}{2}\right) \, dt[/tex]

Simplify:

[tex]\displaystyle W(t)_{\text{avg}} = \frac{1}{24} \int_{0}^{24} \frac{1}{2}\cos \left(3 - \frac{t}{2}\right) \, dt[/tex]

Evaluate using u-substitution. We can let:

[tex]\displaystyle u = 3 - \frac{t}{2} \Rightarrow du = -\frac{1}{2}\, dt\Rightarrow -2\, du = dt[/tex]

Hence:

[tex]\displaystyle W(t)_{\text{avg}} = -\frac{1}{24} \int_{3}^{-9} \cos u \, du[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} W(t)_{\text{avg}} &= \frac{1}{24}\int_{-9}^{3} \cos u\, du \\ \\ &= \frac{1}{24}\left(\sin u\Big|_{-9}^{3}\right) \\ \\ &= \frac{1}{24}\left(\sin3 - \sin -9\right) \\ \\ &=\frac{1}{24}\left(\sin 3 + \sin 9\right) \\ \\ &\approx0.0231 \end{aligned}[/tex]

In conclusion, the average hourly number of inches that the water level changes per day is about 0.0231 inches per hour.

Answer:

It depends if the number is an integer {-1,+7,-7}

e.g -7+4

these numbers are integers that is why you can write both addition and subtraction expressions

Answer:

x = 16.1051577

Step-by-step explanation:

tan0 = opp/adj

tan0 = 14/x

tan(49)× 14 = 16.1051577

Answer:

Concept:

Intersecting lines are lines that overlap upon only one point. The number of lines can be two or more.

Intersecting lines can intersect at any angle.

Solve:

There are in total four intersecting points in the given figure.

As we can see from the figure, any two lines would intersect each other

Therefore, 2 pairs of intersecting lines can be any pairings of lines that are not in the same orientation.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Irrational

Step-by-step explanation:

Because irrational this number do not repeat so there for it is not rational.

Answer:

c

Step-by-step explanation:

The answer is C. To find the answer all you need to do is divide the money per pound for each option until you find the lowest deal.

A is not a good deal because its about $3.14 for a pound

B is not a good deal because its about $3.33 per pound

D is not a good deal because its $3.50 per pound

C IS a good deal because it's $2.95 per pound

Answer:

c

Step-by-step explanation:

The answer is C. To find the answer all you need to do is divide the money per pound for each option until you find the lowest deal.

A is not a good deal because its about $3.14 for a pound

B is not a good deal because its about $3.33 per pound

D is not a good deal because its $3.50 per pound

C IS a good deal because it's $2.95 per pound

Answer:

Marginal relative frequency is the ratio of the sum of the joint relative frequency in a row or column and the total number of data values. Remember, the marginal frequency numbers are the numbers on the edges of a table, kind of like the margins are the areas on the edge of a paper.

Answer:

[tex] {a}^{4} {b}^{4} [/tex]

Step-by-step explanation:

[tex](ab) \times (ab) \times (ab) \times (ab)[/tex]

[tex] {a}^{1 + 1 + 1 + 1} {b}^{1 + 1 + 1 + 1} [/tex]

[tex] = {a}^{4} {b}^{4} [/tex]

Points A , B and C are collinear......

Answer:

hence the required midpoint of the given line is (9,5)

Answer:

[tex]( \frac{6 + 2}{2} +\frac{12 + 8}{2}) = ( \frac{8}{2} + \frac{20}{2} ) = (4 \: comma10)[/tex]

The answer is :(4, 10)

Answer:

>

Step-by-step explanation:

1,404,000 > 1,040,000

Answer:

[tex]x < 0[/tex]

Step-by-step explanation:

[tex] - 4x - 8x > 0[/tex]

➡️ [tex] - 12x > 0[/tex]

➡️ [tex]x < 0[/tex]

Answer:

B

Step-by-step explanation:

Answer:

y = 1/2x + 11

Step-by-step explanation:

y = 1/2x + b

9 = 1/2(-4) + b

9 = -2 + b

b = 11

Answer:

I HOPE IT WILL HELP YOU A LOT.

Have a great day ahead.

Answer:

Can u help me

Step-by-step explanation:

With my maths question

Answer:

C

Step-by-step explanation:

0.112 + (-16)/75 is equivalent to 0.112 - 16/75

Answer:

(45/v) hours

Step-by-step explanation:

that is the answer yep

Answer:

45/v =t

Step-by-step explanation:

Cuz the normal formula is

V= d/t

Therefore

t= d/v

And u know D = 45km so..

t=45/v

Answer:

hope it help u

Step-by-step explanation:

2sinx/(2cosx – secx)

=2 sinx/(2cosx–1/cosx)

as secx = 1/ cosx

multiplying both the denominator and numerator by cost,we get

2sinxcosx/( 2cos^2x –1) =cos2x

since,2sinxcosx = sin2x and 2cos^2 –1=cos2x

2sinxcosx/(2cos^2x– 1)= sin2x/ cos2x = tan2x

Answer:

x = 4, y = 3

Step-by-step explanation:

Equating corresponding coordinates , gives

2x = 8 ( divide both sides by 2 )

x = 4

and

3y = 9 ( divide both sides by 3 )

y = 3

Answer:

It is 3y = 4x + 10

Step-by-step explanation:

Let's first get the slope of the curve.

