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3 years ago

What is the volume of a hemisphere with a radius of 9.2 cm, rounded to the nearest tenth of a cubic centimeter?

Mathematics

1 answer:

NARA [144]3 years ago

6 0

Answer:

volume of the hemisphere ≈1577.5 cm³

Step-by-step explanation:

To find the formula for calculating the volume of a hemisphere, we will follow the steps below:

write the formula for calculating the volume of a hemisphere.

volume of a hemisphere = volume of a sphere ÷2

= $\frac{4}{3}$ πr³ ÷ 2

= $\frac{2}{3}$ πr³

WHERE r is the radius

from the question given, radius= 9.2 cm

π is a constant and is ≈ 3.14

we can now proceed to insert the values into the equation

volume of a hemisphere = $\frac{2}{3}$ πr³

= $\frac{2}{3}$ × 3.14 ×9.2³

= $\frac{2}{3}$ × 3.14 ×753.571

≈1577.5 cm³ to the nearest tenth of cubic centimeter

volume of the hemisphere ≈1577.5 cm³

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Your time in a 5k race. Is this discrete or continuous? Write a reasonable

Aneli [31]

Answer:

For intermediate runners (generally those who run 10 – 20 miles per week) an average 5K time would be around 20-25 minutes, which is an average speed of around 7-9mph over the course.

Step-by-step explanation:

https://www.ukfitnessevents.co.uk/event/5k-runs/average-5k-time

3 0

3 years ago

Please help me. Noura is redecorating her house. She needs to work out the area of the wall around her triangular window in orde

Vinvika [58]

Answer:

a. 277.3 m²

b. $307.86

Step-by-step explanation:

a. Area of the wall to be painted = area of rectangle - area of triangle

= L × W + ½×a×b×sin θ

L = 17 m

W = 14 m

a = 8.7 m

b = 9.5 m

θ = 72°

Plug in the values into the equation

Area of the wall = (17×14) + (½*8.7×9.5×sin 72)

Area of the wall = 238 + 39.3024105

Area of the wall to paint ≈ 277.3 m²

b. 20 liters of paint of 1 container cost $21.99

If 1 liter of paint covers 1m², therefore,

277.3 m² will need = 277.3 × 1 = 277.3 liters of paint.

20 liters = 1 container of paint

277.3 liters = 277.3/20 = 13.865 ≈ 14 containers

1 container = $21.99

14 containers = 21.99 × 14 = $307.86

8 0

3 years ago

2,17,82,257,626,1297 next one please ?

In-s [12.5K]

The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule $n^4+1$ . The next number would then be fourth power of 7 plus 1, or 2402.

And the harder way: Denote the n-th term in this sequence by $a_n$ , and denote the given sequence by $\{a_n\}_{n\ge1}$ .

Let $b_n$ denote the n-th term in the sequence of forward differences of $\{a_n\}$ , defined by

$b_n=a_{n+1}-a_n$

for n ≥ 1. That is, $\{b_n\}$ is the sequence with

$b_1=a_2-a_1=17-2=15$

$b_2=a_3-a_2=82-17=65$

$b_3=a_4-a_3=175$

$b_4=a_5-a_4=369$

$b_5=a_6-a_5=671$

and so on.

Next, let $c_n$ denote the n-th term of the differences of $\{b_n\}$ , i.e. for n ≥ 1,

$c_n=b_{n+1}-b_n$

so that

$c_1=b_2-b_1=65-15=50$

$c_2=110$

$c_3=194$

$c_4=302$

etc.

Again: let $d_n$ denote the n-th difference of $\{c_n\}$ :

$d_n=c_{n+1}-c_n$

$d_1=c_2-c_1=60$

$d_2=84$

$d_3=108$

etc.

One more time: let $e_n$ denote the n-th difference of $\{d_n\}$ :

$e_n=d_{n+1}-d_n$

$e_1=d_2-d_1=24$

$e_2=24$

etc.

