Hi there! Assume that this is your question.
[tex] \large{ \int \limits^a_b ( {x}^{2} + 2x)dx}[/tex]
Before we get to Integral, you have to know Differentiation first. If you know how to differentiate a polynomial function then we are good to go in Integral!
We call the function that we are going to integrate as Integrand. Integrand is a function that's differentiated. In Integral, Integrating requires you to turn the function from differentiated to an original function.
For Ex. If the Integrand is x² then the original function is (1/3)x³ because when we differentiate (1/3)x³, we get x²
[tex] \large{f(x) = \frac{1}{3} {x}^{3} \longrightarrow f'(x) = {x}^{2} } \\ \large{f'(x) = 3( \frac{1}{3} ) {x}^{3 - 1} } \\ \large{f'(x) = {x}^{2} }[/tex]
So when we Integrate, make sure to convert Integrand as in original function. From the question, our Integrand is x²+2x. The function is in differentiated form. We know that x² is from (1/3)x³ and 2x comes from x²
[tex] \large{ f(x) = {x}^{2} \longrightarrow f'(x) = 2x} \\ \large{f'(x) = 2 {x}^{2 - 1} } \\ \large{f'(x) = 2x}[/tex]
Thus,
[tex] \large{ \int \limits^a_b ( {x}^{2} + 2x)dx} \\ \large{\int \limits^a_b ( \frac{1}{3} {x}^{3} + {x}^{2}) }[/tex]
Normally, if it's an indefinite Integral then we'd just put + C after (1/3)x³+x² but since we have a and b, it's a definite Integral.
[tex] \large{ \int \limits^b_a f(x)dx = F(b) - F(a)}[/tex]
Define F(x) as our anti-diff
From our problem, substitute x = a in then subtract with the one that substitute x = b
[tex] \large{ (\frac{1}{3}{a}^{3} + {a}^{2} ) - ( \frac{1}{3} {b}^{3} + {b}^{2}) }[/tex]
Simplify as we get:
[tex] \large \boxed{ \frac{1}{3}{a}^{3} + {a}^{2} - \frac{1}{3} {b}^{3} - {b}^{2}}[/tex]
What is the distance between the points (2,4) and (9,9)?
Answer:
I think it is (7,5)
Step-by-step explanation:
Lines s and t intersect so that the measure of ∠1 is 85 °. If ∠2 is a supplement to ∠1, what is the measure of ∠2?
Answer:
95 degrees
Step-by-step explanation:
-2x + 4 = 3
how would you solve this problem?
There are 10 marbles in a bag 1/5 are and the other are blue .What is the ratio of red to blue marbles
Answer:
1 : 4
Step-by-step explanation:
There are 10 marbles in a bag 1/5 are red and the others are blue. What is the ratio of red to blue marbles?
Number of red marbles = fraction of red marbles x total number of marbles
1/5 x 10 = 2
Number of blue marbles = total number of marbles - number of red marbles
10 - 2 = 8
ratio of red to blue marbles
2 : 8
To transform to the simplest form. divide both numbers by 2
1 : 4
What is the common ratio of the geometric sequence whose first term is 5 and third term is 245?
Answer:
7
Step-by-step explanation:
The common ratio of the geometric sequence is 7.
What is geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
According to the question,
First term = a = 5
Third term = a×r²
= 245
⇒ ar² = 245
⇒ 5×r² =245
⇒ r² = 245/5
⇒ r² = 49
⇒ r = 7.
Hence the common ratio = 7
To learn more on geometric progression click :
https://brainly.com/question/4853032
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When 3 is subtracted from one third of a number n, the result is less than 6. Which inequality and solution represent this situation?
Answer:
1/3n-3÷6
Step-by-step explanation:
3 is subtraced form 1/3
Answer:
n < 27
Step-by-step explanation:
1/3n - 3
1/3n - 3 < 6
Add 3 to each side.
1/3n - 3 + 3 < 6 + 3
Combine like terms.
1/3n < 9
Divide each side by 1/3.
1/3n ÷ 1/3 < 9 ÷ 1/3
Combine like terms.
n < 27
help me plzz nowwwwww plzz
Answer:
18
Step-by-step explanation:
colored: white
3 :8
We have 48 white papers so multiply each side by 6
colored: white
3*6 : 8*6
18 48
There are 18 colored papers
Answer:
C) 18
Step-by-step explanation:
3/8 = c/48
cross-multiply to get:
8c = 144
c = 18
Darcy sold lemonade in rhe summer. Lemonade is her favorite summertime drink. 1/2 of her recipe is fresh lemons . 1/3 of her recipe is sugar. The rest of the recipe is water. What fraction of the recipe is water
Answer:
1/6
Step-by-step explanation:
fraction of water = 1 - (1/2 + 1/3)
)[tex]\frac{1}{2} + \frac{1}{3}[/tex]
[tex]\frac{3 + 2}{6}[/tex]
5/6
1 - 5/6
6/6 - 5/6 = 1/6
how to get easy points: make two acounts, on the second acount answer random question to get points, then make questions that have a lot of points, on the first acount answer the questions that you made. repeat.
