Mrs little and jack go on a hike. After 2 hours, they have gone 300 feet. After 6 hours, they have gone 800 feet. What is the average rate of change?

First integral:

Parameterize -C (the reverse of C) by [tex]z = e^{it}[/tex] where [tex]0\le t \le\frac\pi2[/tex]. Then the contour integral is

[tex]\displaystyle \int_{-C} (z^2 - z + 2) \, dz = \int_0^{\frac\pi2} \left(e^{2it} - e^{it} + 2\right) i e^{it} \, dt[/tex]

[tex]\displaystyle = i \int_0^{\frac\pi2} \left(e^{3it} - e^{2it} + 2e^{it}\left) \, dt[/tex]

[tex]\displaystyle = i \left(\frac1{3i} e^{3it} - \frac1{2i} e^{2it} + \frac2i e^{it}\right) \bigg|_0^{\frac\pi2}[/tex]

[tex]\displaystyle = \left(\frac13 e^{3it} - \frac12 e^{2it} + 2 e^{it}\right) \bigg|_0^{\frac\pi2}[/tex]

[tex]\displaystyle = -\frac43 + \frac53i[/tex]

Then

[tex]\displaystyle \int_C (z^2-z+2) \, dz = -\int_{-C} (z^2+z-2) \, dz = \boxed{\frac43 - \frac53i}[/tex]

Second integral:

The integrand has a pole of order 2 at z = 3i which is contained in C. By the residue theorem,

[tex]\displaystyle \int_C \frac{z^2+z}{(z-3i)^2} \, dz = 2\pi i\, \mathrm{Res}\left(\frac{z^2+z}{(z-3i)^2}, z=3i\right)[/tex]

Compute the residue:

[tex]\displaystyle \mathrm{Res}\left(\frac{z^2+z}{(z-3i)^2},z=3i\right) = \lim_{z\to3i} \frac{d}{dz}\left[z^2+z\right] = \lim_{z\to3i} (2z+1) = 1 + 6i[/tex]

Then the value of the integral is

[tex]\displaystyle \int_C \frac{z^2+z}{(z-3i)^2} \, dz = 2\pi i (1 + 6i) = \boxed{-12\pi + 2\pi i}[/tex]

Answer:

Step-by-step explanation:

Original coordinates of F

It is reflected across the y-axis.

Transformation of coordinates across y-axis

Therefore, on reflection, the coordinates of F' will be :

Answer:

The question has some missing details such as ; Use cylindrical shells to find the volume of the remaining solid if the remaining solid is 8cm high. I have however solved it using the value of 8cm, you can use the same approach to solve for the volume irrespective of the value of the height you are given.

Step-by-step explanation:

The detailed step by step analysis and appropriate Integration by susbtitution in order to get the volume of the remaining solid is as shown in the attached file.

Answer:

126

Step-by-step explanation:

[tex]V = A * h = \frac{1}{4} * \pi * d^{2} * h = A * h = \frac{1}{4} * 3.14 * 36 * 5 = 141.3\\ \\V_{empty} = A * h = \frac{1}{4} * \pi * d^{2} * h = \frac{1}{4} * \pi * 4 * 5 = 15.7[/tex]

[tex]V_{full} = V - V_{empty} = 141.3 - 15.7 = 125.6 \approx 126[/tex]

Given  ↓

[tex]\blue{\boxed{\mathsf{V=\frac{4}{3} \pi r^3}}[/tex]

↑ formula for volume of a sphere

r = 5 in

Plug in the value of r and solve :

[tex]\blue{\boxed{\mathsf{V=\frac{4}{3}\pi (5)^3}}}[/tex]

Simplify as follows :

[tex]\blue{\boxed{\mathsf{V=\frac{4}{3}\pi *125} }}[/tex]

[tex]\blue{\boxed{V=\frac{4}{3} *392.7}}[/tex]

Final Step :

[tex]\blue{\boxed{\pmb{V=523.6\:in\:^3}}[/tex]

[tex]\footnotesize\text{hope\:helpful}[/tex]

