Dana is skating laps to train for a speed skating competition. She can skate one lap in 40 seconds.
1. Write a ratio in simplest form comparing Dana's time to her number of laps.
2. Suppose Dana skates for 20 seconds. How many laps will she skate?
3. Write a ratio of Dana's times from number 2 to her number of laps.
4. How could you simplify the ratio you wrote in 3?

Answer:

The rate at which the volume is decreasing when the snowball has a diameter of 4 inches is approximately 251.327 cubic inches per minute.

Step-by-step explanation:

Let suppose that snowball geometry correspond to a sphere. In this case, the volume of the sphere is:

[tex]V = \frac{4\pi}{3}\cdot R^{3}[/tex] (Eq. 1)

Where:

[tex]R[/tex] - Radius of the sphere, measured in inches.

[tex]V[/tex] - Volume of the sphere, measured in cubic inches.

We know that volume decreases due to melting, so we need an expression of the rate of change of volume in time. By differentiating (Eq. 1) we get:

[tex]\frac{dV}{dt} = 4\pi\cdot R^{2}\cdot \frac{dr}{dt}[/tex] (Eq. 2)

Where:

[tex]\frac{dV}{dt}[/tex] - Rate of change of the volume of the snowball in time, measured in cubic inches per minute.

[tex]\frac{dr}{dt}[/tex] - Rate of change of radius of the snowball in time, measured in inches per minute.

If we know that [tex]R = 2\,in[/tex] and [tex]\frac{dr}{dt} = -5\,\frac{in}{min}[/tex], the rate at which the volume of the snowball is decreasing is:

[tex]\frac{dV}{dt} = 4\pi\cdot (2\,in)^{2}\cdot \left(-5\,\frac{in}{min} \right)[/tex]

[tex]\frac{dV}{dt}\approx -251.327\,\frac{in^{3}}{min}[/tex]

The rate at which the volume is decreasing when the snowball has a diameter of 4 inches is approximately 251.327 cubic inches per minute.

Answer:

C dont trust me wait for someone else to anser

Step-by-step explanation:

Answer:

i cant see

Step-by-step explanation:

make a more clear pic

Answer:

From the image, we can see that ∠AOC = ∠AOB + ∠BOC

We are given the following values:

∠AOC = 104

∠AOB = 7x + 30

∠BOC = 9x + 42

Plugging these values in the equation above:

∠AOC = ∠AOB + ∠BOC

104 = 7x + 30 + 9x + 42

104 = 16x + 72

16x = 32

x = 2

Now that we have the value of x, we can easily find the value of ∠BOC

We are given that:

∠BOC = 9x + 42

∠BOC = 9(2) + 42           (since x = 2)

∠BOC = 18 + 42

∠BOC = 60°

Therefore, ∠BOC is 60 degrees

is this angilic from vista hills and dessert view if so this is josh a

Answer:

5.5 liters hope this works for u

Step-by-step explanation:

Answer:

stupid noob

Step-by-step explanation:

Given:

The point P(-2, - 5) is rotated 90° about the origin, and then the image is reflected across the line  x= 3.

To find:

The the coordinates of the final image P’’.

Solution:

The point P(-2, - 5) is rotated 90° about the origin. It means the point is rotated 90° counter clockwise about the origin

[tex](x,y)\to (-y,x)[/tex]

[tex]P(-2,-5)\to P'(-(-5),(-2))[/tex]

[tex]P(-2,-5)\to P'(5,-2)[/tex]

Then the image is reflected across the line  x= 3.

[tex](x,y)\to (-x+6,y)[/tex]

[tex]P'(5,-2)\to P''(-5+6,-2)[/tex]

[tex]P'(5,-2)\to P''(1,-2)[/tex]

Therefore, the \coordinates of the final image P'' are (1,-2).

Answer: the first opion is correct

as pentagon is concave so one angle mist be greater than 180°

Step-by-step explanation:

Answer:

4y-12

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

2x - 3 = 9 - 4x

6x - 3 = 9 (added 4x to both sides)

6x = 12 (added 3 to both sides)

x = 2 (divided 12 by 6)

hope this helps :)

Answer:

Alternate Interior Angles Theory

Step-by-step explanation:

Any number inside the angle is known as an Alternate Interior Angle.

Answer:

36 boys

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer:

BRuh

Step-by-step explanation:

Girl my math skills are no where near subpar to that. Good luck!

