Answers
Answer:
[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegral NotationIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = \left \{ {{9x^9 ,\ 0 \leq x \leq 1} \atop {4x^3 ,\ 1 \leq x \leq 2}} \right.[/tex]
[tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \ ?[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {f(x)} \, dx + \int\limits^2_1 {f(x)} \, dx[/tex][Integrand] Substitute in function: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {9x^9} \, dx + \int\limits^2_1 {4x^3} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \int\limits^1_0 {x^9} \, dx + 4 \int\limits^2_1 {x^3} \, dx[/tex][Integrals] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{x^{10}}{10} \bigg) \bigg| \limits^1_0 + 4 \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^2_1[/tex]Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{1}{10} \bigg) + 4 \bigg( \frac{15}{4} \bigg)[/tex]Simplify: [tex]\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:
Step-by-step explanation:
[tex]\int\limits^1_0 {9x^9} \, dx +\int\limits^2_1 {4x^3} \, dx[/tex]
=[tex]\frac{9x^{10}}{10} |_0^1 + x^4|_1^2[/tex]
[tex]=\frac{9}{10}+2^4 -1 = 15\frac{9}{10}[/tex]
Related Questions
Suppose a special discount makes the price of Nike air max shoes 10% lower. As result, there is a 20% increase in the quantity demanded for the shoes, which statement is correct ____?
Answers
It is evident from the problem statement that an overall price reduction of Nike air max shoes will lead to an increase in the demand for the shoe.
In Economics, the relationship between price and demand is stated as follows "If all other factors remain equal, the higher the price of a good, the fewer people will demand that good. In other words, the higher the price, the lower the quantity demanded and vice versa."
In all, the Law of Demand tells us that if more people want to buy something, given a limited supply, the price of that thing will be bid higher, also of the price of something is low the demand will be high.
learn more:
https://brainly.com/question/25585026
Angle wxz is congruent to angle zxy. Find the value of X
Answers
Answer:
x = 18
Step-by-step explanation:
Congruent angles have equal measures.
74° = (4x +2)°
72 = 4x . . . . . . divide by °, subtract 2
18 = x . . . . . . . divide by 4
how do i do math in division fractions?
Answers
Answer:
The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.
Answer:
Keep change flip!
Step-by-step explanation:
Example 1/2 divided 3/4
We simply keep 1/2 and then we flip the 3/4 which is now 4/3
now we also flip the division sign which its opposite is multiplying now its simply 1/2 x 4/3 and you get 4/6. Hope this helps please mark brainliest!
I need help on my homework.
Answers
Answer:
[tex] \frac{3}{4} > \frac{ - 2 + 2x}{4} \\ \\ (4 \times) \frac{3}{4} > \frac{ - 2 + 2x}{4} ( \times 4) \\ \\ 3 > - 2 + 2x \\ \\ 3 + 2 > - 2 + 2 + 2x \\ \\ 5 > 2x \\ \\ 5 \div 2 > 2x \div 2 \\ \\ \frac{5}{2} > x \\ \\ x < \frac{5}{2} [/tex]
I hope I helped you^_^
Use green’s theorem to evaluate
Answers
By Green's theorem (all the conditions are met), we have
[tex]\displaystyle \int_C \sqrt y \, dx + \sqrt x \, dy = \iint_D \frac{\partial(\sqrt x)}{\partial x} - \frac{\partial(\sqrt y)}{\partial y} \, dx \, dy[/tex]
where D is the interior of the path C, or the set
[tex]D = \left\{ (x, y) : 0 \le y \le \dfrac{x^2}2 \text{ and } 0 \le x \le 2 \right\}[/tex]
So, the line integral reduces to the double integral,
[tex]\displaystyle \frac12 \int_0^2 \int_0^{\frac{x^2}2} x^{-\frac12} - y^{-\frac12} \, dy \, dx[/tex]
[tex]\displaystyle = \frac12 \int_0^2 x^{-\frac12}\left(\frac{x^2}2\right) - 2\left(\frac{x^2}2\right)^{\frac12} \, dx[/tex]
[tex]\displaystyle = \frac12 \int_0^2 \frac12 x^{\frac32} - \sqrt 2 \, x \, dx[/tex]
[tex]\displaystyle = \frac14 \int_0^2 x^{\frac32} - 2\sqrt 2 \, x \, dx[/tex]
[tex]\displaystyle = \frac14 \left(\frac25\cdot2^{\frac52} - \sqrt2\cdot2^2\right) = \boxed{-\frac{3\sqrt2}5}[/tex]
A girl ran to the store at a speed of 6 miles per hour, and then walked back at a speed of 4 miles per hour. If her round trip took 15 minutes, how far away is the store?
