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2 years ago

Find the volume of the composite solid. Round your answer to the nearest tenth.

Mathematics

2 answers:

GalinKa [24]2 years ago

6 0

The answer is 1474ft

vazorg [7]2 years ago

5 0

Answer:

The volume of the composite solid is $1206.4(ft^{3})$

Step-by-step explanation:

The composite solid is formed by a cone and a cylinder.

The cone has 16 ft of diameter and its height is 6 ft. Also, its radius is 8 ft (half of the diameter).

The cylinder has 16 ft of diameter and its height is 4 ft. Also, its radius is 8 ft.

Given a cone of radius ''R'' and height ''h'' we can calculate its volume as :

$V(cone)=\pi .R^{2}.\frac{1}{3}.h$ (I)

Given a cylinder of radius ''R'' and height ''h'' we can calculate its volume as :

$V(cylinder)=\pi .R^{2}.h$ (II)

We can calculate the volume of the composite solid as the sum of the volume from the cone and the cylinder ⇒

$V(CompositeSolid)=V(cone)+V(cylinder)$

If we apply (I) and (II) ⇒

$V(CompositeSolid)=\pi .(8ft)^{2}.(\frac{1}{3}).(6ft)+\pi .(8ft)^{2}.(4ft)$

$V(CompositeSolid)=128\pi (ft^{3})+256\pi (ft^{3})$

$V(CompositeSolid)=384\pi (ft^{3})$

$V(CompositeSolid)=1206.4(ft^{3})$

We find that the volume of the composite solid rounded to the nearest tenth is $1206.4(ft^{3})$

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B) Let g(x) =x/2sqrt(36-x^2)+18sin^-1(x/6)<br><br> Find g'(x) =

jolli1 [7]

I suppose you mean

$g(x) = \dfrac x{2\sqrt{36-x^2}} + 18\sin^{-1}\left(\dfrac x6\right)$

Differentiate one term at a time.

Rewrite the first term as

$\dfrac x{2\sqrt{36-x^2}} = \dfrac12 x(36-x^2)^{-1/2}$

Then the product rule says

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 x' (36-x^2)^{-1/2} + \dfrac12 x \left((36-x^2)^{-1/2}\right)'$

Then with the power and chain rules,

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12\left(-\dfrac12\right) x (36-x^2)^{-3/2}(36-x^2)' \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} - \dfrac14 x (36-x^2)^{-3/2} (-2x) \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12 x^2 (36-x^2)^{-3/2}$

Simplify this a bit by factoring out $\frac12 (36-x^2)^{-3/2}$ :

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-3/2} \left((36-x^2) + x^2\right) = 18 (36-x^2)^{-3/2}$

For the second term, recall that

$\left(\sin^{-1}(x)\right)' = \dfrac1{\sqrt{1-x^2}}$

Then by the chain rule,

$\left(18\sin^{-1}\left(\dfrac x6\right)\right)' = 18 \left(\sin^{-1}\left(\dfrac x6\right)\right)' \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac x6\right)'}{\sqrt{1 - \left(\frac x6\right)^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac16\right)}{\sqrt{1 - \frac{x^2}{36}}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{3}{\frac16\sqrt{36 - x^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18}{\sqrt{36 - x^2}} = 18 (36-x^2)^{-1/2}$

So we have

$g'(x) = 18 (36-x^2)^{-3/2} + 18 (36-x^2)^{-1/2}$

and we can simplify this by factoring out $18(36-x^2)^{-3/2}$ to end up with

$g'(x) = 18(36-x^2)^{-3/2} \left(1 + (36-x^2)\right) = \boxed{18 (36 - x^2)^{-3/2} (37-x^2)}$

5 0

2 years ago

The product of two positive integers is 176. One number is 5 more than the other. Find the smaller number.

svlad2 [7]

Hello from MrBillDoesMath!

Answer:

Discussion:

Let "n" be the smaller number. Then

n * (n+5) = 176.

My first reaction to this problem was to factor 176 in my head. That's 176 = 16 * 11 and 16 is 5 more than 11. So that's the solution!.... Now let's solve it using the brute force approach:

n(n+5) = 176 =>

n^2 + 5n - 176 = 0 => use the quadratic formula

n = ( -5 +\- sqrt( 5^2 - 4(1)(-176)) ) /2

= ( -5 +\- sqrt( 25 + 704) )/ 2

= ( -5 +\- sqrt (729) ) /2 => as sqrt(729) = 27

= (-5 +\- 27) / 2 =>

= (-5 + 27)/2 or ( -5 -27)/2 =>

= 22/2 or -32/2 =>

= 11 or -16

But -16 is not allowed as the question wants a positive value.

Thank you,

MrB

4 0

3 years ago

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Meg found one treasure at − 3 4 foot. Which of these location are higher than − 3 4 foot? Check all that apply. Negative StartFr

Neporo4naja [7]

Answer:

$\frac{-1}{4}$ and $\frac{-5}{8}$ are the locations higher than $\frac{-3}{4}$ foot

Step-by-step explanation:

We are given that Meg found one treasure at $\frac{-3}{4}$ foot

We are supposed to find Which of these location are higher than $\frac{-3}{4}$ foot?

i) $-\frac{7}{8}$

So, this location is not higher than $\frac{-3}{4}$ foot

ii) $-\frac{1}{4}$

So, $-\frac{1}{4}>\frac{-3}{4}$

So, this location is higher than $\frac{-3}{4}$ foot

iii) - 1 foot

$-1 < \frac{-3}{4}$

So,this location is not higher than $\frac{-3}{4}$ foot

iv)-2 feet

So,this location is not higher than $\frac{-3}{4}$ foot

v) $\frac{-5}{8}$

So, this location is higher than $\frac{-3}{4}$ foot

5 0

3 years ago

Which of the following are exact numbers?

Mademuasel [1]

Answer:

Explanation with the help of discrete variables and continuous variables.

Step-by-step explanation:

We have to tell that which of the following can be an exact number.

This can be done with the approach of discrete and continuous variables.

Discrete variables are the variables that are countable and cannot be expressed in decimal form. They are point estimated.

Continuous variable are the variable that are estimated with the help of an interval. Their values can be expressed with the help of a decimal expansion. They are not countable.

a) Mass of a paper clip, Surface are of dime, Inches in a mile, Ounces in pound, microseconds in a week

Since all mass, area, weight(ounces), time, length(inches) are continuous variable, they can be estimated with the help of an interval. Thus, they can have exact number but not always.

b) Number of pages in a worksheet

Since this is a discrete quantity and it is countable. Thus, it will always have a point estimation and are exact numbers always.

4 0

3 years ago

There are 10 boys and 12 girls in the tennis club. The coach wants to select two players to practice first. Which statements are

Sidana [21]

Since there are 22 participants all in all. The possible combinations of the two picked for practice first is,
22C2 = 231
The probability of picking one from each gender will be solved through the calculation below.
(10C1)x(12C1) / 231 = 40/77
In percentage, the answer would be approximately 52%. Thus, the answer is the first choice.

6 0

3 years ago

Read 2 more answers