Answer:
[tex]\displaystyle \int {xe^{7x}} \, dx = \frac{e^{7x}}{7} \bigg( x - \frac{1}{7} \bigg) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {xe^{7x}} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = x[/tex][u] Basic Power Rule: [tex]\displaystyle du = dx[/tex]Set dv: [tex]\displaystyle dv = e^{7x} \ dx[/tex][dv] Exponential Integration [U-Substitution]: [tex]\displaystyle v = \frac{e^{7x}}{7}[/tex]Step 3: integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \int {\frac{e^{7x}}{7}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{1}{7} \int {e^{7x}} \, dx[/tex]Step 4: Integrate Pt. 3
Identify variables for u-substitution.
Set u: [tex]\displaystyle u = 7x[/tex][u] Basic Power Rule [Derivative Property - Multiplied Constant]: [tex]\displaystyle du = 7 \ dx[/tex]Step 5: Integrate Pt. 4
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{1}{49} \int {7e^{7x}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{1}{49} \int {e^u} \, dx[/tex][Integral] Exponential Integration: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{e^u}{49} + C[/tex][u] Back-Substitute: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{e^{7x}}{49} + C[/tex]Factor: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{e^{7x}}{7} \bigg( x - \frac{1}{7} \bigg) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
x - 4y = 1 and 3x + 2y = -11. What is the solution to the system of equations?
Answer:
x=-3 y=-1
Step-by-step explanation:
The solution is
The value of x = -3
The value of y = -1
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be = A
Now , the value of A is
x - 4y = 1 be equation (1)
Let the first equation be = B
Now , the value of B is
3x + 2y = -11 be equation (2)
Now , on simplifying both equations , we get
Multiply equation (1) by 3 , we get
3x - 12y = 3 be equation (3)
Subtracting equation (2) from equation (3) , we get
-12y - 2y = 3 - ( -11 )
-14y = 14
Divide by -14 on both sides of the equation , we get
y = -1
So , the value of y = -1
Substitute the value of y in equation (1) , we get
x - 4y = 1
x - 4 ( -1 ) = 1
x + 4 = 1
Subtracting 4 on both sides of the equation , we get
x = -3
So , the value of x = -3
Hence , the value of x is -3 and value of y is -1
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The sum of 8 times b and twice g is equal to 32
write the equation of the line that is parallel to y=4x-1 and passes through the point (4.9)
9514 1404 393
Answer:
y = 4x -7
Step-by-step explanation:
Rearranging the slope-intercept for equation, we can find the intercept:
y = mx +b
y -mx = b . . . . . subtract mx
We know the slope of the parallel line is the same as that of the given line (m=4), so we only need to find 'b'.
b = 9 -4(4) = -7
The desired equation is ...
y = mx +b
y = 4x -7
Explain your answer
Thank you so much !
Will give brainlst
Answer:
D
Step-by-step explanation:
The amount of oil and natural gas a given region produces is not always proportionate to the size of its proven reserves. For example, the Middle East contains approximately 50 percent of the world’s proven reserves but accounts for only about 30 percent of global oil production (though this figure is still higher than in any other region). The United States, by contrast, lays claim to less than 2 percent of the world’s proven reserves but produces roughly 16 percent of the world’s oil.
Which of the following is a quadratic equation whose roots are 3 and -1?
Answer:
JK up FMyRick they rock TBD Trinity scrump TV TM in
Is The order that you perform the similarity transformations important?
Answer:
yes i think it is
Step-by-step explanation:
The product of two numbers is 42.63. If one number is 21. What is the other number
Answer:
21.63 is the other number
Step-by-step explanation:
21 + 21.63 equals 42.63
Answer:
Hi dear. I'm helping you to solve the question and in return you help me with my question.
Step-by-step explanation:
Question : The product of two numbers is 42.63. If one number is 21. What is the other number?
Solution :-
Product of two numbers = 42.63
One of the number = 21
Therefore , the other number = 42.63 ÷ 21 = 2.03
Hope my solution helps you and don't forget to help me with maths questions in return...
5th grade math. Correct answer will be marked brainliest.