Answer:

I think the answer is 35 hours to get the same amount of money

Answer: The equation that represents the road is y= - 1/3x +1/3

Step-by-step explanation:

The perpendicular equation that represents the road that passes through the point is [tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]

The points of the red line (see attachment) are given as:

[tex]\mathbf{(x,y) = (0,2), (2,8)}[/tex]

Start by calculating the slope (m) of the line using:

[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{8 - 2}{2 -0}}[/tex]

[tex]\mathbf{m = \frac{6}{2}}[/tex]

[tex]\mathbf{m = 3}[/tex]

Next, calculate the slope (m2) of the perpendicular line using:

[tex]\mathbf{m_2 = -\frac 1m}[/tex]

So, we have:

[tex]\mathbf{m_2 = -\frac 13}[/tex]

The perpendicular line passes through point (1,0).

So, the line equation is calculated using:

[tex]\mathbf{y = m_2(x - x_1) + y_1}[/tex]

This gives

[tex]\mathbf{y = -\frac 13(x - 1) + 0}[/tex]

[tex]\mathbf{y = -\frac 13(x - 1) }[/tex]

Open bracket

[tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]

Hence, the line equation is [tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]

Read more about perpendicular equations at:

https://brainly.com/question/21740769

Answer:

each green line is 45 degrees

Step-by-step explanation:

Answer:

first box should be EAF then next FAL and the last would be ray AL and its a ray because it has one endpoint which is A.

Step-by-step explanation:

Answer:

If [tex]k > 0[/tex], then [tex]x[/tex] must be greater than 0.

Step-by-step explanation:

If [tex]k > 0[/tex], then we state that [tex]e^{5\cdot x} > 0[/tex] and [tex]e^{5\cdot x}[/tex] is a trascendental function with a lower bound so that [tex]e^{5\cdot x}> 1[/tex]. Then, the minimum value of [tex]k[/tex] is 1 and we proceed to solve the latter equation to find the value of [tex]x[/tex]:

[tex]e^{5\cdot x}> 1[/tex]

[tex]\ln e^{5\cdot x} > \ln 1[/tex]

[tex]5\cdot x > 0[/tex]

[tex]x > 0[/tex]

Therefore, [tex]x[/tex] must be greater than 0.

Answer:

The length of the midsegment is 9 ⇒ (B)

Step-by-step explanation:

In a triangle,

Let us use this rule to solve our question

In Δ AC

∵ DE is the midsegment of it

∵ DE is opposite to the side AC

∴ The length of DE = 1/2 the length of AC

∵ The length of AC = 18

∴ The length of DE = 1/2 × 18

∴ The length of DE = 9

∴ The length of the midsegment is 9

The correct answer is B

Answer:

∠FJH ≅ ∠BJA

Step-by-step explanation:

From the image we can see that the only congruent relation ∠FJH has is with ∠BJA which is due to these angles being vertically opposite

So, ∠FJH and ∠BJA are vertically opposite and hence, congruent. We can say that ∠FJH ≅ ∠BJA

Answer:

BBBBBB

Step-by-step explanation:

Answer:

i have no idea. But i will answer because i'm still learning.

Step-by-step explanation:

-2 (3a – 2) = 1/3(7 – 3a)

is whats the question

ok its i'm guessing      -2 (3a – 2) = 1/3(7 – 3a)

-2.15384615385

                         Hope this helps    ;)

Answer:

4= Sx+10/2 simplifies to -s*x-1=0

Step-by-step explanation:

Answer:

18π

Step-by-step explanation:

Arc length for a parametric equation is:

s = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt

dx/dt = -9 sin(9t)

dy/dt = 9 cos(9t)

s = ∫₀²ᵖⁱ √((-9 sin(9t))² + (9 cos(9t))²) dt

s = ∫₀²ᵖⁱ √(81 sin²(9t) + 81 cos²(9t)) dt

s = ∫₀²ᵖⁱ 9 dt

s = 9t |₀²ᵖⁱ

s = 18π

You can check your answer with geometry.  The curve is a circle centered at the origin with radius 1.  From 0 to 2π, the particle makes 9 revolutions, or travels 18π radians.  So the arc length is 1 × 18π = 18π.

Answer:

18π

Step-by-step explanation:

Answer:

w=3

Step-by-step explanation:

Answer:

the answer is 95

Answer:

The measure of angle 7=95*

Step-by-step explanation:

I just got the question correct.

Answer:

a=7.44...

Step-by-step explanation:

9a-2=65 (+2)

9a=67 (/9)

a=7.44...

Answer:

-7 I believe is the answer hope this helps