Which travels faster: a car that travels 6 miles in 10 minutes at a constant speed, or a train that travels 6 miles in 8 minutes at a constant speed? Explain how
you

Answer:

4/3 - 1/2= 5/6 hope this helped

Complete question is;

A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm/hr. At what rate is its diameter decreasing?

Answer:

Diameter is decreasing at the rate of 5/(2πr) cm/hr

Step-by-step explanation:

We are told the stone is wearing away at a rate of 50 cm/hr. This means the volume is decreasing. Thus;

dV/dt = -50 cm/hr

Now, a grindstone is in the shape of a cylinder. Thus, volume of grindstone is;

V = πr²h

dV/dr = 2πrh

Now,to find the rate at which the diameter is decreasing, we'll write;

dr/dt = (dV/dt)/(dV/dr)

dr/dt = -50/(2πrh)

We are given;

Diameter = 200 cm

Radius; r = 200/2 = 100 cm

Thickness; h = 10 cm

Thus;

dr/dt = -50/(2π × r × 10)

dr/dt = -5/(2πr) cm/hr

The rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex] and this can be determined by using the given data.

Given :

A 10 cm thick grindstone is initially 200 cm in diameter and it is wearing away at a rate of 50 [tex]\rm cm^3/hr[/tex].

The following steps can be used in order to determine the rate at which grindstone diameter decreases:

Step 1 - According to the given data, the rate at which grindstone volume decreases is:

[tex]\dfrac{dV}{dt} = 50\;{\rm cm^3/hr}[/tex]        --- (1)

Step 2 -  The formula of the volume of the cylinder (grindstone) is given below:

[tex]V = \pi r^2 h[/tex]

Step 3 - Differentiate the above expression with respect to 'r'.

[tex]\dfrac{dV}{dr} = 2\pi r h[/tex]          --- (2)

Step 4 - So, using the expression (1) and (2) the rate at which grindstone diameter decreases is:

[tex]\dfrac{dr}{dt}=\dfrac{\frac{dV}{dt}}{\frac{dV}{dr}}[/tex]

[tex]\dfrac{dr}{dt}=\dfrac{-50}{2\pi r \times 10}\\[/tex]

[tex]\dfrac{dr}{dt} = -\dfrac{5}{2\pi r }\; {\rm cm/hr}[/tex]

So, the rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex].

For more information, refer to the link given below:

https://brainly.com/question/12748872

Answer:

-8 < 8

Step-by-step explanation:

-8 is less than 0 so it is definitely less than 8

Hope this helped :)

Answer: 178

Step-by-step explanation:

18x13

234 area of white granite

8x7

56 area of blue granite

234-56 to find the area of the white granite

Answer:

0.1% were returned

Answer:

C 1,600

Step-by-step explanation:

because If you multiply 37*43 It will get you 1591 and it's asking for the estimated answer which is 1600

Answer:

QR=3, PQ=3, RP=6, SP=9, RS=3, ST=11, RT=14, QR=3

Step-by-step explanation:

Answer:

m = − 2

Step-by-step explanation:

Answer: Choice A)  [tex]3 \sqrt{26}[/tex]

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

Work Shown:

[tex]\text{The two points are } (x_1,y_1) = (6,7) \text{ and } (x_2,y_2) = (3,-8)\\\\d = \text{Distance between } (x_1,y_1) \text{ and } (x_2,y_2)\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} = \text{Distance Formula}\\\\d = \sqrt{(6-3)^2+(7-(-8))^2}\\\\d = \sqrt{(6-3)^2+(7+8)^2}\\\\[/tex]

[tex]d = \sqrt{(3)^2+(15)^2}\\\\d = \sqrt{9+225}\\\\d = \sqrt{234}\\\\d = \sqrt{9*26}\\\\d = \sqrt{9}*\sqrt{26}\\\\d = 3\sqrt{26}\\\\[/tex]

When going from 234 to 9*26, the idea here is to factor where one factor is the largest perfect square possible. That way we can use the rule [tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex] to break up the root and simplify.

Answer:

D. 11.6 cm

Step-by-step explanation:

The missing length of the right angled triangle can be calculated using Pythagorean Theorem as shown below:

[tex] c^2 - b^2 = a^2 [/tex]

Where,

a = x cm

b = 11 cm

c = 16 cm

Thus:

[tex] 16^2 - 11^2 = x^2 [/tex]

[tex] 256 - 121 = x^2 [/tex]

[tex] 135 = x^2 [/tex]

[tex] \sqrt{135} = \sqrt{x^2} [/tex]

[tex] \sqrt{135} = x [/tex]

[tex] 11.61895 = x [/tex]

[tex] x = 11.6 cm [/tex] (nearest tenth)

Answer:

Step-by-step explanation:

11.16

Answer:

D

Step-by-step explanation:

Answer:

E.

Step-by-step explanation:

Area=7*10=70

Perimeter=7+7+10+10=34

Answer    2,290 of total sheets of paper she bought.

Step-by-step explanation:

65x36=2340

subtract 50 for the black pages that she did not use.

2340-50=2,290

Answer:

743487 uhy7ujnuh

Answer:

933 seats

Step-by-step explanation:

Given that :

4 different group of seats are in a movie theater :

The middle group ; 2 side groups and the back group

Number of seats in the movie theater :

THE MIDDLE GROUP:

21 Rows and 21 seats per row

Number of seats = 21 * 21 = 441 seats

THE SIDE GROUPS:

21 rows and 7 seats per row

Number of seats = 2(21 * 7) = 294 seats

BACK GROUP:

6 rows and 33 seats per row

Number of seats = 6 * 33 = 198 seats

Total number of seats :

441 + 294 + 198 = 933 seats

Answer:

so so so so srry i cant see that pic

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

i did the test.