Answer:

[tex]\textsf{a)}\quad y=8x^2+2x-3[/tex]

[tex]\textsf{b)}\quad y=x^2-2x-4[/tex]

Step-by-step explanation:

Given information:

[tex]x^2+bx+c=0[/tex]

[tex]x_1+x_2=-b[/tex]

[tex]x_1x_2=c[/tex]

Part (a)

[tex]\textsf{If}\quad x_1=\dfrac12\quad\textsf{and}\quad x_2=-\dfrac34[/tex]

[tex]\begin{aligned}\implies -b & =\dfrac12+\left(-\dfrac34\right)\\ & = \dfrac24-\dfrac34\\ & =-\dfrac14\end{aligned}[/tex]

[tex]\begin{aligned}\implies c & =\dfrac12 \cdot \left(-\dfrac34\right)\\ & = \dfrac{1 (-3)}{2 \cdot 4}\\ & =-\dfrac38\end{aligned}[/tex]

Substituting the found values of b and c into [tex]x^2+bx+c=0[/tex]

[tex]\implies x^2+\dfrac14x-\dfrac38=0[/tex]

Multiply both sides by 8 so that coefficients are integers:

[tex]\implies 8x^2+2x-3=0[/tex]

Therefore, the final quadratic equation is:

[tex]y=8x^2+2x-3[/tex]

----------------------------------------------------------------------------------------------

Part (b)

[tex]\textsf{If}\quad x_1=1+\sqrt{5}\quad\textsf{and}\quad x_2=1-\sqrt{5}[/tex]

[tex]\begin{aligned}\implies -b & =(1+\sqrt{5})+(1-\sqrt{5})\\ & = 1+1+\sqrt{5}-\sqrt{5}\\ & =2\end{aligned}[/tex]

[tex]\begin{aligned}\implies c & =(1+\sqrt{5})(1-\sqrt{5})\\ & = 1-\sqrt{5}+\sqrt{5}-5\\ & =-4\end{aligned}[/tex]

Substituting the found values of b and c into [tex]x^2+bx+c=0[/tex]

[tex]\implies x^2-2x-4=0[/tex]

Therefore, the final quadratic equation is:

[tex]y=x^2-2x-4[/tex]

Answer:

the answer is 90 degrees

Step-by-step explanation:

y=mx+c

2=2(1)+c

c=2-2

c=0

Answer:

291.

Step-by-step explanation:

(x - 147) / 12 = 12

x - 147 = 144

x = 144 + 147

x = 291.

Answer:

Joaquin Phoenix Has the Fastest Joker Makeup at Just 15 Minutes.

Answer:

Step-by-step explanation:

radius = 16/2 = 8

Then you can apply the formula to calculate the base area, lateral surface or surface or even perimeter

Answer:

0

Step-by-step explanation:

5^2-4(5)-5=2(5)-10

0=0

Answer:

(3)   {5,7}

Step-by-step explanation

135 people voted for it on gauth math

i believe it is called a parameter

its the one on the right :) x goes up 5 each time, y goes up 3 each time ; no jumps

Answer:

c. $750

Step-by-step explanation:

the perimeter is 80m

80÷8=10

10*75=750

Answer:

-0.45

Step-by-step explanation:

put that in a calculator

round off to 2 decimal places

[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]

═════════════════════

1.[tex]- 5x - y = 8[/tex]

[tex]-5x-y=8[/tex]

[tex]-5x=8+y [/tex]

[tex]-5x=y+8 [/tex]

[tex]\frac{-5x}{-5}=\frac{y+8}{-5} [/tex]

[tex]x=\frac{y+8}{-5} [/tex]

[tex]x=\frac{-y-8}{5} [/tex]

[tex]-5x-y=8[/tex]

[tex]-y=8+5x [/tex]

[tex]-y=5x+8 [/tex]

[tex]\frac{-y}{-1}=\frac{5x+8}{-1} [/tex]

[tex]y=\frac{5x+8}{-1} [/tex]

[tex]y=-5x-8 [/tex]

