Answers
Answer:
\(\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}\)
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegral NotationIntegration Rule [Reverse Power Rule]: \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Rule [Fundamental Theorem of Calculus 1]: \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)
Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Property [Addition/Subtraction]: \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)
Integration Property [Splitting Integral]: \(\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx\)
Step-by-step explanation:
Step 1: Define
Identify.
\(\displaystyle f(x) = \left \{ {{9x^9 ,\ 0 \leq x \leq 1} \atop {4x^3 ,\ 1 \leq x \leq 2}} \right.\)
\(\displaystyle \int\limits^2_0 {f(x)} \, dx = \ ?\)
Step 2: Integrate
[Integral] Rewrite [Integration Property - Splitting Integral]: \(\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {f(x)} \, dx + \int\limits^2_1 {f(x)} \, dx\)[Integrand] Substitute in function: \(\displaystyle \int\limits^2_0 {f(x)} \, dx = \int\limits^1_0 {9x^9} \, dx + \int\limits^2_1 {4x^3} \, dx\)[Integrals] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \int\limits^1_0 {x^9} \, dx + 4 \int\limits^2_1 {x^3} \, dx\)[Integrals] Integration Rule [Reverse Power Rule]: \(\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{x^{10}}{10} \bigg) \bigg| \limits^1_0 + 4 \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^2_1\)Integration Rule [Fundamental Theorem of Calculus 1]: \(\displaystyle \int\limits^2_0 {f(x)} \, dx = 9 \bigg( \frac{1}{10} \bigg) + 4 \bigg( \frac{15}{4} \bigg)\)Simplify: \(\displaystyle \int\limits^2_0 {f(x)} \, dx = \frac{159}{10}\)Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:
Step-by-step explanation:
\(\int\limits^1_0 {9x^9} \, dx +\int\limits^2_1 {4x^3} \, dx\)
=\(\frac{9x^{10}}{10} |_0^1 + x^4|_1^2\)
\(=\frac{9}{10}+2^4 -1 = 15\frac{9}{10}\)
Related Questions
Let u =(3,4). What is 3u?
(6,7)
(6,12)
(9,7)
(9,12)
Answers
If u equals (3,4), 3 times 3 is nine, and 4 times 3 is 12. That’s makes 3u (9,12)
The value of 3u is (9, 12).
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given:
u= (3, 4)
Now, we have to find 3u for which we have to multiply each coordinate by 3 as
x- coordinate : 3 x 3= 9
and, y- coordinate : 4 x 3= 12
So, 3u = 3(3, 4) = (9, 12)
Hence, the value of 3u is (9, 12).
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A line has a slope of 2/3 while another line has a slope of -3/2 What can you conclude about the lines
Answers
Answer:
They are perpendicular
Step-by-step explanation:
If 2 slopes are negative reciprocals of each other, it means they are perpendicular
Answer:
The lines are perpendicular because they have opposite reciprocal slopes.
Step-by-step explanation:
y=7/x, x≠0 need the graph answer!!
Answers
Answer:
so the first picture is it graphed without solving it and the second graph is the answer to it graphed
Step-by-step explanation:
D9: 36
A bus has 14 rows with 4 passenger seats in each row. What is the total number
of passenger seats on the bus?
A
18
B
46
48
D 56
Answers
56 passenger seats
Can someone pls help
Answers
Answer: Graph A and Graph C hope this helps
Step-by-step explanation:
Answer:
A and C
Step-by-step explanation:
They both pass though the origin.
Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'. What are the coordinates of X'Y'Z'?
Answers
Answer:
59
Step-by-step explanation:
6 plus 4 equals 8 plus 9
Identify the coordinates of each vertex of triangle XYZ.
Apply the 90° counterclockwise rotation rule, which states that when rotating a point 90° counterclockwise about the origin, the new coordinates of the point will be (-y, x).
Substitute the coordinates of each vertex into the rotation rule to find the coordinates of the corresponding vertex in X'Y'Z'.
