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OlgaM077 [116]
3 years ago
13

Please help me with this question

Mathematics
1 answer:
san4es73 [151]3 years ago
5 0

Step-by-step explanation:

Given: f'(x) = x^2e^{2x^3} and f(0) = 0

We can solve for f(x) by writing

\displaystyle f(x) = \int f'(x)dx=\int x^2e^{2x^3}dx

Let u = 2x^3

\:\:\:\:du=6x^2dx

Then

\displaystyle f(x) = \int x^2e^{2x^3}dx = \dfrac{1}{6}\int e^u du

\displaystyle \:\:\:\:\:\:\:=\frac{1}{6}e^{2x^3} + k

We know that f(0) = 0 so we can find the value for k:

f(0) = \frac{1}{6}(1) + k \Rightarrow k = -\frac{1}{6}

Therefore,

\displaystyle f(x) = \frac{1}{6} \left(e^{2x^3} - 1 \right)

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pantera1 [17]

Answer:

  • 8 3/4
  • 2, 3
  • 4 1/2, 11 1/4
  • 9 3/4, 16 1/4
  • Y/B = 2/3

Step-by-step explanation:

<h3>a)</h3>

The first line is simply the sum of the two given numbers.

  3 1/2 +5 1/4 = (3+5) +(2/4+1/4) = 8 3/4

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To find values on the remaining lines, it is convenient to find the ratios of the numbers involved. The ratio of yellow to blue is ...

  Y/B = (3 1/2)/(5 1/4) = (7/2)/(21/4) = (7/2)(4/21) = 2/3

Then ...

  Y : B : total = 2 : 3 : 5

This tells you the numbers on the second line are ...

  Y = 2; B = 3

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The value for B on the third line is the basic ratio number multiplied by (6 3/4)/3 = 2 1/4. Then the other two numbers are ...

  Y = 2(2 1/4) = 4 1/2

  total = 5(2 1/4) = 11 1/4

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The value for Y on the fourth line is the basic ratio number multiplied by (6 1/2)/2 = 3 1/4. Then the other two numbers are ...

  B = 3(3 1/4) = 9 3/4

  total = 5(3 1/4) = 16 1/4

_____

<h3>b)</h3>

The equation is the one we used to find the values on the second line:

  Y/B = 2/3

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Answer:

x<-1

Step-by-step explanation:

I think and hope it helps

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Y varies directly as x. Y=42 when x=6. Find the value of y when x =15.
pentagon [3]

Answer:

y=120

Step-by-step explanation:

Y varies directly as x is written as

y \alpha x

introducing a constant

y=kx

<em>from</em><em> </em><em>the</em><em> </em><em>ques</em><em>tion</em><em>,</em><em> </em><em>whe</em><em>n</em><em> </em><em>y</em><em>=</em><em>4</em><em>8</em><em>,</em><em> </em><em> </em><em>x</em><em>=</em><em>6</em>

<em>sub</em><em>stitute</em><em> </em><em>it</em><em> </em><em>in</em><em> </em><em>the</em><em> </em><em>form</em><em>ula</em>

<em>4</em><em>8</em><em>=</em><em>6</em><em>k</em>

<em>making</em><em> </em><em>k</em><em> </em><em>the</em><em> subject</em><em> </em><em>by </em><em>divi</em><em>ding</em><em> </em><em>thr</em><em>ough</em><em> </em><em>by</em><em> </em><em>6</em>

<em>\frac{48}{6}  =  \frac{6k}{6}</em>

k=48/6

k=8

<em>put</em><em> </em><em>the</em><em> </em><em>va</em><em>lue</em><em> </em><em>of</em><em> </em><em>k</em><em> </em><em>in</em><em> </em><em>the </em><em>expression</em><em> </em><em>y</em><em>=</em><em>kx</em>

<em>y</em><em>=</em><em>8</em><em>x</em>

from the question,the value of y when x=15 is given by

y=8×15

y=120.

4 0
3 years ago
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