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3 years ago

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Mathematics

1 answer:

9966 [12]3 years ago

6 0

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.

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Question 2 of 5

AlekseyPX

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is $f(n)=f(n-1)+d, f(1)=a,n\geq 2$ and the explicit formula is $f(n)=a+(n-1)d$ , where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is $f(n)=rf(n-1), f(1)=a,n\geq 2$ and the explicit formula is $f(n)=ar^{n-1}$ , where a is the first term and r is the common ratio.

The first recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+5$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(5)$

$f(n)=5+5(n-1)$

Therefore, the correct option is A, i.e., $f(n)=5+5(n-1)$ .

The second recursive formula is:

$f(1)=5$

$f(n)=3f(n-1)$ for $n\geq 2$ .

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

$f(n)=5(3)^{n-1}$

Therefore, the correct option is F, i.e., $f(n)=5(3)^{n-1}$ .

The third recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+3$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(3)$

$f(n)=5+3(n-1)$

Therefore, the correct option is D, i.e., $f(n)=5+3(n-1)$ .

6 0

3 years ago

Read 2 more answers

Kristin is 20 miles behind a truck that is driving 50 miles per hour. How long will it take her to catch up to the truck? How fa

creativ13 [48]

t = 20/(r-50)t=20/r-50 hours

8 0

3 years ago

Plz help!!

inysia [295]

1. 5564÷91
I know that 9 * 6 = 56
5564 rounds to 5600
91 rounds to 9
Since 56/9 = 6, then 5600/90 is the same as 560/9 = 60
The estimate is 60

2. 5391÷25
5391 sounds to 5400
25 is 1/4 of 100.
That means when you divide by 25, you can divide by 100 and multiply by 4.
5400/100 = 54
54 * 4 = 216
Estimate: 216

3. explain how to estimate 498÷12
48/12 = 4
498 is little more than 480, so 498/12 is little more than 40

4. which is the closest estimate for 2130÷ 33
A.7 B.17 C.70 D.700

2130/33
Round off the numerator and denominator to
2100/30
Reduce the fraction
210/3
Since I know that 21/3 = 7, then 210/3 = 70
Estimate: 70

8 0

3 years ago

Coleman uses his graphing calculator to find all of the solutions to the equation shown below.

Phoenix [80]

Answer:

The correct option is;

D. x = -1.38 and 0.82

Please find attached the combined function chart

Step-by-step explanation:

The given equation is x³ + 3 = -x⁴ + 4

Plotting the equation using Excel, we have;

f(x) = x³ + 3, h(x) = -x⁴ + 4

x f(x) h(x)

-1.4 0.256 0.1584

-1.39 0.314381 0.26699

-1.38 0.371928 0.373261

-1.37 0.428647 0.477246

-1.36 0.484544 0.57898

Which shows an intersection at the point around -1.38

x f(x) h(x)

0.77 3.456533 3.64847

0.78 3.474552 3.629849

0.79 3.493039 3.610499

0.8 3.512 3.5904

0.81 3.531441 3.569533

0.82 3.551368 3.547878

0.83 3.571787 3.525417

Which shows the intersection point around 0.82

Therefore, the correct option is x = -1.38 and 0.82

From the graphing calculator the intersection point is given as

x = -1.3802775691 and 0.81917251339.

8 0

3 years ago

At a local election there were two propositions on the ballot, R and S. Twice as many voters voted "yes" for R as for S. If the

Over [174]

Answer:

c. 130

Step-by-step explanation:

Let call B the quantity of voters who voted yes for both propositions.

From the question we know that twice as many voters voted "yes" for R as for S, that can be written as the following equation:

R+B=2(S+B)

Where R is the number who voted "yes" for R but "no2 for S and S is the number who voted "yes" for S but "no" for R.

Replacing R by 750 and S by 310 and solving for B, we get:

750+B=2(310+B)

750+B=620+2B

2B-B=750-620

B=130

So, 130 voters voted yes for both propositions

7 0

3 years ago