For example, let's say that the coordinates of triangle XYZ are:
X = (2, 3)
Y = (-1, 4)
Z = (0, -2)
To find the coordinates of X'Y'Z', we can apply the rotation rule to each vertex as follows:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Therefore, the coordinates of X'Y'Z' after rotating triangle XYZ 90° counterclockwise about the origin are:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Note that the order of the vertices may change after the rotation, but the coordinates of each vertex will correspond to the same vertex in the original triangle.
The following quadrilateral is a parallelogram. Solve for x, y, and z.
Answers
Answer:
X = 44Y = 31Z = 105Step-by-step explanation:
The measurements of a quadrilateral will add up to be 360. Additionally, we know these two triangles created within the parallelogram will be congruent, so their corresponding angles will also be congruent by CPCTC.
(44 * 2) + (105 * 2) + (31 * 2) = 360
Have a nice day, fam. Spread The Love.
what is the simplified for the expression below?
Answers
Answer:
Option 1: \(-2x+3\)
Step-by-step explanation:
\(-\frac{1}{5}\left(5x+20\right)-\frac{1}{4}\left(4x-28\right)\)
Expand:
\(-\frac{5x+20}{5}-\frac{4x-28}{4}\)
\(-\left(x+4\right)-\left(x-7\right)\)
Remove brackets:
\(-x-4-x+7\)
Group similar terms together:
\(-x-x-4+7\)
\(-2x+3\)
find a solution y = 3 x − 4
Answers
Answer: The equation y = 3x - 4 is a linear equation in slope-intercept form, where the slope (3) is the coefficient of x and the y-intercept (-4) is the constant term. To find a solution for this equation, we can substitute a specific value of x and solve for the corresponding value of y.
For example, if we let x = 2, we can substitute it into the equation:
y = 3(2) - 4 = 6
So the solution for x=2 is y=6
We can also graph this equation, it will be a straight line with slope 3 and y-intercept (-4)
Step-by-step explanation:
Simplify the following expression.
5 [13 + 10 = (3 + 2)] + 9 x 2
Answers
Answer:
i BELIEVE ITS
Step-by-step explanation:
5 [13 + 10 = (3 + 2)] + 9 x 2
65+50=25+18
115=43
f(x)=4x^2-7x-15 how do i factor it and find the x-intercepts? Also please describe the end behavior of the graph of f(x) and the steps you would use to graph. Pleaseee im really lost
Answers
Given:
The function is
\(f(x)=4x^2-7x-15\)Required:
Find the x-intercepts and describe the end behavior of the graph of f(x).
Explanation:
The given function is:
\(f(x)=4x^{2}-7x-15\)To find the x-intercepts put f(x)=0
\(4x^2-7x-15=0\)This is a quadratic equation solved by using the middle term splitting method.
\(\begin{gathered} 4x^2-12x+5x-15=0 \\ 4x(x-3)+5(x-3)=0 \\ (x-3)(4x+5)=0 \end{gathered}\)\(\begin{gathered} x-3=0 \\ x=3 \end{gathered}\)\(\begin{gathered} 4x+5=0 \\ x=-\frac{5}{4} \\ x=-1.25 \end{gathered}\)Thus the x-intercept are: -1.25 and 3.
Compare the given equation with the standard equation
\(y=ax^2+bx+c\)\(a=4,b=-7,c=-15\)The vertex is (h,k).
\(\begin{gathered} h=-\frac{b}{2a} \\ h=-\frac{-7}{2\times4} \\ h=\frac{7}{8} \\ h\approx0.9 \end{gathered}\)\(\begin{gathered} k=f(h) \\ k=f(0.9) \\ k=4(0.9)^2-7(0.9)-15 \\ k=3.24-6.3-15 \\ k\approx-18.1 \end{gathered}\)Thus the vertex of the parabola is:
\((0.9,-18.1)\)We will plot the points of the vertex and the x-intercepts and then draw the graph of the parabola as:
Here the leading coefficient a = 4>0
So the parabola opens upwards.
In the given function the degree is 2 which is even so as
\(\begin{gathered} x\rightarrow\infty,\text{ f\lparen X\rparen}\rightarrow\infty \\ x\operatorname{\rightarrow}\times-\infty,\text{f}\operatorname{\lparen}\text{X}\operatorname{\rparen}\operatorname{\rightarrow}\infty \end{gathered}\)Final Answer:
As explained in the explanation part.
