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Andreyy89
3 years ago
10

A fruit bowl is shaped like half of a sphere. The radius of the bowl is 15 cm.

Mathematics
1 answer:
vivado [14]3 years ago
6 0

Answer:

the volume is 14137.17

Step-by-step explanation:

V=(4/3)πr³

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What is the value of 4*(-1+2-3+4-3+6-7+....+100) Show your work. [Pls help I am really drowning in work. 50 points + brainliest
KengaRu [80]

Answer:

200

Step-by-step explanation:

We have:

4(-1+2-3+4-5+6-7...+100)

We can rearrange the numbers to obtain:

4((-1-3-5-7-...-99)+(2+4+6...+100))

From the left, we can factor out a negative. So:

4(-(1+3+5+7+...+99)+(2+4+6...+100))

In other words, we want to find the sum of all the odd numbers from 1 to 99.

And the sum of all the even numbers from 2 to 100.

Let's do each one individually:

Odd Terms:

We have:

(1+3+5+7+...+99)

We can use the arithmetic series formula, where:

S=\frac{k}{2}(a+x_k)

Where k is the number of terms, a is the first term, and x_k is the last term.

Since it's all the odd numbers between 1 and 99, there are 50 terms.

Our first term is 1 and our last term is 99. So, the sum of all the odd terms are:

S=\frac{50}{2}(1+99})

Divide the fraction. Add within the parentheses:

S=25(100)

Multiply:

S=2500

So, the sum of all the odd terms is 2500.

Even Terms:

We have:

(2+4+6+...+100)

Again, we can use the above formula.

Our first term is 2, last term is 100. And since it's from 2-100, we have 50 even terms. So:

S=\frac{50}{2}(2+100)

Divide and add:

S=25(102)

Multiply:

S=2550

We originally had:

4(-(1+3+5+7+...+99)+(2+4+6...+100))

Substitute them for their respective sums:

4(-(2500)+2550)

Multiply:

4(-2500+2550)

Add:

=4(50)

Multiply:

=200

So, the sum of our sequence is 200.

And we're done!

Note: I just found a <em>way</em> easier way to do this. We have:

4\cdot(-1+2-3+4-5+6-7+...+100)

Let's group every two terms together. So:

=4((-1+2)+(-3+4)+(-5+6)...+(-99+100))

We can see that they each sum to 1:

=4((1)+(1)+(1)+...+(1))

Since there are 100 terms, we will have 50 pairs, so 50 times 1. So:

=4(50)

Multiply:

=200

Pick which one you want to use! I will suggest this one though...

Edit: Typo

8 0
3 years ago
Choose the correct description of the graph of the compound inequality : x - 1 &lt; 12 or 2x &gt; 30.
sveta [45]
I think it’s d to be honest I also may be wrong.
7 0
3 years ago
Please guys I keep getting this question wrong What letter is located at approximately right answers only
liubo4ka [24]
Answer:
B) F
You put √22 in a calculator and it gives you ≈ 4.69
4 0
2 years ago
What is the invers function of f(x)=(n+1)^3?
zimovet [89]

Answer:

f^{-1}(x)=\sqrt[3]{x}-1

Step-by-step explanation:

f(x)=(x+1)^3\\\\y=(x+1)^3\\\\x=(y+1)^3\\\\\sqrt[3]{x}=y+1\\\\y=\sqrt[3]{x}-1\\ \\f^{-1}(x)=\sqrt[3]{x}-1

Graphing both inverses, they will be symmetrical about the line y=x.

8 0
2 years ago
Use the replacement set {3, 4, 9} to find the solution of the equation below.<br> 3n−18=9
Mrac [35]

Answer:

n=9

Step-by-step explanation:

3n-18=9

3n+18= +18

3n=27

3(9)=27

n=9

5 0
3 years ago
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