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3 years ago

Does anyone know the answer.

Mathematics

1 answer:

leonid [27]3 years ago

5 0

Answer:

The volume is approx. 170 cubic inches.

Step-by-step explanation:

The total volume is the sum of the volume of the cylinder and half the volume of a sphere with the given diameter.

Cylinder:

(volume) = 2 * (disc area) * (height)

$V_C=\pi r^2 h = \pi \frac{d^2}{4}h=3.14\cdot 6.25\cdot 7=137.4 \,\,in.^3$

Hemisphere:

$V_H=\frac{1}{2}\cdot\frac{4}{3}\pi r^3=\frac{2}{3}\cdot 3.14\cdot 2.5^3=32.7\,\,in^3\\$

Total:

137.4+32.7 = approx. 170 cubic inches

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If c(x) = 4x - 2 and d(x) = x + 5x what is (c×d)(x)?

g100num [7]

Answer:

24x^2 - 12x

Step-by-step explanation:

C=4x -2

D=x + 5x

(4x - 2) * (x +5x)

4x^2 + 20x^2 - 2x - 10x

=24x^2 - 12x

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2 years ago

Question 1

Svetach [21]

The answer to the question is $5.40

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3 years ago

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13. A smoothie shop has 40 stores, and 55% of the stores are in

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Answer:

You could answer this two ways.

Step-by-step explanation:

Method 1: Set up proportion

x/40=55/100

Cross-multiply and you will get..

2200=100x

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Method 2: Use decimals

As we saw in the first method, 55 percent is equal to 55/100. 55/100 is equal to 0.55.

You can multiply 0.55 and 40 to get the answer as well.

0.55 times 40 is 22.

Hope this explanation helped! ☺️

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3 years ago

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INSERT TWO RATIONAL NUMBERS BETWEEN 2 AND 3. How to find them?

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There are an infinite number of them.
Here are a few:

2.1
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2.3
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etc.

How to find them:

You probably never heard this before, but I'll bet
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ANY number that you can write down on paper completely, using digits
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3 years ago

Given that 'n' is a natural number. Prove that the equation below is true using mathematical induction.

LenaWriter [7]

<h3>To ProvE :- </h3>

1 + 3 + 5 + ..... + (2n - 1) = n²

Method :-

If P(n) is a statement such that ,

P(n) is true for n = 1
P(n) is true for n = k + 1 , when it's true for n = k ( k is a natural number ) , then the statement is true for all natural numbers .

$\sf\to \textsf{ Let P(n) : 1 + 3 + 5 + $\dots$ +(2n-1) = n$^{\sf 2}$ }$

Step 1 : Put n = 1 :-

$\sf\longrightarrow LHS = \boxed{\sf 1 } \\$

$\sf\longrightarrow RHS = n^2 = 1^2 = \boxed{\sf 1 }$

Step 2 : Assume that P(n) is true for n = k :-

$\sf\longrightarrow 1 + 3 + 5 + \dots + (2k - 1 ) = k^2$

Add (2k +1) to both sides .

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1)=k^2+(2k+1)$

RHS is in the form of ( a + b)² = a²+b²+2ab .

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1)= (k +1)^2$

Adding and subtracting 1 to LHS .

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+1) + 1 -1 = (k +1)^2 \\$

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+(2k+2) - 1 = (k +1)^2$

Take out 2 as common .

$\sf\longrightarrow 1 + 3+5+\dots+(2k-1)+\{2(k+1)-1\}= (k +1)^2$

P(n) is true for n = k + 1 .

Hence by the principal of Mathematical Induction we can say that P(n) is true for all natural numbers 'n' .

**Edits are welcomed**

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