MATHEMATICS HIGH SCHOOL

The area of a circle of radius r is given by A=\pi r^2A=πr 2 and its circumference is given by C=2\pi rC=2πr. At a certain point in time, the radius of the circle is r=8r=8 inches and the area of the circle is changing at a rate of \frac{dY}{dt}=\pi\sqrt{2} dt dA ​ =π 2 ​ square inches per second. How fast is the radius of the circle changing at this time

Answers

Answer 1
Answer:

Answer:

Step-by-step explanation:

If I'm understanding this correctly, your problem is as follows:

The area of a circle is given by the formula

A=\pi r^2

The area of the circle is changing at a rate of (dA)/(dt)=√(2)\pi.  Find the rate of change of the radius, (dr)/(dt) , when r = 8.

Assuming that is what you are asking, we will begin by finding the derivative of the area of a circle using implicit differentiation.

(dA)/(dt)=\pi2r(dr)/(dt)

Filling in what we have:

√(2)\pi=\pi(2)(8)(dr)/(dt) which simplifies a bit to

√(2)\pi=16\pi(dr)/(dt)

Divide both sides by 16π to get:

(√(2)\pi )/(16\pi)=(dr)/(dt)

The π's cancel leaving the rate of change of the radius as

(dr)/(dt)=.0883883476 inches per second

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I traveled 117 miles in 2.25 hours. What was my average speed? How would I solve this ?

The Apache Taxi Company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another. If x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?

Answers

Answer:  Isaac traveled approximately 13 miles by the taxi.

Step-by-step explanation:

Since we have given that

Amount charges to pick up a passenger = $2.50

Amount per mile = $1.95

Total amount charged = $27.46

Let x be the number of miles driven by the taxi.

According to question, it becomes,

2.50+1.95x=27.46\n\n1.95x=27.46-2.50\n\n1.95x=24.96\n\nx=(24.96)/(1.95)\n\nx=12.8\n\nx\approx 13\ miles

Hence, Isaac traveled approximately 13 miles by the taxi.
27.46 - 2.50 = 24.96 / 1.95 = 12.8 miles

If my grade is a "80.85" and I turn in a paper that is 5 points what is my grade?

Answers

Answer:

81%-82%

Step-by-step explanation:

A car is traveling at a rate of 90 kilometers per hour. what is the car rate in kilometers per minute. how many kilometers can the car travel per 20 minutes?

Answers

The car rate in km/min is found by,
90km / 60mins = 1.5 (km)/(mins)
Then the car will travel this in 20mins,
1.5 (km)/(mins) * 20mins = 30km

(OFFERING ALL THE POINTS I HAVE) Word Problem. Please help!! Part 1 of problem: The main tank has a radius of 70 feet. What is the volume of the quarter-sphere sized tank? Round your answer to the nearest whole number and use 3.14 for Pi. (Use sphere volume formula) Part 2: The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up? Part 3: Using the information from part 2, answer the following question by filling in the blank: The volume of the actual tank is __% of the mock-up of the tank.

Answers

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

Answer:

Part 1: 359,007 ft³

Part 2: 216 times smaller

Part 3: 21600%

Step-by-step explanation:

Part 1:

The parameters for the tank are;

The radius of the tank = 70 feet

The volume of a sphere = 4/3·π·r³

Therefore, the volume of a quarter sphere = 1/4×The volume of a sphere

The volume of a quarter sphere = 1/4×4/3·π·r³ = π·r³/3

Plugging in the value for the radius gives

Volume = π×70³/3 = 114,333.33×3.14 = 359,006.7≈ 359,007 ft³.

Part 2:

The dimension of the scale model  = 1/6 × Actual dimension

Therefore, we have the radius of the sphere of the scale model = 1/6 × 70

Which gives;

The radius of the sphere of the scale model = 35/3 = 11.67 feet

The volume of the scale model = π·r³/3 = (3.14×11.67³)/3 = 1662.07 ≈ 1662 ft³

The number of times smaller the scale model is than the actual volume = (Actual volume)/(Scale model) = (359,007 ft³)/(1662 ft³) = 216 times

The number of times smaller the scale model is than the actual volume =  216 times = (1/Scale of model)³ = (1/(1/6))³ = 6³.

Part 3:

The percentage of the mock-up, x, to the volume of the actual tank is given as follows

x/100 ×  1662  = 359,007

∴ x = 216 × 100 = 21600%

The percentage of the mock-up, to the volume of the actual tank is 21600%.

2700=2300(1+r)^5 solve for r Please show all work

Answers

2700=2300(1+r)^5\ /:2300\n\n(1+r)^5= (27)/(23) \ \ \ \Rightarrow\ \ \ 1+r= \sqrt[5]{ (27)/(23)} \ \ \ \Rightarrow\ \ \ r= \sqrt[5]{ (27)/(23)} -1\n\n r= \sqrt[5]{ (27\cdot23^4)/(23^5)}-1= \frac{ \sqrt[5]{ 27\cdot23^4} }{23} -1= \frac{ \sqrt[5]{7555707} }{23} -1
2700=2300(1+r)^5\n \n (1+r)^5=(2700)/(2300)\n \n (1+r)^5=(27)/(23)\n \n \sqrt[5]{(1+r)^5}= \sqrt[5]{(27)/(23)}\n \n 1+r= 1.032\n \n r=1.032-1\n \n \boxed{r=0.032}

The cost of 4 cartons of fresh cream is $7.96. What is the cost of 14 such cartons?$15.99
$21.96
$24.56
$27.86

Answers

7.96/4=1.99
1.99*14= 27.86 Monies
The answer is $27.86. Hope this helps
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