Dominic is going to invest $1,800 and leave it in an account for 17 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Dominic to end up with $4,700?
Answers
Answer: 5.8%
Step-by-step explanation: got it right lol
The Hudson family is saving for a
family vacation to Disney World.
They determine that the trip will
cost $3,200. Mr. and Mrs.
Hudson have already set aside
$1,500 for the trip. If they leave
in 16 weeks, then how much
will they need to save
each week?
Answers
The amount of money that Hudson will need to save each week is $106.25.
How to calculate the value?From the information, they determine that the trip will cost $3,200. Mr. and Mrs. Hudson have already set aside $1,500 for the trip.
Let the amount saved each week be represented as w.
Based on the information given, this will be illustrated as:
1500 + 16w = 3200
Collect like terms
16w = 3200 - 1500
16w = 1700
Divide
w = 1700 / 16
w = 106.25
The amount is $106.25.
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Select all the algebraic expressions equivalent to m5/n5
A: (mn–1)5
b: (mn)5
C :[(mn2)]–3
d: (mn)–5
e: m5n–5
Answers
244-33456/3456*345+13.55-2=
Answers
The order of operations (PEMDAS) states that we should perform multiplication and division before addition and subtraction. Using this order, we get:
244 - (33456 / 3456) * 345 + 13.55 - 2
= 244 - 97.02 * 345 + 13.55 - 2
= 244 - 33494.1 + 13.55 - 2
= -33238.55
Therefore, 244-33456/3456*345+13.55-2 = -33238.55.
Simplify 5(x - 2) - 3x + 7.
A. 8x - 3
B. -10x + 25
C. 2x-5
D. 2x - 3
Answers
2x-3
Step-by-step explanation:
5(x-2) is 5x-10 then add the -3x + 7, add 5x and -3x to get 2x then add -10 and 7 and get 3 so its gonna be D. 2x-3
Answer:
D. 2x - 3
Step-by-step explanation:
5(x - 2) - 3x + 7 = 5 · x - 5 · 2 - 3x + 7 = 5x - 10 - 3x + 7 = 2x - 3
What is the slope of the line that passes through the points ( 9 , 5 ) (9,5) and ( 21 , − 5 ) (21,−5)? Write your answer in simplest form.
Answers
Answer:
-5/6
Step-by-step explanation:
(9, 5) and (21, -5)
slope = m = (difference in y)/(difference in x)
m = (-5 - 5)/(21 - 9)
m = -10/12
m = -5/6
Answer: -5/6
The slope of the line that passes through points (9,5) and (21,-5) is -5/6.
We can use the two-point formula to find the slope for the given line. The formula is as follows:
(y2 - y1) = m*(x2 - x1)
Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.
In the given case:
x1=9, x2=21
y1=5, y2=-5
Using these values in the two-point formula, we get:
(-5-5)=m*(21-9)
-10=m*12
m=-10/12
m=-5/6
Hence the slope of the line is -5/6.
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Khadija bought 8 chicken wings for $10.40. If Khadija spent $3.90, how many chicken wings did she buy?
Answers
Answer:
she bought 3 chicken wings
Step-by-step explanation:
8c = 10.4 --> where c is the cost of a chicken wing
c = 10.4 divided by 8
= 1.3
xc = 3.9 (x = number of chicken wings)
1.3x = 3.9
x = 3.9 divided by 1.3
which is 3
You have 60 students in the café assigned the numbers 1-60. You select the first five odd numbers to take your survey. Those students picked are numbers
Answers
Answer:
The answer would be 1, 3, 5, 7, 9.
Hey I was wondering if you can help me with this question
Answers
According to the given diagram, x is the complement to the angle that is vertical to the known angle.
Vertical angles have the same measure, it means that the complement of x is 73°.
Using the definition of complementary angles, we have that the sum of x and 73 is 90, find x using this information:
\(\begin{gathered} x+73=90 \\ x=90-73 \\ x=17 \end{gathered}\)x has a value of 17.