Answer:

1. 7.5 mph

2. 400

Step-by-step explanation:

1. You would just do 60/8 to find the answer.

2. You would take the answer you got from the previous question and do 3000/7.5

Hope I helped!! :)

Answer:

-4√10 / 5 or -8√10 / 5

Step-by-step explanation:

See attachment for calculation

Answer:

128 girls

Step-by-step explanation:

boys : girls = 5 : 8

Number of boys  = 5x

Number of girls = 8x

Total students  = 208

5x + 8x = 208

       13x = 208

           x = 208/13

x =  16

Number of girls = 8x = 8 * 16 = 16 * 8

                         = 128

Answer:

12

Step-by-step explanation:

Answer:

rise over run

Step-by-step explanation:

In this case it is undefined

Answer:

Step-by-step explanation:

18x-2 = 17x +2

⇒18x-17x - 2  = 2

⇒x - 2 = 2

∴ x = 4

Answer:

x=4

Step-by-step explanation:

18x-2=17x+2

step 1: isolate the x by subtracting 17x from both sides

18x-2-17x=17x+2-17x

x-2=2

then add 2 to both sides

x-2+2 = 2+2

x=4

Answer:

$15, 805.00

Step-by-step explanation:

Tax is based on the state you live in.

Answer:

Kindly check explanation

Step-by-step explanation:

1.) regular time hours = 160

Overtime hours = 18

Gross pay = (9.28 * 160) + (1.5 * 9.28 * 18) = $1735.36

2.) Last year, Ida Zolen worked 2,000 hours at regular time pay of $8.20 an hour. She also worked 75 hours over time at double his regular rate. What was Ida’s gross pay last year?

Gross pay:

(2000 * 8.20) + (2 * 8.20 * 75) = $17,630

3. Alan Kirbaum works on an 8-hour day basis and is paid $8 an hour for regular time work and time-and-a half for overtime work. Last week he worked these hours: Monday:9 ; Tuesday:6 ; Wednesday:11 ; Thursday:8 ; Friday:9.

A) How many regular hours did he work?

Regular hours = (8 + 6 + 8 + 8 + 8).= 38 hours

B) How many overtime?

Overtime = (1 + 3 + 1). = 5 hours

C) What is his overtime rate?

2.5 * $8 = $20

D) What is his overtime pay?

$20 * 5 = $100

E) Find Alan’s gross pay.

(38 * $8) + $100 = $404

4. Stephen Woll’s regular pay is $20 an hour. He is paid time and a half for overtime work beyond 40 hours a week. He

worked: Monday:11 ; Tuesday:10 ; Wednesday:10 ; Friday:12. Find Stephen

Total Hour = (11 + 10 + 10 + 12) = 43 hours

Answer:

5 package

Step-by-step explanation:

1 bag = $3

X bag = $15

1 * 15/3 = 5 bags

hence : 5 bag can be bought out of $15

Answer:

Step-by-step explanation:

Distance has to do with how far an object or a body has travelled. If a hiker starts at point P and walks 2.0 kilometers due east and then 1.4 kilometers due north, the total distance covered by the hiker will be:

Distance = 2.0km + 1.4km

Total distance travelled = 3.4km

The displacement is the distance covered in a specified direction. This is expressed using the Pythagoras theorem as shown:

R² = 2.0²+1.4²

R² = 4+1.96

R² = 5.96

R = √5.96

R = 2.44km

Hence the magnitude of the hiker’s displacement vector R is 2.44km

Find the diagram attached

Answer:

D

Step-by-step explanation:

I did this already

Answer:

c = 4

Step-by-step explanation:

Solve for"c" in the following equation:

- 8 c + 7 = - 25

Subtract 7 from both sides:

- 8 c = - 25 - 7

combine like terms

- 8 c = -32

divide both sides by "-8" to isolate c on the left

c = - 32 / (-8)

c = 4

Answer:

The coordinate of the point 3/10 of the way from A to B = (0.5, -4.4)

Step-by-step explanation:

to calculate the point 3/10 of the way from A to B, let us first find the difference in the coordinates of the point

Change in x coordinate: x₁ = -3,  x₂ = 11

= x₂ - x₁ = 11 - (-4) = 11 + 4 = 15

3/10 of 15 = 0.3 × 15 = 4.5

This means that the point on the x axis is 4.5 points away from x₁

= -4 + 4.5 = 0.5

Change y coordinate: y₁ = -8,   y₂ = 4

= y₂ - y₁ = 4 - (-8) = 4 + 8 = 12

3/10 of 12 = 0.3 × 12 = 3.6

This means that the point on the y axis is 3.6 points away from y₁

= -8 + 3.6 = -4.4

Therefore the coordinate of the point 3/10 of the way from A to B = (0.5, -4.4)

Answer:

5/2

Step-by-step explanation:

Parallel lines have the same slopes

Answer:

Step-by-step explanation:

because the new line is parallel, it will have the same slope as the original equation.

slope

=

−

3

we know the slope and a point, so we can use the point slope formula:

y

−

y

1

=

m

(

x

−

x

1

)

y

1

is the y coodinate,

x

1

is the x coordinate,

and m is the slope

plug the values in

y

+

2

=

−

3

(

x

+

5

)