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zimovet [89]
2 years ago
10

Drag and drop an answer to each box to correctly complete the explanation for deriving the formula for the volume of a sphere.

Mathematics
2 answers:
Advocard [28]2 years ago
5 0
The volume of a sphere is given by:

V= \frac{4}{3} \pi r^{3}

So, we need to deduct this equation. We will walk through Calculus on the concept of a solid of revolution that is a solid figure that is obtained by rotating a plane curve around some straight line (the axis of revolution<span>) that lies on the same plane. We know from calculus that:

</span>V=\pi \int_{a}^{b}[f(x)]^{2}dx
<span>
Then, according to the concept of solid of revolution we are going to rotate a circumference shown in the figure, then:

</span>x^{2}+y^{2}=r^{2}
<span>
Isolationg y:

</span>y= \sqrt{r^{2}-x^{2}}<span>

So,

</span>f(x)=y=\sqrt{r^{2}-x^{2}}<span>

</span>V=\pi \int_{a}^{b}[\sqrt{r^{2}-x^{2}}]^{2}dx
<span>
</span>V=\pi \int_{a}^{b}(r^{2}-x^{2})dx<span>

being -r and r the limits of this integral. 

</span>V=\pi \int_{-r}^{r}(r^{2}-x^{2})dx
<span>
Solving:

</span>V=\pi[r^{2}x-\frac{x^{3}}{3}]\right|_{-r}^{r}

Finally:
<span>
</span>V=\pi(r^{3}-\frac{r^{3}}{3})-\pi(-r^{3}+\frac{r^{3}}{3})= \frac{4}{3} \pi r^{3}<span>
</span><span>
</span>

Vesna [10]2 years ago
5 0

Answer:

idk the answer but its not what that dude said

Step-by-step explanation:

hehe

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According to DeMorgan 's theorem, the complement of W · X + Y · Z is W' + X' · Y' + Z'. Yet both functions are 1 for WXYZ = 1110
sergeinik [125]

Answer:

The parenthesis need to be kept intact while applying the DeMorgan's theorem on the original equation to find the compliment because otherwise it will introduce an error in the answer.

Step-by-step explanation:

According to DeMorgan's Theorem:

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Note that it is important to keep the parenthesis intact while applying the DeMorgan's theorem.

For the original function:

(W . X + Y . Z)'

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= (1 + 0) = 1

For the compliment:

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=(1' + 1') . (1' + 0')

=(0 + 0) . (0 + 1)

=0 . 1 = 0

Both functions are not 1 for the same input if we solve while keeping the parenthesis intact because that allows us to solve the operation inside the parenthesis first and then move on to the operator outside it.

Without the parenthesis the compliment equation looks like this:

W' + X' . Y' + Z'

1' + 1' . 1' + 0'

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Here, the 'AND' operation will be considered first before the 'OR', resulting in 1 as the final answer.

Therefore, it is important to keep the parenthesis intact while applying DeMorgan's Theorem on the original equation or else it would produce an erroneous result.

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Joe wants to paint the outside of a wooden box. He needs to find the surface area of the box
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4*2=8

4*1.5=6

2*1.5=3

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16+12+6=34 ft

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2 years ago
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Please help. I am getting in trouble so please try to be correct...
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Answer: The answer is A 17in2

Step-by-step explanation:

In the question it states that the triangles are congruent (both the same).

  first I found the area of the top orange triangle.

the formula to find the area of a triangle is \frac{1}{2} bh (base times Height).

so I did  \frac{1}{2} 3.23* 5.12  which gave me 8.27.

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the question also stated to find the APPROXIMATE area (close to the actual, but not completely accurate or exact.)

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NNADVOKAT [17]

Answer:

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If It Helped u do mark me as brainliest

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Answer:

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Step-by-step explanation:

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