Answers
Answer:
.6 miles
Step-by-step explanation:
Answer:
0.6 miles
Step-by-step explanation:
6 × t = 4 × (15 - t)
6t = 60 - 4t
6t + 4t = 60 - 4t + 4t
10t = 60
t = 6
6 × [tex]\frac{1}{10}[/tex] = 0.6
In a survey of 1900 people who owned a certain type of car, 1140 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answers
Answer:
60% of the people surveyed were satisfied with the car
Step-by-step explanation:
1140 satisfied people / 1900 total people = 0.60 = 60% satisfied people
What does Point P on the number line represent? (Use the hyphen for negative numbers, such as −9)
Number line from negative 8 to positive 10 in increments of 1 is shown. Only the even numbers are labeled. A point labeled P is placed at the third tick mark to the left of 0.
(5 points)
Answers
Answer:
P = -3, each line in the negative direction is 1 number
so you would have -1, -2, -3 , -4, etc.
P is on the -3 line.
See attached picture.
Step-by-step explanation:
factor this polynomial completely x^2-10x+25
Answers
x^2-10x+25
=x^2-5x-5x+25
x(x-5)-5(x-5)
=(x-5)(x-5)
x=5 , x=5
hope it's helpful to you
[tex]x^2 -10x +25\\\\=x^2 -2 \cdot 5 \cdot x +5^2\\\\=(x-5)^2\\\\=(x-5)(x-5)[/tex]
hlep me plsssssssssssssssssssssssss
Answers
{(-1, -3),(0,-1),(1,1),(2,3),(3,5)}
Answer:
B.
Step-by-step explanation:
It is not A because it does not make sense and does not match up.
It Is not C because that is just points and it is asking for a function.
D is wrong.
So It is B.
Here is the graph for B. It matches up.
[tex]\mathrm{Axis\:interception\:points\:of}\:2x-1:\quad \mathrm{X\:Intercepts}:\:\left(\frac{1}{2},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:-1\right)[/tex]
[tex]\mathrm{Slope\:of\:}2x-1:\quad m=2[/tex]
Need help on True or False PLEASE answer!!!!
Answers
Answer:
Step-by-step explanation:
1. False
2. False
3. True
4. True
5. True
6. True
7. True
8. True
9. True
Hassan made a vegetable salad with 2 3/8 pounds of tomatoes, 1 1/4 pounds of asparagus, and 2 7/8 pounds of potatoes. How many pounds of vegetables did he use altogether?
Btw please show work.
Answers
Step-by-step explanation:
OK so
Tomatoes = 2 3/8 = 19/8 (turned into improper fraction)
Asparagus = 1 1/4 =5/4
Potatoes = 2 7/8 = 23/8
Total vegetables used =
19/8 + 5/4 + 23/8 = 42/8 + 5/4 = 42+10/8 =52/8
Answer is 52/8 = 6.5
Answer : 52/8 pounds were used altogether
See picture for solution.
help me please please
Answers
Answer:
17/18
Step-by-step explanation:
To add fractions, you need to have common denominators. (4/9)*(2/2)=8/18.
Now that they have common denominators, you can add 8 and 9 to get 17. So, the answer would be the second one, 17/18.
Answer:
r u just cheating ur way through a whole test lol
Step-by-step explanation:
its B or 17/18
Two parallel lines are cut by a transversal, as shown below. Solve for b. Then explain your reasoning.
Answers
Answer:
b = 14
Step-by-step explanation:
Since both angles are diagonal each other, they are equal to each other.
5b = b + 56
-b -b (subtract b from both sides)
4b = 56
4 4 (divide both sides by 4 to solve for b)
b = 14
Genes are sections of DNA that code for a particular trait. Genes are?
Answers
Answer:
Genes are DNA transferred to off spring by parents
Answer:
Genes are sections of DNA that code for a particular trait. Genes are nucleic acids.
Step-by-step explanation:
Which of the following cannot be used to prove that two triangles are congruent?
A.AAA
B.ASA
C.SSS
D.HL
Answers
Answer:
A
Step-by-step explanation:
:)
hope it helps
25. Solve for x:
4x-3/2=5/3
Answers
Answer:
X = 19/24
Step-by-step explanation:
Move the constant: 4x = 5/3 + 3/2
Add The Fractions: 5/3 + 3/2 = 19/6
Divide Both sides by 4: 4x/4 = 0. 19/6 ÷ 4 = 19/24
Riley is saving up to buy a new television. She needs a total of $966.42. Riley has saved $200.92 already and earns $76.55 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television
Answers
Answer:
10 weeks
Step-by-step explanation:
76.55x+200.92=966.42
76.55x=966.42-200.92
76.55x=765.5
x=765.5/76.55
10
pls help me, pls pls plss help
Answers
Answer:
1. given
2. inscribed circle theorem
3. substitution
4. definition of congruent angles
Answer asap! Need help before I go to sleep.
