1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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)

You might be interested in
Algebraic Reasoning please help!
stiv31 [10]

Answer:

\left[\begin{array}{ccc}7\\4\\2\end{array}\right]

The answer is a single-column matrix (7,4,2)

Step-by-step explanation:

In such multiplication of matrices, you have to proceed by multiplying each ROW of the first matrix by the COLUMN of the second matrix.  So,

\left[\begin{array}{ccc}3&6&1\end{array}\right] * \left[\begin{array}{ccc}2\\0\\1\end{array}\right] = (3 * 2) + (6 * 0) + (1 * 1) = 6 + 0 + 1 = 7

then...

\left[\begin{array}{ccc}2&4&0\end{array}\right] * \left[\begin{array}{ccc}2\\0\\1\end{array}\right] = (2 * 2) + (4 * 0) + (0 * 1) = 4 + 0 + 0 = 4

and

\left[\begin{array}{ccc}0&6&2\end{array}\right] * \left[\begin{array}{ccc}2\\0\\1\end{array}\right] = (0 * 2) + (6 * 0) + (2 * 1) = 0 + 0 + 2= 2

I hope it helps.

5 0
3 years ago
In the diagram below, P and Q are points on a circle with centre O.
Gnoma [55]

Answer:

<h2>∠PQT = 72°</h2>

Step-by-step explanation:

According to the diagram shown, ∠OPQ = ∠OQP = 18°. If PQT is a tangent to the circle, it can be inferred that line OQ is perpendicular to line QT. Ths shows that ∠OQT = 90°.

Also from the diagram, ∠OQP + ∠PQT = ∠OQT;

∠PQT  = ∠OQT -  ∠OQP

Given ∠OQP = 18° and ∠OQT = 90°

∠PQT = 90°-18°

∠PQT = 72°

8 0
4 years ago
The sum of two numbers is 67 and the difference is 13 . What are the numbers?
svet-max [94.6K]

Answer:

27 and 40

Step-by-step explanation:


3 0
3 years ago
Jason has 5 shirts for every 2 pairs of pants. His brother John has 7 shirts for every 3 pairs of pants. Compare the ratio by co
postnew [5]

Answer:

john has a greater ratio of shirts to pants

Step-by-step explanation:

jason- 5:2

table:

shirt :5 10 15 20 25 30 35 40 45

pants:2 4   6   8   10 12  14 16 18 20

john-7:3

table:

shirts:7 14 21 28 35 42 49 56 63

pants:3  6 9 1 2  15  18  21 24  27

4 0
2 years ago
Which statement is true about this argument? Premises: If a triangle has an angle that measures 150°, then it is an obtuse trian
vfiekz [6]
What is JkL

Because i need to know.Btw sorry for using p the answer board <span />
7 0
3 years ago
Other questions:
  • Which statement about the two-way frequency table is true?
    8·1 answer
  • A circular garden has a circumference of 113 yards. Lars is digging a straight line along a diameter of the garden at a rate of
    14·1 answer
  • At a pet store the ratio of cats to dogs sold was 5 : 3. If there were 40 cats that were sold, how many dogs were sold?
    13·1 answer
  • Convert decimal .008 to a fraction
    9·2 answers
  • Paula is given a litre bottle of water during her fitness assessment at the gym. She drinks 375 millilitres of the water.   
    9·1 answer
  • Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction? f (x) = Sta
    10·2 answers
  • What is the answer to this question?
    9·1 answer
  • 2.
    12·1 answer
  • Can someone help me with this really quick?
    15·2 answers
  • The graph of the function f(x) = (x-3)(x + 1) is shown.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!