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nataly862011 [7]
2 years ago
14

Ms. Lui earned an annual income of 775,000, what is the weekly salary?

Mathematics
1 answer:
jok3333 [9.3K]2 years ago
4 0

Answer:

$14,903.85

Step-by-step explanation:

So, Ms. Lui earns $775,000 each year. To find the weekly salary, we have to divide the annual income by the amount of weeks in a year. There are about 52 weeks in one year. Let's find the weekly salary:

\frac{775000}{52} = 14,903.85

Therefore, Ms. Lui earns $14,903.85 a week.

Hope this helps! If you have questions about my work, please leave them in the comments!

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99 POINT QUESTION, PLUS BRAINLIEST!!!
VladimirAG [237]
First, we have to convert our function (of x) into a function of y (we revolve the curve around the y-axis). So:


y=100-x^2\\\\x^2=100-y\qquad\bold{(1)}\\\\\boxed{x=\sqrt{100-y}}\qquad\bold{(2)} \\\\\\0\leq x\leq10\\\\y=100-0^2=100\qquad\wedge\qquad y=100-10^2=100-100=0\\\\\boxed{0\leq y\leq100}

And the derivative of x:

x'=\left(\sqrt{100-y}\right)'=\Big((100-y)^\frac{1}{2}\Big)'=\dfrac{1}{2}(100-y)^{-\frac{1}{2}}\cdot(100-y)'=\\\\\\=\dfrac{1}{2\sqrt{100-y}}\cdot(-1)=\boxed{-\dfrac{1}{2\sqrt{100-y}}}\qquad\bold{(3)}

Now, we can calculate the area of the surface:

A=2\pi\int\limits_0^{100}\sqrt{100-y}\sqrt{1+\left(-\dfrac{1}{2\sqrt{100-y}}\right)^2}\,\,dy=\\\\\\= 2\pi\int\limits_0^{100}\sqrt{100-y}\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=(\star)

We could calculate this integral (not very hard, but long), or use (1), (2) and (3) to get:

(\star)=2\pi\int\limits_0^{100}1\cdot\sqrt{100-y}\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=\left|\begin{array}{c}1=\dfrac{-2\sqrt{100-y}}{-2\sqrt{100-y}}\end{array}\right|= \\\\\\= 2\pi\int\limits_0^{100}\dfrac{-2\sqrt{100-y}}{-2\sqrt{100-y}}\cdot\sqrt{100-y}\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\,\,dy=\\\\\\ 2\pi\int\limits_0^{100}-2\sqrt{100-y}\cdot\sqrt{100-y}\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\cdot\dfrac{dy}{-2\sqrt{100-y}}=\\\\\\

=2\pi\int\limits_0^{100}-2\big(100-y\big)\cdot\sqrt{1+\dfrac{1}{4(100-y)}}\cdot\left(-\dfrac{1}{2\sqrt{100-y}}\, dy\right)\stackrel{\bold{(1)}\bold{(2)}\bold{(3)}}{=}\\\\\\= \left|\begin{array}{c}x=\sqrt{100-y}\\\\x^2=100-y\\\\dx=-\dfrac{1}{2\sqrt{100-y}}\, \,dy\\\\a=0\implies a'=\sqrt{100-0}=10\\\\b=100\implies b'=\sqrt{100-100}=0\end{array}\right|=\\\\\\= 2\pi\int\limits_{10}^0-2x^2\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx=(\text{swap limits})=\\\\\\

=2\pi\int\limits_0^{10}2x^2\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx= 4\pi\int\limits_0^{10}\sqrt{x^4}\cdot\sqrt{1+\dfrac{1}{4x^2}}\,\,dx=\\\\\\= 4\pi\int\limits_0^{10}\sqrt{x^4+\dfrac{x^4}{4x^2}}\,\,dx= 4\pi\int\limits_0^{10}\sqrt{x^4+\dfrac{x^2}{4}}\,\,dx=\\\\\\= 4\pi\int\limits_0^{10}\sqrt{\dfrac{x^2}{4}\left(4x^2+1\right)}\,\,dx= 4\pi\int\limits_0^{10}\dfrac{x}{2}\sqrt{4x^2+1}\,\,dx=\\\\\\=\boxed{2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx}

