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torisob [31]
3 years ago
7

Evaluate the definite integral. 1 x4(1 + 2x5)5 dx.

Mathematics
1 answer:
Nata [24]3 years ago
5 0

Answer:

Step-by-step explanation:

Given the definite integral \int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx, we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}

= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} }  \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du }  \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}]  \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\

= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C

substitute u = 1-2x⁵ into the result

= \dfrac{1}{40(1-2x^5)^4} +C

Hence\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx = \dfrac{1}{40(1-2x^5)^4} +C

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pentagon [3]

Answer:

= x 3048

Step-by-step explanation:

6 0
2 years ago
You bike 1 mile the first day of your​ training, 1.3 miles the second​ day, 1.9 miles the third​ day, and 3.1 miles the fourth d
JulsSmile [24]

Answer:

19.9 miles

Step-by-step explanation:

In this problem we have:

d_1=1 mi is the distance travelled during the 1st day

d_2=1.3 mi is the distance travelled during the 2nd day

d_3=1.9 mi is the distance travelled during the 3rd day

d_4=3.1 mi is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

d_2-d_1=0.3\\d_3-d_2=2\cdot 0.3 = 0.6\\d_4-d_3=2\cdot 0.6 = 1.2

Which can be rewritten using the general formula:

d_{n+1}-d_n=2(d_n-d_{n-1})

This means that

d_{n+1}=d_n+2(d_n-d_{n-1})

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

d_1=1\\d_2=1.3\\d_3=1.9\\d_4=3.1\\d_5=3.1+2\cdot 1.2=5.5\\d_6=5.5+2\cdot 2.4=10.3\\d_7=10.3+2\cdot 4.8=19.9 mi

So, the  distance travelled on the 7th day is 19.9 miles.

7 0
3 years ago
Your CLASS is selling boxes of flower
denis-greek [22]

Answer:

1.50

Step-by-step explanation:

3 0
3 years ago
Help me please do today please help
lara31 [8.8K]

Answer:

1)

A family buys 6 tickets to a show. They also pay a $3 parking fee. They spend $27 to see the show. - 6x + 3 = 27

Explanation: As it is revealed in the situation, the family buys six tickets and the price of these tickets is unknown, so we must replace that with a variable, which gives us 6x so far. Next, it is shown that an additional three dollars were spent for a parking fee, so the next part of the equation is + 3. In total, they spend twenty-seven dollars, including the three dollars spent for the parking fee, which gives us the final part of the equation; = 27. Therefore, the equation will be 6x + 3 = 27.

Diego has 27 ounces of juice. He pours equal amounts for each of his three friends and has six ounces left for himself. - 3x + 6 = 27

Explanation: From the situation, we are told that Diego has three friends he shared the juice with and was left with six ounces for himself, meaning how much the friends took was unknown, but what was left after giving it away is clear, which was six ounces. So, the first part of the equation would be 3x + 6. It is also known that there was 27 ounces of juice at first, meaning what he shared and what he had left would equal 27, so the equation would be 3x + 6 = 27.

Jada worked for six hours preparing for the art fair. She spends three hours on a sculpture and then paints 27 picture frames. - 27x + 3 = 6

Explanation: When you first look at the story, you can see that six hours total were spent on the whole project together, meaning the final part of the equation would be = 6. The first part, however, would be concluded through how Jada spent an unknown amount of time for 27 picture frames and spent three more hours on a sculpture, which would lead to equal six. So the first part would be 27x + 3, and the actual equation for the story would be 27x + 3 = 6.

a) First story (6 tickets story) - x = price of tickets

   Second story (27 ounces of juice story) - x = ounces of juice given to each friend

   Third story (art project) - x = time spent on each picture frame

Important note: These are all what is unknown!

b)

6x + 3 = 27 (original equation)

Subtract three on both sides to isolate x: 6x = 24

Divide by four on both sides to isolate x: x = ($)4

3x + 6 = 27 (original equation)

Subtract by six on both sides to isolate x: 3x = 21

Divide by three on both sides to isolate x: x = 7 (oz.)

27x + 3 = 6 (original equation)

Subtract by three on both sides to isolate x: 27x = 3

Divide by twenty-seven on both sides to isolate x: x = 1/9 (hours)

c)

Diego gave each of his friends seven ounces of juice.

Inferred: We can infer that Diego had more than one friend that we was giving to. Seven ounces of juice were being given, and there are unknown amount of friends that are getting the ounces of juice.

Mommy spent $4 per person to attend the show.

Inferred: There was probably more than one person attending. The cost for one person('s ticket) was four dollars. The cost was at least $8 dollars as the mother also attended. They were trying to attend a show with an unknown amount of people.

Hope this helped somewhat! Please give brainliest, if that's okay with you! It just took a lot of effort lol :P Have a great night!

6 0
2 years ago
You are designing a ramp where the horizontal distance is twice the vertical rise. what will be the ramp angle to the nearest te
ankoles [38]
Use the definition of tangent

or inv tangent (arctan or atan)

tan(theta) = opposite side/ adjacent side

the vertical rise would be the opposite side, the horozontal distance would be the adjacent side

let rise = y
let distance= x
x=2y

so tan(theta) = y/2y
tan(theta) = 1/2

theta = atan(1/2)

grab a handy dandy calculator, unless you know this conversion off the top of your head
7 0
3 years ago
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