Simplify
8sqrt48-6sqrt75+7sqrt80
Answer:
2[tex]\sqrt{3}[/tex] + 28[tex]\sqrt{5}[/tex]
Step-by-step explanation:
= 8 [tex]\sqrt{16}[/tex][tex]\sqrt{3}[/tex] - 6[tex]\sqrt{25}[/tex][tex]\sqrt{3}[/tex] + 7[tex]\sqrt{16}[/tex][tex]\sqrt{5}[/tex]
= 8(4)[tex]\sqrt{3}[/tex] - 6(5)[tex]\sqrt{3}[/tex] + 7(4)[tex]\sqrt{5}[/tex]
= 32[tex]\sqrt{3}[/tex] - 30[tex]\sqrt{3}[/tex] + 28[tex]\sqrt{5}[/tex]
= 2[tex]\sqrt{3}[/tex] + 28[tex]\sqrt{5}[/tex]
1/3 divided by 3 1/2
Answer:
2/21
Step-by-step explanation:
The question states:pat needs at least 13 days to make a large order of cupcakes which inequality shows how many ,d, pat needs to make all the ordered cupcakes
Please help first to answer I'll mark brainliest
Answer:
D
Step-by-step explanation:
Elimination method 10x-4y=-8
-5x+6y=10
The volume inside a rectangular storage room is 2061 feet The room is 9 feet high find the area of the floor
Answer:
229 ft²
Step-by-step explanation:
Note that the volume is 2061 ft³, not 2061 ft.
area of floor = volume÷height = (2061 ft³)/(9 ft) = 229 ft²
PLS HELP ILL GIVE BRAINLIEST!
Answer:
C = 55
O = 55
CRA = 64
ORT = 64
T = 61
Answer:
C = 55
O = 55
CRA = 64
ORT = 64
T = 61
Step-by-step explanation:
Determine whether the ratios 1:2 and 3:4 are equivalent
Answer:
They are not equivalent
Step-by-step explanation:
1:2 is the same as 2:4
2:4 does not equal 3:4
What type of angles are these?
Complementary, Supplementary, or Neither
Got It? Do these problems to find out.
-15
85° | 90°
75
Answer:
a: Neither; b: Complementary
Step-by-step explanation:
Complementary= 90 degrees
Supplementary= 180 degrees
For letter a. the answer is neither because 85 +90= 175 degrees, not 90 or 180 degrees.
For letter b. the answer is complementary because 75 +15= 90 degrees.
Sue's bakery sold 850 donuts last week. This week, the number of donuts sold increased 12%. HOW MANY MORE donuts were sold this week as compared to last week
Answer:
102 donuts
Step-by-step explanation:
12% of 850 is 102, so since 12% more donuts are sold this week, we sold 102 more donuts this week compared to last week.
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
5. Find the slope of this line.
Answer:
3/2
Step-by-step explanation:
rise/run
A survey shows that three out of every five teenagers at a particular school with cell phones use text messaging. In a group of 90 teenagers, how many would you expect use text messaging? 34 54 56 150
Answer:
Out of a group of 90 there would be 54 messaging
Step-by-step:
messaging is a weird word
Sarah leans a 20 ft ladder against
the side of her house so that the
base of the ladder is 14 ft from the
house ABOUT how far up the side
of the house does the ladder reach?
Answer:
(a) 14
this is what i got
63 over 22 as a decimal
Answer:
Step-by-step explanation:
63/22 = 2.86363 = 2.86
(x - 5)2 + (y-(-3))2 = 34 (x - 5)2 + ( + 3)2 = 34 Exercises 12.2 Complete the following: 1. Find the equation of the circle having the given center and ra (a) C(0,0), r= 3 (c) C(4, 3), r = 5 (d) C(2, (b) C(-2.
Answer:
Step-by-step explanation:
The general equation of the circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Center = c = (h,k) , radius = r
if C = (0,0) , r = 3
The equation will be :
(x-0)^2+(y-0)^2=3^2
[tex]x^2+y^2=9[/tex]
help please asap i will give you a heart if you do
Answer:
30
Step-by-step explanation:
2(6)=12
3(6)=18
12+18=30
Step-by-step explanation:
its 30 2(6)=12 3(6)=18
30
Inverse of
f(x) = 4x+16
In a right triangle, the hypotenuse has endpoints XY, shown on the graph.
