What does a rational number plus an irrational number equal?

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9966 [12]

Answer:

See below.

Step-by-step explanation:

PROBLEM A

The formula for the volume of a cylinder is

V = πr²h, where πr² is the area of the base.

V = area of base x height

Choose any four numbers that are less than 10 for the height.
Then, substitute into the formula and isolate "r". 10 = πr²h
Double "r" to find the diameter.
The area of the base is found (bolded) while you solve πr².

*I will use the calculator button for pi (π)

Cylinder A: h = 1

10 = πr²h

10 = πr²(1)

10 = πr² Area of the base is 10m².

r = √ (10/π)

r = 1.78 Radius is 1.78m.

d = 2r = 1.78*2 = 3.56 Diameter is 3.56m.

Cylinder B: h = 2

10 = πr²h

10 = πr²(2)

5 = πr² Area of the base is 5m².

r = √ (5/π)

r = 1.26 Radius is 1.26m.

d = 2r = 1.26*2 = 2.52 Diameter is 2.52m.

Cylinder C: h = 4

10 = πr²h

10 = πr²(4)

2.5 = πr² Area of the base is 2.5m².

r = √ (2.5/π)

r = 0.89 Radius is 0.89m.

d = 2r = 0.89*2 = 1.78 Diameter is 1.78m.

Cylinder D: h = 5

10 = πr²h

10 = πr²(5)

2 = πr² Area of the base is 2m².

r = √ (2/π)

r = 0.80 Radius is 0.8m.

d = 2r = 0.80*2 = 1.6 Diameter is 1.6m.

The answers are reasonable if the answer is close to 10 when you substitute the rounded numbers back into the formula and solve.

There are infinite possibilities because any numbers when used in the formula equates to 10 are possible. The height/radius can be any decimal number, which would make the other dimensions change.

PROBLEM B

Follow similar steps if you know the diameter of a cylinder. Use the same formula V = πr²h.

We need the radius, which is half the diameter. r = d/2 = 10/2 = 5

Choose a random number for volume that divides easily by 25.
Substitute "V" and "r²" (r² = 25).
Isolate "h".
The area of the base is 78.54 cm² every time (A = πr²).

Cylinder A: V = 100

100 = π25h

4 = πh

h = 1.27 The height is 1.27m.

Cylinder B: V = 200

200 = π25h

8 = πh

h = 2.55 The height is 2.55m.

Cylinder C: V = 75

75 = π25h

3 = πh

h = 0.95 The height is 0.95m.

Cylinder D: V = 125

125 = π25h

5 = πh

h = 1.59 The height is 1.59m.

The answers are reasonable if I can substitute two rounded values into the formula and get a number close to the third. The height is also a decimal number which occurs because of pi.

6 0

2 years ago

Please Help Me With This file Below

Advocard [28]

The probability of Julia picking 49 is 1/100 ( one number out of 100)

The probability of Shelly picking 49 is also 1/100 ( one number out of 100)

The probability of both picking the same number is

1/100 x 1/100 = 2/100 = 1/50 = 0.02 = 2%

5 0

2 years ago

Help please. i’m cluelesssss

Triss [41]

9514 1404 393

Answer:

G (-2, -3) is in the solution set

Step-by-step explanation:

Finding the solution set

You are given the boundary lines for the inequalities, but the graph does not show the solution set.

The line for inequality y < -2x -4 is the one with negative slope that extends from upper left to lower right. The relation of y to the comparison symbol is ...

y <

indicating that y-values in the solution set will be less than those on the line. The line itself is NOT included in the solution set. That is, "shading" will be below and left of the line.

__

The line for inequality 2x - 4y ≤ 8 is the one with positive slope. Considering the variable with the positive coefficient, its relation to the comparison symbol is ...

x ≤

indicating that x-values in the solution set will be less than (or equal to) those on the line. The line IS included in the solution set. Shading will be above and left of the line with positive slope.

Then the doubly-shaded area is the quadrant at the left side of the X where the lines cross. The lower boundary of that is included in the set, while the upper boundary is not.

__

Considering the points

Now that you know the location of the solution set, you can decide whether any given point is in it, or not.

Plotting the points, you find that F and G are on the boundary lines, and H and J are outside the solution set. Point F(-2, 0) is on the upper boundary line, so is not in the solution set, either.

The point listed in choice G, (-2, -3) is in the solution sets of both inequalities.

4 0

1 year ago

Riley wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 4.5% and t

Volgvan

The bank that offers compound interest should get Riley more money.

let's assume he puts 10,000 in each account, and he is saving for 10 years.

the account that gives him simple interest will give him .045 * 10,000 * 10 = 4500 in interest, which gives him a total of 14,500 at the end of 10 years.

the account that gives him annual compound interest will give him 10,000 * 1.045 ^ 10 = 15,529.69422 at the end of the 10 years.

the difference is that he is earning interest on his interest in the annual compound account, while he is only earning interest on his principal in the simple interest account.

Hope this helps. Good luck !!

5 0

2 years ago

Please answer as soon as possible just answer with a b or c thanks

riadik2000 [5.3K]

Answer:

The answer to the question is a

5 0

2 years ago