Answer:
the bro ik
Step-by-step explanation:
yup yup yup bri
Answer:
heyyyy
Step-by-step explanation:
Given AE and BD bisect each other at point c, which congruence theorem would you use to prove triangle ABC =~ triangle EDC ?
HELP PLEASE!!! NO FLIES OR LINKS
given rhombus ABCD , find the measure of the indicated angle in degrees
Answer:
61
Step-by-step explanation:
180 - 119 =
Yolanda receives a $1,000 dollar raise each year from her starting salary of $40,800.
After 10 years, how much total gross income will she have earned for all 10 years?
For example: $40.800 in year one, $41,800 in year two etc.
helppp
Answer:50,400
Step-by-step explanation:
The equation of a line is 2x + 3y = Select three
lines that are parallel to the given line.
Answer:
The three lines that are parallel to the Given line are :
2x + 3y = 2
9y = -6x + 15
3y = -2x + 12
Step-by-step explanation:
The exact question is as follows :
Given - The equation of a line is 2x + 3y = 4.
To find - Select three lines that are parallel to the given line.
A) 2x + 3y = 2
B) 2x + 5y = 15
C) 9y = -6x + 15
D) 3y = -2x + 12
E) 3x - 2y = 15
Solution -
We know that,
If the slopes are the same and the y-intercepts are different, the lines are parallel.
Given that,
The given line is 2x + 3y = 4
⇒3y = -2x + 4
⇒y = -(2/3)x + (4/3)
So,
Slope = -(2/3)
y-intercept = (4/3)
Now,
A.)
2x + 3y = 2
⇒3y = - 2x + 2
⇒y = -(2/3) + (2/3)
So,
Slope = -(2/3)
y-intercept = (2/3)
By Comparing with the given line's slope and y-intercept
We can see that
slope is same but y-intercept is different
So,
2x + 3y = 2 is parallel to the given line.
Now,
B.)
2x + 5y = 15
⇒5y = - 2x + 15
⇒y = -(2/5) + (15/5)
So,
Slope = -(2/5)
y-intercept = 3
By Comparing with the given line's slope and y-intercept
We can see that slope is different
So,
2x + 5y = 15 is not parallel to the given line.
C)
9y = -6x + 15
⇒y = -(6/9)x + (15/9)
= -(2/3)x + (5/3)
⇒y = -(2/3)x + (5/3)
So,
Slope = -(2/3)
y-intercept = 5/3
By Comparing with the given line's slope and y-intercept
We can see that slope is same and y-intercept is different
So,
9y = -6x + 15 is parallel to the given line.
D)
3y = -2x + 12
⇒y = -(2/3) + (12/3)
So,
Slope = -(2/3)
y-intercept = 4
By Comparing with the given line's slope and y-intercept
We can see that slope is same and y-intercept is different
So,
3y = -2x + 12 is parallel to the given line.
E)
3x - 2y = 15
⇒-2y = -3x + 15
⇒2y = 3x - 15
⇒y = (3/2) - (15/2)
So,
Slope = 3/2
y-intercept = -15/2
By Comparing with the given line's slope and y-intercept
We can see that slope is different
So,
3x - 2y = 15 is not parallel to the given line.
∴ we get
The three lines that are parallel to the given line are :
2x + 3y = 2
9y = -6x + 15
3y = -2x + 12
help me with this the question is in the picture
Answer:
28:12
Step-by-step explanation:
You multiply both sides by the same number to increase a ratio, the only one you can do this with is 28:12 by multiplying the original ratio by 4
I need help with this asap please
Answer:
A
Step-by-step explanation:
Total amount of faces of object = 6
Surface area = length x height
2(4*10) + 2(10*17) + 2(4*17)
=2(40) + 2(170) + 2(68)
= 80 + 340 + 136
= 556cm^2
Find the volume of this right rectangular
prism.
4 cm
4 cm
4 cm
[ ? ]cm3
Answer:
V = 64 cm^3
Step-by-step explanation:
Volume is length times width times height
V = l*w*h
V = 4*4*4
V = 64 cm^3
Answer:
64
Step-by-step explanation:
4x4x4=64
What is the volume, in cubic in, of a cylinder with a height of 12in and a base radius of 6in, to the nearest tenths place?
Answer: Therefore, the volume of cylinder is 1356.5 cubic inches.