Calculate indefinite integral:

\int x\sqrt{4x^2+1}\,dx=\int\sqrt{4x^2+1}\cdot x\,dx=\left|\begin{array}{c}t=4x^2+1\\\\dt=8x\,dx\\\\\dfrac{dt}{8}=x\,dx\end{array}\right|=\int\sqrt{t}\cdot\dfrac{dt}{8}=\\\\\\=\dfrac{1}{8}\int t^\frac{1}{2}\,dt=\dfrac{1}{8}\cdot\dfrac{t^{\frac{1}{2}+1}}{\frac{1}{2}+1}=\dfrac{1}{8}\cdot\dfrac{t^\frac{3}{2}}{\frac{3}{2}}=\dfrac{2}{8\cdot3}\cdot t^\frac{3}{2}=\boxed{\dfrac{1}{12}\left(4x^2+1\right)^\frac{3}{2}}

And the area:

A=2\pi\int\limits_0^{10}x\sqrt{4x^2+1}\,dx=2\pi\cdot\dfrac{1}{12}\bigg[\left(4x^2+1\right)^\frac{3}{2}\bigg]_0^{10}=\\\\\\= \dfrac{\pi}{6}\left[\big(4\cdot10^2+1\big)^\frac{3}{2}-\big(4\cdot0^2+1\big)^\frac{3}{2}\right]=\dfrac{\pi}{6}\Big(\big401^\frac{3}{2}-1^\frac{3}{2}\Big)=\boxed{\dfrac{401^\frac{3}{2}-1}{6}\pi}

Answer D.
6 0
3 years ago
Read 2 more answers
The audience thinks 30\%30%30, percent of Brandon's jokes are funny.
Kisachek [45]

Answer:

3/10

Step-by-step explanation:

Brandon's jokes does the audience think are funny = 30%

What fraction of Brandon's jokes does the audience think are funny?

Express the percentage as a fraction

= 30%

= 30 / 100

= 3/10

The fraction of Brandon's jokes that the audience think are funny is 3/10

6 0
3 years ago
Help with geometry please! will mark brainliest
Vesna [10]
1. The segment LO bisects one of the angles of the triangle shown in the figure attached, and divide the segment NM in two segments: NO and OM. Therefore, you must apply the Triangle Angle Bisector Theorem, which is shown below:

 LN/LM=NO/OM

 LN=10
 LM=18
 NO=4
 OM=x (The value you want to find)

 2. When you substitute this values in LN/LM=NO/OM, you have:

 10/18=4/x
 10x=(18)(4)
 x=(18)(4)/10
 x=72/10

 3. Finally, you obtain:

 x=7.2

 The answer is: The value of "x" is 7.2
5 0
3 years ago
5. Austin left for school at 7:35 A.M He arrived at school 15 minutes later. What time did Austin arrive at school?
snow_lady [41]

Answer:

He arrived at school at 7:50

Step-by-step explanation:

15 plus 7:35 is 7:50


8 0
3 years ago
There are approximately 1.2×10 to the eighth household in the US if the average household uses 400 gallons of water each day wha
lana [24]

Answer:

Total = 4.8 * 10^{10}

Step-by-step explanation:

Given

h = 1.2 * 10^8 --- households

g = 400 --- gallons

Required

The number of households

To do this, we simply multiply the average households by the gallons.

Total = g* h

Total = 400 * 1.2 * 10^8

Total = 480 * 10^8

Rewrite as:

Total = 4.8 * 10^2 * 10^8

Total = 4.8 * 10^{10}

7 0
2 years ago
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