The fact that these last differences are constant is a good sign that $e_n=24$ for all n ≥ 1. Assuming this, we would see that $\{d_n\}$ is an arithmetic sequence given recursively by

$\begin{cases}d_1=60\\d_{n+1}=d_n+24&\text{for }n>1\end{cases}$

and we can easily find the explicit rule:

$d_2=d_1+24$

$d_3=d_2+24=d_1+24\cdot2$

$d_4=d_3+24=d_1+24\cdot3$

and so on, up to

$d_n=d_1+24(n-1)$

$d_n=24n+36$

Use the same strategy to find a closed form for $\{c_n\}$ , then for $\{b_n\}$ , and finally $\{a_n\}$ .

$\begin{cases}c_1=50\\c_{n+1}=c_n+24n+36&\text{for }n>1\end{cases}$

$c_2=c_1+24\cdot1+36$

$c_3=c_2+24\cdot2+36=c_1+24(1+2)+36\cdot2$

$c_4=c_3+24\cdot3+36=c_1+24(1+2+3)+36\cdot3$

and so on, up to

$c_n=c_1+24(1+2+3+\cdots+(n-1))+36(n-1)$

Recall the formula for the sum of consecutive integers:

$1+2+3+\cdots+n=\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2$

$\implies c_n=c_1+\dfrac{24(n-1)n}2+36(n-1)$

$\implies c_n=12n^2+24n+14$

$\begin{cases}b_1=15\\b_{n+1}=b_n+12n^2+24n+14&\text{for }n>1\end{cases}$

$b_2=b_1+12\cdot1^2+24\cdot1+14$

$b_3=b_2+12\cdot2^2+24\cdot2+14=b_1+12(1^2+2^2)+24(1+2)+14\cdot2$

$b_4=b_3+12\cdot3^2+24\cdot3+14=b_1+12(1^2+2^2+3^2)+24(1+2+3)+14\cdot3$

and so on, up to

$b_n=b_1+12(1^2+2^2+3^2+\cdots+(n-1)^2)+24(1+2+3+\cdots+(n-1))+14(n-1)$

Recall the formula for the sum of squares of consecutive integers:

$1^2+2^2+3^2+\cdots+n^2=\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}6$

$\implies b_n=15+\dfrac{12(n-1)n(2(n-1)+1)}6+\dfrac{24(n-1)n}2+14(n-1)$

$\implies b_n=4n^3+6n^2+4n+1$

$\begin{cases}a_1=2\\a_{n+1}=a_n+4n^3+6n^2+4n+1&\text{for }n>1\end{cases}$

$a_2=a_1+4\cdot1^3+6\cdot1^2+4\cdot1+1$

$a_3=a_2+4(1^3+2^3)+6(1^2+2^2)+4(1+2)+1\cdot2$

$a_4=a_3+4(1^3+2^3+3^3)+6(1^2+2^2+3^2)+4(1+2+3)+1\cdot3$

$\implies a_n=a_1+4\displaystyle\sum_{k=1}^3k^3+6\sum_{k=1}^3k^2+4\sum_{k=1}^3k+\sum_{k=1}^{n-1}1$

$\displaystyle\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}4$

$\implies a_n=2+\dfrac{4(n-1)^2n^2}4+\dfrac{6(n-1)n(2n)}6+\dfrac{4(n-1)n}2+(n-1)$

$\implies a_n=n^4+1$

4 0

3 years ago

The Mapleton Middle School band has 41 students. Six students play a percussion instrument. What percent of students in the band

Sedaia [141]

Answer:

the percentage of the students in the band that play a percussion instrument is 14.6%

Step-by-step explanation:

The computation of the percentage of the students in the band that play a percussion instrument is as followS;

= number of students played percussion instrument ÷ total number of students

= 6 students ÷ 41 students

= 14.6%

Hence, the percentage of the students in the band that play a percussion instrument is 14.6%

The same is relevant

3 0

3 years ago

The country of benin in west Africa has a population of 9.05 million people. The population is growing at a rate of 3.1% each ye

Oksanka [162]

The function would be the initial plus growth rate * # years

So: f(x) = 9.05 + 0.031(7)
Where x= # years

3 0

2 years ago