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2 years ago

Two consecutive odd numbers have a sum of 92. What are the numbers?

Mathematics

1 answer:

Tresset [83]2 years ago

6 0

The numbers are 45 and 47.

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The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

3 years ago

Find f(-4) for f(x)=9(3)^x

jeka94

Answer:

$f(-4) = \dfrac{1}{9}$

Step-by-step explanation:

$f(x) = 9(3)^x$

$f(-4) = 9(3)^{-4}$

$f(-4) = 3^2 \cdot 3^{-4}$

$f(-4) = 3^{-2}$

$f(-4) = \dfrac{1}{9}$

3 0

2 years ago

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Write a recursive formula for each sequence given or described below.

valentinak56 [21]

Answer:

$a_{n} =a_{n-1} +3000$ and a₁ =30000 for n = 2,3,4,5,6, ......

Step-by-step explanation:

Doug has joined a job with a starting salary of $30000 per year.

Hence, if a₁ is the salary of Doug in the first year, then

a₁ =30000

Now, each year Doug will receive a raise of $3000 in his salary.

Hence, in the 2nd year, his salary(a₂) will become ( a₁ +3000) per year.

Again, in the 3rd year, his salary(a₃) will become ( a₂ +3000) per year.

Therefor, in the similar manner the recursive formula for his salary in each year will be given as $a_{n} =a_{n-1} +3000$ and a₁ =30000 for n = 2,3,4,5,6, ...... {aₙ is the yearly salary of Doug in the nth year} (Answer)

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3 years ago

Yusuf and some friends are going to the movies. At the theater, they sell a bag of popcorn for $4 and a drink for $3.25. How muc

mylen [45]

Answer:

$42 would be the correct answer.

5 0

2 years ago

Can someone please help me with this ⬆️⬆️⬆️it's the picture above ... 13/78=×/12

ratelena [41]

I am pretty sure x=2

3 0

3 years ago

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