On a coordinate plane, line X Y has points (negative 4, 2), (negative 1, negative 3).
If Z represents the third vertex in the triangle and is located in the second quadrant with integer coordinates, what is the length of YZ?
3
4
5
6
9514 1404 393
Answer:
5
Step-by-step explanation:
A graph can be helpful. It shows possible integer coordinates of Z could be ...
(-1, 2) or (-5, 1)
These have distances 5 and 4√2 from Y, respectively. Of these, only the length YZ = 5 appears on your list of possible answers.
__
The hypotenuse of a right triangle is the diameter of the circumcircle. That is, the right angle vertex (Z) appears on a circle whose center is the midpoint of the hypotenuse. Here, that circle center is C = (-4-1, 2-3)/2 = (-5/2, -1/2). The given point Y differs from this by C - Y = (-5/2 -(-1), -1/2 -(-3)) = (-3/2, 5/2). So, a point with integer coordinates will be 2×(5/2) = 5 units above point Y, which puts it in the 2nd quadrant.
__
Adding any of the 8 combinations (±3/2, ±5/2) or (±5/2, ±3/2) to the circle center coordinates will result in integer coordinates for the right angle vertex. Of these, only the ones listed above are in the second quadrant. A couple are on the y-axis, and two of the possibilities are X and Y. The other two are in the third quadrant.
Cary puts $500 into a savings account that earns 5.5% annually. The amount in her account can be modeled by C(t) = 500(1.055)t, where t is the time in years.
Write the expression best approximates the amount of money in her account using a weekly growth rate. (DO NOT ROUND ANY NUMBERS)
***Just need some clarification, it says there is annual growth rate but the question is asking that I change the function into weekly growth rate so...how do I do that?
Answer:
Answer: a) A(t)= $500(1.055)^t
b) Amount after 9 years A(9) = $809.55
Amount after 17 years A(17) = $1242.40
sorry if im wrong
Step-by-step explanation:
HELP FAST PLSSSS IM DESPERATE RLLY
Marta drew a rectangular poster.
·The length of the rectangle was
2/3 of a yard.
·The width of the rectangle was
3/4 of a yard.
What was the area of Marta’s rectangle?
A. 1/2 yard
B. 5/12 yard
C. 5/7 yard
D. 1 5/12 yards
Answer:
1/2 yard
Step-by-step explanation:
Multiply the top numbers (the numerators). Which would give you 6.
Multiply the bottom numbers (the denominators). Which would leave you with 12.
Simplify the fraction if needed. 6/12 can be simplified down to 1/2
In the figure shown what is the value of x?
Answer:
23 is the right answer hope it's helps you
The value of x from the given congruent triangles is 23 units.
In the figure ΔABC and ΔDEF are given.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Consider, ΔABC and ΔDEF, we have
AB=DE (Given)
∠BAC=∠EDF (Given)
AC=DF (Given)
So, ΔABC ≅ ΔDEF
We know that, by CPCT
BC=FE
⇒ x-4=19
⇒ x=23 units
Therefore, the value of x from the given congruent triangles is 23 units.
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Do you expect the difference between the 25th percentile and the median (50th percentile) to be Group of answer choices Larger than the difference between median and 75th percentile. We need to see the actual data to answer this question Smaller than the difference between median and 75th percentile. Equal to the difference between median and 75th percentile.
Answer:
Equal to the difference between median and 75th percentile.
Step-by-step explanation:
xth percentile:
If a measure is said to be in the xth percentile, it means that x% of the measures are smaller than it, and (100-x)% are larger.
Distance between percentiles:
If the difference between two percentiles is the same, the difference between the measures should also be the same.
Median:
The 50th percentile is called median.
In this question:
75th percentile - 50th percentile = 25
50th percentile - 25th percentile = 25
The differences should be equal.