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
DENIUS [597]
2 years ago
6

Sketch the region enclosed by y=3x and y=x^2 . Then find the area of the region.

Mathematics
1 answer:
kolezko [41]2 years ago
6 0

Answer:

A=4.5u^2

Step-by-step explanation:

The integral of a function gives you the area under the curve, the subtraction of one of the areas from the other will give you the area in between.

The limits of integration are the points where the curves intersect each other(take the curves has a system of equation and solve for x and y):

y=3x, y=x^2\\3x=x^2\\x^2-3x=0\\x(x-3)=0\\x_1=0\\x-3=0\\x_2=3

y_1=3x_1=3(0)=0\\y_2=3x_2=3(3)=9

The integral will be the subtraction of the curve y=3x and y=x^2  (In the graph you can see y=3x is the upper curve):

\int\limits^3_0 {3x-x^2} \, dx =\left\frac{3x^2}{2}-\frac{x^3}{3}\right|^3_0=\frac{3(3)^2}{2}-\frac{(3)^3}{3}-\left(\frac{3(0)^2}{2}-\frac{(0)^3}{3}\right)\\\int\limits^3_0 {3x-x^2} \, dx =\frac{27}{2}-\frac{27}{3} =13.5-9=4.5u^2

You might be interested in
Which expression is equivalent to 5x+3?​<br><br><br>A. 8x<br>B. 3+5x<br>C. 3x+5<br>D. 5(x+3)
MariettaO [177]

Answer:

B

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A small company 's net income for the first 6 months of the year was 76.500 and for the last six months it was 100,000 . What is
inna [77]

Answer:The ratio of net income in the first 6 months, to the last six months is $76,500 / $100,000. This simplifies intuitively as follows:

76500/100000

Dividing by 100: 765/1000

Dividing by 5: 153/200

The denominator 200 is only divisible by the prime numbers 2 and 5, and since the numerator 153 is not divisible by either 2 or 5, this means that this is in simplest form, and the final answer is 153/200.

Step-by-step explanation:i did the research for you this isnt my own answer therefore don't give me the credit. but hope this helped you tho :D

5 0
3 years ago
How to calculate 99 : 5​
Goryan [66]

Answer:

19.8

Step-by-step explanation:

99/5= 19.8

5 0
3 years ago
Help with matrices please? Any wrong/not applicable answers will be reported and BLOCKED
marin [14]

m x H = \left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right]

Step-by-step explanation:

Step 1; Multiply 5 with this matrix  \left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right] and we get a matrix \left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right]

Multiply the fraction  \frac{2}{5} with the matrix  \left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right] and we get \left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right]

Step2; Now equate corresponding values of the matrices with each other.

-5 = \frac{-2m}{5} and so on. By equating we get the value of m as \frac{25}{2}

Step 3; Add the matrices to get the value of matrix m.

Adding the three matrices on the RHS we get  \left[\begin{array}{ccc}2&9&-9\\\end{array}\right].

Step 4; Adding the matrices on the LHS we get the resulting matrix as H +

\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right]. Equating the matrices from step 3 and 4 we get the value of H as \left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]

Step 5; Now to find the value of m x H we need to multiply the value of \frac{25}{2} with the matrix \left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]

Step 6; Multiplying we get the matrix m x H = [ -25  \frac{75}{2}  \frac{-25}{2} ]

8 0
2 years ago
What two decimal<br> are between the square root of 62
viva [34]
7 and 8 because the square root is 7.874
4 0
2 years ago
Other questions:
  • Invited guests shopping list decorations menu planning 2.02
    10·1 answer
  • Is this a true proportion ? 1/2 = 5/10 A sometimes B Yes C none of these D no
    15·2 answers
  • X+5÷9=3<br> What is the number where when you add 5 then divide it by 9 it is 3?
    15·2 answers
  • Help ASAP!! Will give brainliest to correct answer!!
    5·2 answers
  • ASAP!! WILL GIVE BRAINLIEST!! What is the equation of the line through (4, 5) and (0, -3)?
    11·1 answer
  • A 15ft. wire is tied to the top of a tree to provide support. If the wire forms a 25° angle with the ground, what is the height
    12·1 answer
  • Mhanifa can you please help? This is due asap!
    5·1 answer
  • Divide: 2 divided 1/2 <br><br> 2<br><br> 16<br><br> 8<br><br> 4
    8·1 answer
  • FREE BRAINLIEST !!!!!!!!!!!!!!!!!!!!!!!!!!!!
    10·2 answers
  • Edward drove 275 miles in 212 hours and 357.5 miles in 314 hours. If he drove at a constant rate, how much distance did he trave
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!