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goldfiish [28.3K]
3 years ago
15

Simplify √5(8+3√6) using radicals

Mathematics
1 answer:
hichkok12 [17]3 years ago
3 0
Your answer should be 34
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Find the volume of the solid formed by revolving the region bounded by LaTeX: y = \sqrt{x} y = x and the lines LaTeX: y = 1 y =
Strike441 [17]

Answer:

The volume is:

\displaystyle\frac{37\pi}{10}

Step-by-step explanation:

See the sketch of the region in the attached graph.

We set the integral using washer method:

\displaystyle\int_a^b\pi r^2dx

Notice here the radius of the washer is the difference of the given curves:

x-\sqrt{x}

So the integral becomes:

\displaystyle\int_1^4\pi(x-\sqrt{x})^2dx

We solve it:

Factor \pi out and distribute the exponent (you can use FOIL):

\displaystyle\pi\int_1^4x^2-2x\sqrt{x}+x\,dx

Notice: x\sqrt{x}=x\cdot x^{1/2}=x^{3/2}

So the integral becomes:

\displaystyle\pi\int_1^4x^2-2x^{3/2}+x\,dx

Then using the basic rule to evaluate the integral:

\displaystyle\pi\left[\frac{x^3}{3}-\frac{2x^{5/2}}{5/2}+\frac{x^2}{2}\right|_1^4

Simplifying a bit:

\displaystyle\pi\left[\frac{x^3}{3}-\frac{4x^{5/2}}{5}+\frac{x^2}{2}\right|_1^4

Then plugging the limits of the integral:

\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]

Taking the root (rational exponents):

\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]

Then doing those arithmetic computations we get:

\displaystyle\frac{37\pi}{10}

6 0
3 years ago
If you can, please tell how you solved
gizmo_the_mogwai [7]

Answer:

plzz mark me brainlieat if it helps you

x+67 + x+127 = 180

or, 2x + 194 = 180

2x = - 14

: . x = -7

8 0
2 years ago
You randomly select a card from a 52-card deck. Find the probability of selecting a 7 or an Ace.​
erik [133]

Answer:

15.38%

Step-by-step explanation:

There are 4 7's in a deck of 52 cards.

There are 4 Aces in a deck of 52 cards.

4+4 = 8

8/52, or 15.38%

6 0
3 years ago
Read 2 more answers
Anna, Beth and Colleen are softball players. This season, Anne had 65 base hits in 160 at-bats. Beth batting average was 0.399,
zheka24 [161]

Answer:

Anne is the best hitter as she has the best hitting average of 0.406

Step-by-step explanation:

Anne hits 65 bases out of 160 at - bats.

Beth's betting average = 0.399

Collin's hit = 40%

Now, we need to convert all the three hitting rates into same parameters to compare them with each other.

Average hit rate of Anne = \frac{\textrm{Total numberof base}}{\textrm{Total number of  at - bats}}

= \frac{65}{160}  = 0.406

⇒The betting average of Anne = 0.406

Now, The hit - rate of Collin = 40%

Converting the percentage rate into decimal, we get the hit rate of Collin

= \frac{40}{100}  = 0.40

Hence, we get that Hitting Average of :

<u>Anne = 0.406</u>,  Beth = 0.3999 and Collin = 0.400

Hence, from the above data Anne is the best hitter as she has the best hitting average of 0.406.

6 0
3 years ago
Read 2 more answers
Look at the pic and help if you can thxxxx
givi [52]

Answer:

The 1,3,and 4.

Step-by-step explanation:

6 0
3 years ago
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