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vovangra [49]
2 years ago
15

What is the approximate volume of a cylinder with a radius of 3 ft and a height of 4 ft?

Mathematics
1 answer:
Lunna [17]2 years ago
5 0
V≈113.1 ft³ is the answer
You might be interested in
Fine length of BC on the following photo.
MrMuchimi

Answer:

BC=4\sqrt{5}\ units

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

AC^2=AD^2+DC^2

substitute the given values

AC^2=16^2+8^2

AC^2=320

AC=\sqrt{320}\ units

simplify

AC=8\sqrt{5}\ units

step 2

In the right triangle ACD

Find the cosine of angle CAD

cos(\angle CAD)=\frac{AD}{AC}

substitute the given values

cos(\angle CAD)=\frac{16}{8\sqrt{5}}

cos(\angle CAD)=\frac{2}{\sqrt{5}} ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

cos(\angle BAC)=\frac{AC}{AB}

substitute the given values

cos(\angle BAC)=\frac{8\sqrt{5}}{16+x} ----> equation B

step 4

Find the value of x

In this problem

\angle CAD=\angle BAC ----> is the same angle

so

equate equation A and equation B

\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}

solve for x

Multiply in cross

(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units

DB=4\ units

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

BC^2=DC^2+DB^2

substitute the given values

BC^2=8^2+4^2

BC^2=80

BC=\sqrt{80}\ units

simplify

BC=4\sqrt{5}\ units

7 0
2 years ago
James estimate the product of 48 and 53 is that reasonable
Debora [2.8K]
50 x 50= 2500.............
8 0
2 years ago
Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note
Viktor [21]

a. Recall that

\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C

For |x|, we have

\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n

By integrating both sides, we get

\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}

If x=0, then

\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0

so that

\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}

We can shift the index to simplify the sum slightly.

\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n

b. The power series for x\ln(1-x) can be obtained simply by multiplying both sides of the series above by x.

\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n

c. We have

\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)

\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}

4 0
3 years ago
a bag contains Stephanie five marbles, some red some blue. The ratio of red marbles to blue ones is 3:2. how many red marbles ar
Nikolay [14]

Answer:

There are 3 red marbles.

Step-by-step explanation:

The ratio of red marbles to blue marbles is 3:2, so for every two blue marbles there are three red marbles. This means that there are three red marbles for every four marbles in the bag. Therefore, if there are five marbles in the bag, there must be three red marbles and two blue marbles.

7 0
2 years ago
I bought my flat last year for £40,000. The value of my flat increased by 12% in September and then by a further 10%in January t
Leya [2.2K]
The answer is: <span>40,000(1.12)(1.10)

Or 4 more understanding: 12% of £40000
</span>1%= 400, therefore, 12%= 4800.
In January, the value was £44800. 
10% of this is £448.
Add £448 to £44800, giving you £45, 248
7 0
2 years ago
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