Only the top runners in the world can finish a marathon in close to 2 hours. This graph
shows the pace that one such runner followed in a race. What is the unit rate?
Marathon Pace
N
28
24
20
Distance (mi)
10
12
B
8
A
4
0
0 20 40 60 80 100120140
Time (min)

Answer:

If we put x=17/4

f(4×17/4-15)=8×17/4-27

f(2x=34-27

f(x)=7.

Hope i helped you.

Answer:

Step-by-step explanation:multiple 5 times 108 and that gives you your answer..

9514 1404 393

Answer:

  (x, y) = (4, -4)

Step-by-step explanation:

A graphing calculator makes graphing very easy. The attachment shows the solution to be (x, y) = (4, -4).

__

The equations are in slope-intercept form, so it is convenient to start from the y-intercept and use the slope (rise/run) to find additional points on the line.

The first line can be drawn by staring at (0, -2) and moving down 1 grid unit for each 2 to the right.

The second line can be drawn by starting at (0, 2) and moving down 3 grid units for each 2 to the right.

The point of intersection of the lines, (4, -4), is the solution to the system of equations.

I think the given integral reads

[tex]\displaystyle \int_{-3}^3 \int_0^{9-x^2} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

In cylindrical coordinates, we take

x ² + y ² = r ²

x = r cos(θ)

y = r sin(θ)

and leave z alone. The volume element becomes

dV = dx dy dz = r dr dθ dz

Then the integral in cylindrical coordinates is

[tex]\displaystyle \boxed{\int_0^\pi \int_0^{(\sqrt{35\cos^2(\theta)+1}-\sin(\theta))/(2\cos^2(\theta))} \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta}[/tex]

To arrive at this integral, first look at the "shadow" of the integration region in the x-y plane. It's the set

{(x, y) : -3 ≤ x ≤ 3 and 0 ≤ y ≤ 9 - x ²}

which is the area between a paraboloid and the x-axis in the upper half of the plane. So right away, you know θ will fall in the first two quadrants, so that 0 ≤ θ ≤ π.

Next, r describes the distance from the origin to the parabola y = 9 - x ². In cylindrical coordinates, this equation changes to

r sin(θ) = 9 - (r cos(θ))²

You can solve this explicitly for r as a function of θ :

r sin(θ) = 9 - r ² cos²(θ)

r ² cos²(θ) + r sin(θ) = 9

r ² + r sin(θ)/cos²(θ) = 9/cos²(θ)

(r + sin(θ)/(2 cos²(θ)))² = 9/cos²(θ) + sin²(θ)/(4 cos⁴(θ))

(r + sin(θ)/(2 cos²(θ)))² = (36 cos²(θ) + sin²(θ))/(4 cos⁴(θ))

(r + sin(θ)/(2 cos²(θ)))² = (35 cos²(θ) + 1)/(4 cos⁴(θ))

r + sin(θ)/(2 cos²(θ)) = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))]

r  = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))] - sin(θ)/(2 cos²(θ))

Then r ranges from 0 to this upper limit.

Lastly, the limits for z can be converted immediately since there's no underlying dependence on r or θ.

The expression above is a bit complicated, so I wonder if you are missing some square roots in the given integral... Perhaps you meant

[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

or

[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{\sqrt{9-x^2-y^2}} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

For either of these, the "shadow" in the x-y plane is a semicircle of radius 3, so the only difference is that the upper limit on r in either integral would be r = 3. The limits for z would essentially stay the same. So you'd have either

[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

or

[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{\sqrt{9-r^2}} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

Answer:

f(x) can not be equal to g(x)

Step-by-step explanation:

If the result is possible:

f(x) = g(x)

x + 8 = x + 2

x + 8 - (x + 2) = x + 2 - (x + 2)

6 = 0

Because 6 can't be equal to 0, so do f(x) can't be equal to g(x)

Answer:

Step-by-step explanation:

Answer:

Y= -9x+45

y = -9 X + b

-9 = -9(6) + b

-9 = -54 + b

b=45

Step-by-step explanation:

Answer:

πr

Step-by-step explanation:

radius = r/2

so circumference = 2π(r/2)

= 2πr/2

= πr

Answer:

The answer is B which is C=2πr

Step-by-step explanation:

i just did it

Answer:

False

Step-by-step explanation:

To find the inverse of a function, switch the variables and solve for y.

The inverse of f(n)=-(n+1)^3:

[tex]y=-(n+1)^3[/tex]

[tex]n=-(y+1)^3[/tex]

[tex]\sqrt[3]{n} =-(y+1)[/tex]

[tex]\sqrt[3]{n} =-y-1[/tex]

[tex]\sqrt[3]{n} +1=-y[/tex][tex]-(\sqrt[3]{n} +1)=y[/tex]

[tex]-\sqrt[3]{n} -1=y[/tex]

Answer:

False

Step-by-step explanation:

Answer:

please tell me the complete question

The maximum length of the seesaw is option c  4.00 meters.

A right-angled triangle is one in which one of the angles is equal to 90 degrees. A 90 degree angle is called a right angle, which is why a triangle made up of right angle is termed a right angled triangle.

A right-angled triangle has three sides- hypotenuse, base and height. Hypotenuse is the longest and also the opposite side of the right angle of the triangle, base and height of a right triangle are always the sides adjacent to the right angle.

The formula for measuring the hypotenuse is,

Height / Hypotenuse = Sinθ , where θ is the angle opposite to the height of the triangle.