Answers
Answer:
Step-by-step explanation:
Parallel lines have identical slopes
4x - 7y = 9
7y = 4x - 9
y = (4/7)x - 9/7
so the parallel line has form
y = (4/7)x + b
plug in the point on the line
3 = (4/7)7 + b
b = -1
y = (4/7)x - 1
As you did not tell us where you live and what time you intend to go to bed, we have NO way of knowing your actual deadline
Sammy's Chipmunk & Squirrel Observations
For a science project, Sammy observed a chipmunk and a squirrel stashing
acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The
squirrel hid 4 acorns in each of the holes it dug. They each hid the same number
of acorns, although the squirrel needed 4 fewer holes. How many acorns did the
chipmunk hide?
Answers
Answer:12 accorns
Step-by-step explanation:
If they each hid the same number of acorns, although the squirrel needed 4 fewer holes, the chipmunk hid 3 acorns in each hole
Let's assume the number of holes the chipmunk dug is 'c', and the number of acorns it hid in each hole is 'x'. Similarly, let's assume the number of holes the squirrel dug is 's', and the number of acorns it hid in each hole is 'y'.
According to the information provided, the chipmunk hid 3 acorns in each of the holes it dug, so x = 3. The squirrel hid 4 acorns in each of the holes it dug, so y = 4.
Both the chipmunk and squirrel hid the same number of acorns, so cx = sy.
Also, the squirrel needed 4 fewer holes, so s = c - 4.
Now, we can use the information to set up a system of equations:
cx = sy
c - 4 = s
Substitute the value of s from the second equation into the first equation:
c(c - 4) = 3(c - 4)
Expand the equation:
c² - 4c = 3c - 12
Now, bring all terms to one side of the equation:
c² - 4c - 3c + 12 = 0
Combine like terms:
c² - 7c + 12 = 0
Now, factor the quadratic equation:
(c - 3)(c - 4) = 0
Now, set each factor to zero and solve for 'c':
c - 3 = 0 => c = 3
c - 4 = 0 => c = 4
Since the chipmunk hid 3 acorns in each hole, the correct answer is The chipmunk hid 3 acorns.
To learn more about equations click on,
https://brainly.com/question/28975436
#SPJ2
Suppose you select 4 skittles at random from the bowl. What is the proba- bility exactly 1 of those skittles is green
Answers
Answer:
1/4
Step-by-step explanation:
4 skittles and one being green
Answer:
4/5
Step-by-step explanation:
According to the Wrigley's Consumer Care Department, the fruit candies are produced in equal proportions— 20% of each of the five colors (green, red, orange, yellow, and purple). However, although these candies are made in equal proportions, the individual Skittles bags are filled by weight and by machines but on average I'd say 4/5 chance its a green.
6 divided by x squared
Answers
Answer:
I think x should be equal to 0.
The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one of the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.) You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left on the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one?
Answers
Answer:
I'd swap with one on the table (the left one) but with my luck it would be a sword made of rubber
What is the diameter of circle 0?
Answers
Answer:
8
Step-by-step explanation:
diameter is the radius times 2
Write the following phrases as ratios in lowest terms. 1) 3 out of 8 balloons, 2) 5 losses to 7 wins,3) 4 girls to 5 boys,4) 6 books for every 18 students, 5) 2 cars to 3 trucks,6) 11 out of 18 games
Answers
Answer:
1) 3:8
2)5:7
3)4:5
4)1:3
5)2:3
6)11:18
Help Will give Branliest
Answers
need help solving this
Answers
Answer:
x ≈ 41.6°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{JK}{KL}[/tex] = [tex]\frac{80}{90}[/tex] = [tex]\frac{8}{9}[/tex] , then
x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{9}[/tex] ) ≈ 41.6° ( to the nearest tenth )
Which inequality matches the graph? A)x >4.B)x < 4.C)x = 4.D)x >_ 4 the line is at bottom of it for d
Answers
Answer: D
Step-by-step explanation: less than or equal to 4. graph leads to negative
A rule for creating a pattern is given below.
Rule: Subtract 7 from 2 to get y.
Which ordered pair, (x, y), works for the rule?
Answers
Answer:
(any real number, 5)
Step-by-step explanation:
Well given that y=7-2 and that y=5, we do not know the value of x, therefore x could be any real number with y being 5. I'm pretty sure that answered your question. So, a example of an ordered pair that would fit this rule would be say (5,5) or (7,5)