────────────────────

2.[tex]-4x-y=2 [/tex]

[tex]-4x-y=2 [/tex]

[tex]-4x=2+y [/tex]

[tex]-4x=y+2 [/tex]

[tex]\frac{-4x}{-4}=\frac{y+2}{-4} [/tex]

[tex]x=\frac{y+2}{-4} [/tex]

[tex]x=-\frac{y}{4}-\frac{1}{2} [/tex]

[tex]-4x-y=2[/tex]

[tex]-y=2+4x [/tex]

[tex]-y=4x+2 [/tex]

[tex]\frac{-y}{-1}=\frac{4x+2}{-1} [/tex]

[tex]y=\frac{4x+2}{-1} [/tex]

[tex]y=-4x-2 [/tex]

════════════════════

Explanation:

#Carry on learning

The standard form of the expression (4 × 10) + (3 × 1/100) + (5 × 1/1000) is 40.035

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have expression:

= (4 × 10) + (3 × 1/100) + (5 × 1/1000)

= 40 + 0.03 + 0.005

= 40.035

Thus, the standard form of the expression (4 × 10) + (3 × 1/100) + (5 × 1/1000) is 40.035

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ1

Option 2 is correct.

The axis of symmetry is, x= 3

Step-by-step explanation:

Given: The zeros of the quadratic function f are 1 and 5.

If the zeroes are at x =1 and at x  =5, then,

the factor equations were  x- 1=0 and x-5 = 0.

Then. the factors were x -1 and x-5 .

Any factorable quadratic is going to have just the two factors, so these are must be them.

Then, the original quadratic was :

or

     [by distributive property  ]

Combine like terms;

               ......[1]

A quadratic equation is of the form: ; where a, b, c are the coefficient ]

On comparing equation [1] with general equation we have;

the value of  a = 1 , b = -6 and c =5

Axis of symmetry states that a parabola is a vertical line that divides the parabola into two congruent halves.

i,e

Then;

Axis of symmetry (x) =

Therefore, the equation of the axis of symmetry is;  x = 3

Answer:

1  3/5 bags left

Step-by-step explanation:

If she gives 2/5 away, she keeps 3/5

3/5  *  2 2/3 = 3/5 * 8/3 =   24/15  = 1 9/15  = 1 3/5 bags left

Answer:

problem 8= 769.3

problem 16=A

problem 11= independent-x , dependent-y

problem 12= independent- s , dependent- v

problem 17= C

Answer:

Range :24

Mode: No mode

Median:13

Mean:46.5 OR 13.30

Answer:

-2

Step-by-step explanation:

a negative divided by a negative is a positive

Answer:

n = -2

Step-by-step explanation:

-6/n = 3

multiply n on both sides

-6 = 3n

divide 3

-2 = n

n = -2

Answer:A

Step-by-step explanation:

because i just know iot is

Answer:

Yes

Step-by-step explanation:

put point (3,28) in the above equation

28=19+3(3)

28=28

[tex]\LARGE{\text{please\:refer\:to\:the\:"explanation"\:section\:of\:this\:ans}}[/tex]

An easy way to check whether or not a point lies on a line is to plug in the x-coordinate in lieu of x and the y - coordinate in lieu of y As follows :

x - coordinate : 3

y=19+3(3)

y - coordinate : 28

28 = 19 + 9

28 = 28 [tex]\Large\checkmark[/tex]

LHS = RHS

[tex]\footnotesize{\text{hope\:helpful}}[/tex]

Step-by-step explanation:

green = surface area

volume = 9/5 × 2/3

= 18/15

= 6/5 = 1.2 or 1 1/5

Answer:

it’s 8 and 2 and 4 and 0

Step-by-step explanation:

this is because when you multiply 2x the x is an 8 so 2 times 8 is 16 then minus 2 is 14 which is greater than -4 same for my other answer

Answer:

You are making 25$ in profit. You do this by subtracting 150-125. to get 25.

Step-by-step explanation:

Hope This Helps

Have A Great Day

~Zero~