Step-by-step explanation: First I took an ESTIMATE and then after I did my estimate I did the real deal, I took everything I knew and put it all together.
Answer:
12*8.49*8.49 = 8649612in^3
Step-by-step explanation:
solve the equation x - 4 = -3 help yall-
Answer:
x = 1
Step-by-step explanation:
x - 4 = -3
(add 4 to both sides)
x - 4 + 4 = -3 + 4
x = 1
Answer:
x = 1
Step-by-step explanation:
So you have to separate the x from the rest of the equation
so you can add 4 to both sides so x is by itself
so ur left with:
x = -3 + 4
and that is equal to x = 1
Hope that helps :)
Use the equation 135 x 42 = 5.670 and what you know about fractions, decimals, and place value to explain how to place the decimal point when you compute 1.35 x 4.2
Answer:
5.670
Step-by-step explanation:
To compute 1.35 x 4.2
First, we need to convert both decimals to fraction
1.35 = 135/100
4.2 = 42/10
Taking the product
1.35 x 4.2
= 135/100 * 42/10
= (135*42)/(100*10)
= 5670/1000
= 5.670
Hence the product of both numbers is 5.670
Find h.
11 in.
h = [?] in
in.
14 in.
PLEASE OH PLEASE HELP ME IM DESPERATE
11^2 = h^2 + ( 14/2)^2
11^2 = h^2 + 7^2
121 = h^2 + 49
h^2 = 121 - 49
h^2 = 72
h = √72
I had $36. I spent 1/2 of my money on Thursday and 2/3 of the remainder on Wednesday. How much money did I have left?
Where are you genius people? I know you hella smart
Answer:
$12
Step-by-step explanation:
Half of $36 would be $18. $18 divided by 3 would be $6. $6 times 2 would be $12. Half comes from the 1/2 of money spent on Thursday. Dividing it by 3 comes from the remainder on Wednesday. We divide it by 3 since the denominator of 2/3 is 3. We then multiply it by 2, since the numerator in 2/3 is 2.
PLEASE HELP!! I'LL MARK BRAINLIEST AND GIVE POINTS!!
Fiona and Rachel went to determine the most popular lunch choice in the school cafeteria among seventh graders. They decide to collect data from a sample of seventh graders at school. Fiona surveys twenty seventh graders that are in line at the cafeteria. Rachel surveys twenty seventh graders whose ID numbers end in 9.
ALL YOU HAVE TO DO IS FIND WHICH REPRESENTATION IS BIGGER, FIONA'S OR RACHEL?
Answer:
Rachel
Step-by-step explanation:
Rachel has the greater representation; if the students are in the lunch line, they are buying food (this does not account for students who bring lunch from home).
The last number in an ID has nothing to do with lunch choice.
What is the sum of 4n² + 2n+ 12
Answer:
hope this helps <33
Step-by-step explanation:
2(2n^2+n=6)
Please help!!!
If O is the center of the circle, what can you conclude from the diagram?
Answer:
H. AB < AD
Step-by-step explanation:
_________________
read and answer please. thanks
helppppppppppppppppppp
Answer:
B
Step-by-step explanation:
You just substitute the values in for A and B and then you simplify
The 10 A would be 10x17 which is 170 and then plus B, which we know is 12, so it would equal 182
hope this helped
Answer:
182
Step-by-step explanation:
First, plug in 17 for a
10·17+b=170+b
Then plug in 12 for b
170+12=182
There you go!
182
will give brainlist, pls help lol
Answer:
D, 144
Step-by-step explanation:
Find x first by solving 9x+27=6x+66, and plug x in to the angle RSL.
solve the inequality t/4 > 7
Answer:
t > 28
Step-by-step explanation:
Given
> 7 ( multiply both sides by 4 to clear the fraction )
t > 28
Answer:
[tex]t > 28[/tex]
Step-by-step explanation:
Multiply both sides of the inequality by 4:
[tex]4 \times \frac{t}{4} > 4 \times 7[/tex]
Reduce the number with the greatest common factor 4:
[tex]t > 4 \times 7[/tex]
Multiply the number:
[tex]t > 28[/tex]
On a number line, what is the distance between -5 and
72
Solve for x in the following proportion?
1.6
722.5
0.4
10
Answer:
option D. 10
Step-by-step explanation:
[tex]\frac{34}{85} = \frac{4}{x}\\\\34 \times x = 4 \times 85\\\\x = \frac{340}{34} = 10[/tex]
Answer:
x = 10
Step-by-step explanation:
[tex] \dfrac{34}{85} = \dfrac{4}{x} [/tex]
Cross multiply.
34x = 4 × 85
34x = 340
Divide both sides by 34.
x = 10