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3 years ago

13

How much water is in the cylinder ?

1 answer:

Mariulka [41]3 years ago

5 0

Answer:

339π in³

Step-by-step explanation:

The amount of water is the difference between the volume of the cylinder and the volume of the ball. The appropriate volume formulas are ...

cylinder V = πr²h

sphere V = (4/3)πr³

For the given numbers, the volumes are ...

cylinder V = π(5 in)²(15 in) = 375π in³

sphere V = (4/3)π(3 in)³ = 36π in³

The water volume is the difference of these ...

water volume = cylinder V - sphere V

= 375π in³ - 36π in³ = 339π in³

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A 20-year loan of 1000 is repaid with payments at the end of each year. Each of the first ten payments equals 150% of the amount

Alja [10]

Answer:

$x = 97$

Step-by-step explanation:

Given

$t = 20$ --- time (years)

$A =1000$ --- amount

$r = 10\%$ --- rate of interest

Required

The last 10 payments (x)

First, calculate the end of year 1 payment

$y_1(end) = 10\% * 1000 * 150\%$

$y_1(end) = 150$

Amount at end of year 1

$A_1=A - y_1(end) - r * A$

$A_1=1000 - (150 - 10\% * 1000)$

$A_1 =1000 - (150- 100)$

$A_1 =950$

Rewrite as:

$A_1 = 0.95 * 1000^1$

Next, calculate the end of year 1 payment

$y_2(end) = 10\% * 950 * 150\%$

$y_2(end) = 142.5$

Amount at end of year 2

$A_2=A_1 - (y_2(end) - r * A_1)$

$A_2=950 - (142.5 - 10\%*950)$

$A_2 = 902.5$

Rewrite as:

$A_2 = 0.95 * 1000^2$

We have been able to create a pattern:

$A_1 = 1000 * 0.95^1 = 950$

$A_2 = 1000 * 0.95^2 = 902.5$

So, the payment till the end of the 10th year is:

$A_{10} = 1000*0.95^{10}$

$A_{10} = 598.74$

To calculate X (the last 10 payments), we make use of the following geometric series:

$Amount = \sum\limits^{9}_{n=0} x * (1 + r)^n$

$Amount = \sum\limits^{9}_{n=0} x * (1 + 10\%)^n$

$Amount = \sum\limits^{9}_{n=0} x * (1 + 0.10)^n$

$Amount = \sum\limits^{9}_{n=0} x * (1.10)^n$

The amount to be paid is:

$Amount = A_{10}*(1 + r)^{10}$ --- i.e. amount at the end of the 10th year * rate of 10 years

$Amount = 1000 * 0.95^{10} * (1+r)^{10}$

So, we have:

$Amount = \sum\limits^{9}_{n=0} x * (1.10)^n$

$\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+r)^{10}$

$\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+10\%)^{10}$

$\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+0.10)^{10}$

$\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1.10)^{10}$

The geometric sum can be rewritten using the following formula:

$S_n = \sum\limits^{9}_{n=0} x * (1.10)^n$

$S_n =\frac{a(r^n - 1)}{r -1}$

In this case:

$a = x$

$r = 1.10$

$n =10$

So, we have:

$\frac{x(r^{10} - 1)}{r -1} = \sum\limits^{9}_{n=0} x * (1.10)^n$

$\frac{x((1.10)^{10} - 1)}{1.10 -1} = \sum\limits^{9}_{n=0} x * (1.10)^n$

$\frac{x((1.10)^{10} - 1)}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n$

$x * \frac{1.10^{10} - 1}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n$

So, the equation becomes:

$x * \frac{1.10^{10} - 1}{0.10} = 1000 * 0.95^{10} * (1.10)^{10}$

Solve for x

$x = \frac{1000 * 0.95^{10} * 1.10^{10} * 0.10}{1.10^{10} - 1}$

$x = 97.44$

Approximate

$x = 97$

4 0

3 years ago

This is a two-part question: A 12-pack of bottled mineral water sells for $3.85. For the following, state whether to use multipl

AlekseyPX

Answer:

division

Step-by-step explanation:

12-pack of bottled mineral water sells for $3.85

The cost of one bottle of water= $3.85/12= $0.32

4 0

3 years ago

The ratio of length and breadth of a rectangular ground is 4:3 and the breadth is 75m. Find the length of the ground.

Crank

Answer:

the answer is 100m

Step-by-step explanation:

let 4:3 be 4x and 3x respectively

3x=75m

x=75÷3

x=25

Then,

4x=4*25

=100m

7 0

3 years ago

Just need help with 2 and 4 :)

vesna_86 [32]

2.)

0 = 6x + 3y +9
-3y = 6x + 3y - 3y +9

$\frac{ - 3y}{ - 3} = \frac{6x + 9}{ - 3} \\ \\ y = - 2x - 3$
By isolating y we now have the equation in slope intercept form:
$y = mx + b$

Where m = slope and b = y- intercept. Therefore, the slope is -2 and the y - intercept is -3.

4.)

Similarly, #4 is already in slope intercept form so we can solve it by inspection. So for #4 the slope is -1 and the y - intercept is 2.

7 0

3 years ago

The Jones family plans to borrow $22,000 for 15 years. If the interest rate is 4.25%, how much will the family pay in interest ?

Umnica [9.8K]

Answer:

344025

Step-by-step explanation:

20,000 x decimal multiplier

decimal multiplier = 1.0425

20,000 x 1.0425 = 20850

20850 x 15 = 344025

4 0

4 years ago

Read 2 more answers