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vichka [17]
3 years ago
5

Michael has a set of 24 math problems to do for homework. Michael completed of his homework

Mathematics
1 answer:
RoseWind [281]3 years ago
5 0

Answer:

3/8 easy-peasy

Step-by-step explanation:

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Find the length of the following curve. If you have a​ grapher, you may want to graph the curve to see what it looks like.
stepladder [879]

The length of the curve y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6 is 192 units

<h3>How to determine the length of the curve?</h3>

The curve is given as:

y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6

Start by differentiating the curve function

y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x

Evaluate

y' = x(9x^2 + 6)^\frac 12

The length of the curve is calculated using:

L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx

This gives

L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx

Expand

L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx

This gives

L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx

Express as a perfect square

L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx

Evaluate the exponent

L =\int\limits^6_3 {3x^2 + 1} \ dx

Differentiate

L = x^3 + x|\limits^6_3

Expand

L = (6³ + 6) - (3³ + 3)

Evaluate

L = 192

Hence, the length of the curve is 192 units

Read more about curve lengths at:

brainly.com/question/14015568

#SPJ1

7 0
2 years ago
Plz help !!!!!!!!1
rosijanka [135]

Answer:

As outdoor temperatures increased, residents' electric bills increased.

Step-by-step explanation:


7 0
3 years ago
Sis Avila (STUDEN...
vesna_86 [32]

Answer:

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3 0
3 years ago
Roberto wants to make $2.00 using half of dollar, and quarters.how many different ways can he make $2.00
Alik [6]
A half a dollar is 50 cents. If you want to use quarters, you would need 6 more quarters to make 2 dollars.
6 0
3 years ago
A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price.The customer was charged a 7%
Tems11 [23]

Answer:

The customer's total cost for the DVD is $19.26

Step-by-step explanation:

Store buy the dvd for $12.00.

The store price is $12.00+50% more

The store price= $12.00 *(1+0.5)= $18.00

Final price (tax added)= $18.00 + 7%

Final price= $18.00 * (1 + 0.07)= $19.26

3 0
3 years ago
Read 2 more answers
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