[ slope is the derivative of the equation ]

[tex] {x}^{2} - xy + {y}^{2} = 7[/tex]

introduce dy/dx :

[tex] \frac{d}{dx} ( {x}^{2} - xy + {y}^{2} ) = \frac{d}{dx} (7) \\ \\ 2x - (y + \frac{dy}{dx} ) + 2y \frac{dy}{dx} = 0[/tex]

make dy/dx the subject:

[tex]2x - y - \frac{dy}{dx} + 2y \frac{dy}{dx} = 0 \\ \\ 2y \frac{dy}{dx} - \frac{dy}{dx} = y - 2x \\ \\ \frac{dy}{dx} (2y - 1) = y - 2x \\ \\ \frac{dy}{dx} = \frac{y - 2x}{2y - 1} [/tex]

At point (-1, 2):

[tex] \frac{dy}{dx} = \frac{2 - 2( - 1)}{2(2) - 1} \\ \\ slope = \frac{4}{3} [/tex]

but a tangent has the same slope as the curve:

[tex]y = mx + c[/tex]

m is the slope

c is the y-intercept

At (-1, 2):

[tex]2 = ( - 1 \times \frac{4}{3} ) + c \\ \\ c = 2 + \frac{4}{3} \\ \\ c = \frac{10}{3} [/tex]

equation:

[tex]y = \frac{4}{3} x + \frac{10}{3} \\ \\ { \boxed{3y = 4x + 10}}[/tex]

Answer:

Step-by-step explanation:

Here is an other way:

z=f(x,y)=x²-xy+y²-7=0

[tex]\dfrac{\partial f(x,y)}{\partial x} =2x-y\\\\\dfrac{\partial f(x,y)}{\partial y} =-x+2y\\\\\\\dfrac{dy}{dx} =-\dfrac{\dfrac{\partial f(x,y)}{\partial x} }{\dfrac{\partial f(x,y)}{\partial y}} =-\dfrac{2x-y}{-x+2y} \\\\(-1;2)\\Slope=-\dfrac{2*(-1)-2}{1+2*2} =\dfrac{4}{5} \\\\y-2=\frac{4}{5} (x+1)\\\\\\\boxed{y=\dfrac{4x}{5} +\dfrac{14}{5} }[/tex]

Answer:

7 sides

Step-by-step explanation:

formula for sum of interior angles

(n-2)× 180= 10 right angles

(n-2)× 180 = 900

n-2= 900÷180

n= 5+2

n= 7

Answer:

y = 1/2x - 2

Step-by-step explanation:

In order for a line to be perpendicular to another, the lines must have opposite reciprocal slopes.

Example of an opposite reciprocal slope: -2 ⇒ 1/2

Insert the information into the point-slope formula:

[tex]y-y_1=m(x-x_1)\\\\y-2=\frac{1}{2}(x-8)\\\\y-2=\frac{1}{2}x-4\\\\y=\frac{1}{2}x-2[/tex]

Answer:

The correct answer is D. The bicycle is not in motion.

Step-by-step explanation:

In the position-time graph we can see that the position of the cycle hasn't changed when the time has changed (e.g. when time changes from 2s to 3s, the position remains 3m). Therefore, we can conclude that the cycle is not moving, and therefore answer D. is correct.

Answer:

its d

Step-by-step explanation:

answer =-51/2,-11/2,-5.025,-✓25

-✓25=-5

-11/2=-5.5

-51/2=-25.5

-5.025

Answer:

3x square + 5 is your answer

Answer:

Step 1:

Let x represent the amount of each friend donate

Website keeps = 5%

Total funding I receive = $ 47.50

4.75x = $47.50

Step 2:

4.75 = $47.50       - Write the equation

[tex]\frac{4.75x}{4.75}[/tex] = [tex]\frac{47.50}{4.75}[/tex]            - Divide both sides of the equation by 4.75

The solution is x = 10

ANSWER: Each friend donates $10

hope this helps Have a good day.

Each friend donates $10.

It is required to find How much does each friend donate.

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.

Given :

The website keeps 5% of each donation.

Five of your friends each donate the same amount.

Total funding receive is $47.50.

Let x represent the amount of each friend donate

According to question we have,

4.75x = $47.50

Divide both sides of the equation by 4.75 we get,

x = 10

Therefore, each friend donates $10.

Learn more about arithmetic here:

brainly.com/question/24423838

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