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2 years ago

A ball is released at a height of 16 inches to roll inside a half-cylinder. It rolls

Mathematics

1 answer:

docker41 [41]2 years ago

8 0

Answer:

Step-by-step explanation:

Using the given formula, we put n = 5

$h = 8* {(\frac{1}{2}) ^{n-1}$

h = 8 / 16

h = 1 / 2 inches

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The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in min

Deffense [45]

Answer:

f'(t) is negative

The unit is degC/min

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

Step-by-step explanation:

From the question we are told we are told that

The equation for the temperature of a cup of coffee place on a counter is

$H= f(t)$

Here t is the time in minutes the coffee was put on the counter

Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time

Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative

Generally the unit of the temperature is in degrees Celsius while that of time is in minutes

So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)

From the question we are told that

$|f(35)'| = 1.5$

i.e the rate of change of temperature after 35 minutes is 1.5

and

$|f(35)| = 68$

i.e the temperature of the cup of coffee after 35 minutes is 67 degC

Now after another t= 30 seconds = $\frac{30}{60}= 0.5 \ minutes$ the rate of change of the temperature of the cup of coffee is

$R = |f(35)'| * t$

=> $R = 1.5 * 0.5$

=> $R = 0.75$

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

5 0

2 years ago

Multi-Step Max's school bought boxes of

Dovator [93]

Answer:

564 pencils

Step-by-step explanation:

1 box = 12 pencils

25 boxes = 25 × 12 pencils = 300 pencils

22 boxes = 22 × 12 pencils = 264 pencils

300 + 264 = 564 pencils

8 0

2 years ago

Please help, I keep getting bots. Using front-end estimation, find a reasonable estimate of:

Aleks [24]

Answer:

Roughly 18,000

Step-by-step explanation:

When you need to do rough mental math, you can do something like 720 vs 25 or 30 which is pretty simple to do in your head.

If you are very proficient in mental math, you can do something like 720 * 25, which is harder, but if you know the tricks, you can do this quickly.

720 * 25

Multiply 25 by 7.

175

Add two zeros.

17,500

Multiply 25 by 2

Add a zero.

500.

17500 + 500 = 18000

5 0

2 years ago

Read 2 more answers

Please solve. -7 = z over 2 + 1

mafiozo [28]

-7=z/2+1

What you first need to do is to multiply both sides of the equation by 2

-14=z+2

Now you move the variable to the left side and change within it’s own sign

-z-14=2

Into

-z=2+14

Now you then add the numbers

-z=16

The last part you do is change the sign on both sides in this equation

z=-16

Therefore, z=-16 is your answer in number 16.

6 0

2 years ago

Read 2 more answers

Triangle BAC was rotated 90° clockwise and dilated at a scale factor of 2 from the origin to create triangle XYZ. Based on these

ANEK [815]

Answer:

The correct option is;

∠A ≅ ∠X

Step-by-step explanation:

The given coordinates of the points of triangle ACB are;

A(-4, 4), C(-1, 3), B(-4, 0)

The given coordinates of the points of triangle XYZ are;

X(0, 8), Y(8, 8), Z(6, 2), therefore, we have

The length. l. of segment is given by the following formula;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

For the length of the segment AC; (x₁, y₁) = (-4, 4), (x₂, y₂) = (-1, 3), l = √(10)

For the length of the segment AB; (x₁, y₁) = (-4, 4), (x₂, y₂) = (-4, 0), l = 4

For the length of the segment BC; (x₁, y₁) = (-4, 0), (x₂, y₂) = (-1, 3), l = 3·√2

For the length of the segment XY; (x₁, y₁) = (0, 8), (x₂, y₂) = (8, 8), l = 8

For the length of the segment XZ; (x₁, y₁) = (0, 8), (x₂, y₂) = (6, 2), l = 6·√2

For the length of the segment ZY; (x₁, y₁) = (6, 2), (x₂, y₂) = (8, 8), l = 2·√(10

Therefore;

XY ~ AB, XZ ~ BC, ZY ~ AC

Which gives;

∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z

8 0

2 years ago

Read 2 more answers