In the given question, the seesaw should make an angle of 30° with the ground and the maximum height it should rise is 2 meters so the height here is 2 meters. So the seesaw will make a right angled triangle.

Height = 2 meters, θ = 30°,

Now using the formula,

2 / Hypotenuse = Sin30°

Rearranging we get,

Hypotenuse = 2 / Sin30°

The value of Sin30° is 1/2 and putting the value we get,

Hypotenuse = 2 / (1/2)

                     = 2 × 2

                     = 4 meters.

Therefore, the maximum length of the seesaw (that is the hypotenuse ) is 4 meters.

To learn more about right-angled triangles and finding sides of it click here-brainly.com/question/10331046

#SPJ2

Answer:

30

Step-by-step explanation:

To compare the numbers, divide the first number by the second number.

(7.4 x 10^8)/(2.5 x 10^7) = (74 x 10^7)/(2.5 x 10^7) = 74/2.5 = 29.6

Answer: 30

Answer:Mark Brainliest please

Answer is 4.86 which is rounded to 5

Step-by-step explanation:

Cos 40 degree = VW/7

0.694 =VW/7

0.694 * 7 =VW

4.858 =VW

VW=4.86 is the answer

Answer:

3

Step-by-step explanation:

Please Mark me brainliest

Answer:

aren't one of the numbers in the equations supposed to be negative?

Answer:

100.48

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

V = 3.14 ( 2)^2 * 8

V = 3.14 (4)(8)

V = 100.48

Answer:

Step-by-step explanation:

If you mean √200, you cannot write it as V200.

√200 = √(10²×2) = 10√2

Answer:

B.) 2/10

Step-by-step explanation:

Answer: hello your question is poorly written attached below is the complete question

answer:

1 ) =  I (

2) = F

3) = Z

4) = D

Step-by-step explanation:

attached below is the required solution.

1 ) =  I ( The sequence diverges to infinity )

2) = F ( The sequence has a finite non-zero limit )

3) = Z ( The sequence converges to zero )

4) = D ( The sequence diverges )

Answer:

-6

Step-by-step explanation:

Answer:

[tex]24 + x = 13 \\ x = 13 - 24 \\ x = - 11 \\ thank \: you[/tex]

Answer:

RS 17.10

Step-by-step explanation:

If they earn 0.95 a day, you can multiply that income by the number of days, which is 18.

RS 17.10

Answer:

y=(3/7)*x+52/7

Step-by-step explanation:

The slope of the line will be (3/7). The equation of line will be y=(3/7)*x+52/7

Answer:

Step-by-step explanation:

In order to find out how long it takes for the rocket to hit the ground, we only need set that position equation equal to 0 (that's how high something is off the ground when it is sitting ON the ground) and factor to solve for t:

[tex]0=-4.9t^2+112t+395[/tex]

Factor that however you are factoring in class to get

t = -3.1 seconds and t = 25.9 seconds.

Since time can NEVER be negative, it takes the rocket approximately 26 seconds to hit the ground.

Hi! I'm happy to help!

To solve this problem, we need to divide the recipe amount in 1/6 amounts. So, we will do a fraction division problem like this:

15[tex]\frac{1}{6}[/tex]÷[tex]\frac{1}{6}[/tex]

This problem is hard to do with mixed numbers, so we need to turn 15[tex]\frac{1}{6}[/tex] into an improper fraction. To do that we need to multiply 15 by 6, because that is our denominator, then add the extra [tex]\frac{1}{6}[/tex].

(15×6)+1

90+1

91

So, our improper fraction would be[tex]\frac{91}{6}[/tex], now, let's solve.

[tex]\frac{91}{6}[/tex]÷[tex]\frac{1}{6}[/tex]

It is difficult to do division problems on their own, so we can change this into an easier problem. We can do the inverse operation and turn this into multiplication. We do this by changing it to multiplication (obviously), then flip the second fraction.

[tex]\frac{91}{6}[/tex]×[tex]\frac{6}{1}[/tex]

Now, we just multiply the top by the top, and bottom by the bottom.

[tex]\frac{546}{6}[/tex]

We could end it here, but we want a whole number, so, we simplify the number by dividing both the top and bottom by 6.

[tex]\frac{91}{1}[/tex]

Anything over 1, is just a whole number

91.

Therefore, the recipe should require 91 uses of the 1/6 cup.

I hope this was helpful, keep learning! :D

Answer:

C

Step-by-step explanation:

sin(theta)=7/8, theta=arcsin(7/8)=61

Answer:

B. 1/2

Step-by-step explanation:

Slope formula = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

[tex]\frac{(-4)-(-8) }{(6)-(-2)}[/tex]

[tex]\frac{4}{8}[/tex]

[tex]\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

(-4 - 5i)⋅(1 - i) = (-4)(1) + (-4)(-i) + (-5i)(1) + (-5i)(-i)

= -4 + 4i - 5i + 5i²

= -4 - i -5

= -9 - i

Answer: 7 / 50

Step-by-step explanation:

Given

0.14

Convert to 100-denominator fraction

= 14 ÷ 100

= 14/100

Divide both numerator and denominator by 2

=(14 ÷ 2) / (100 ÷ 2)

=7 / 50

Hope this helps!! :)

Please let me know if you have any questions

Answer:

1/19

Step-by-step explanation:

There are a total of 36+2 = 38 spaces

2 are green

P(green) = green / total

             = 2/38

            =1/19

            .052631579