Answer:
73°
Step-by-step explanation:
Because it is a ray intercepting two parallel lines... the are the same if they are across from each other. therefore it is 73°
2
6. В одном мотке было 75 сантиметров проволоки.
После того как от проволоки отрезали несколько
сантиметров, в мотке осталось 32 сантиметра.
Сколько сантиметров проволоки отрезали от
мотка?
Answers
Answer:
Step-by-step explanation:
После того как от проволоки отрезали несколько
сантиметров, в мотке осталось 32 сантиметра.
Сколько сантиметров проволоки отрезали от
мотка?
La suma de los ángulos externos de un triángulo es 360º.?
Answers
Answer:
children formerly truths former formerly upright justification
Find the measure of the indicated angle.
99⁰
96⁰
98⁰
92°
L
120°
K
N
M
64
Answers
Answer:
? = 92°
Step-by-step explanation:
the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°
I will mark Brainlyist write a equation for the line shown below
Answers
Answer:
5 1/2 and -5 1/2
Step-by-step explanation:
thats just what the arrows point to
Working alone, Mr. Tough can grade the final exams in 12 hours. His assistant, Mrs. Nice, cam grade the same exams in 15 hours. What fraction of the exams can Mr.Tough and Mrs.Nice grade in 1 hour if they work together?
Answers
Answer:
9n/60
Step-by-step explanation:
add 1/12 + 1/15 which = 5/60 + 4/60.
= 9/60
YAY!!!!!!!
The fraction of the exams that Mr Tough and Mrs Nice grade in 1 hour if they work together is 3/20
What are fractions?In Maths, a fraction is used to represent the portion/part of the whole thing. A fraction has two parts, namely numerator and denominator. There are proper fractions, improper fractions and mixed fractions.
Example: 2/5, 1/4 etc.
How to solve Work and Time problems:We will this equation,
rate × time = work done
For this problem:
Mr Tough's rate:
Mr Tough's rate × 12 hours = final exam
Mr Tough's rate = 1/12
Mrs.Nice's' rate:
Mrs .Nice's' rate × 15 hours = final exam
Mrs .Nice's' rate = 1/15
To make this into a solvable equation, find the total time (T) needed for Mr Tough and Mrs.Nice to grade the final exam. This time is the sum of the rates of Mr Tough and Mrs.Nicea, or:
Total time:
T(1/12 hours + 1/15 hours) = final exam
T = final exam / (1/12 + 1/15)
Simplifying we get,
T = final exam / (0.15)
Now, to finish in 1 hour we will find what fraction of the final exam they can grade, so taking T = 1 hour,
1 hour = final exam / (0.15)
By further simplifying,
final exam = 1 × 0.15
= 0.15
= 15/ 100
= 3/20
Therefore, 3/20 fraction of the final exam they can grade if they work together for 1 hour.
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Helppppppppppp unicorn
Answers
Answer:
angle BAC = angle DAC it is correct answer of this question ....
plz mark my answer as brainlist plzzzz vote me also so
Select the correct answer. Which function represents the inverse function of the function f(x)=x^2 +5
Answers
Answer:
f^(-1)(x) = ±√(x - 5).
Step-by-step explanation:
Replace f(x) with y: y = x^2 + 5.
Swap the x and y variables: x = y^2 + 5.
Solve the equation for y. To do this, we'll rearrange the equation:
x - 5 = y^2.
Take the square root of both sides (considering both positive and negative square roots):
±√(x - 5) = y.
Swap y and x again to express the inverse function:
f^(-1)(x) = ±√(x - 5).
what is 7/14 fractions im in class and i dont know.? Can anyone help me????.
Answers
Answer:
\(\frac{7}{14} = \frac{1}{2}\)
Step-by-step explanation:
Answer:
7/14 as a simplified fraction is 1/2
Step-by-step explanation:
if you divide the numerator and denominator by 7 then 7(numerator) simplifies to 1 and 14(denominator) simplifies to 2
Find the height of the tower using the information given in the illustration.
Answers
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
14=14^_
HELPPP!!!!!
Answers
Answer:
0
Step-by-step explanation:
14=14 so plus 0 is 14 i gues