Can someone check whether its correct or no? this is supposed to be the steps in integration by parts
Answers
Answer:
[tex]\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x[/tex]
[tex]\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:[/tex]
[tex]\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x[/tex]
Use integration by parts.
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
[tex]\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)[/tex]
[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]
Substituting the defined parts into the formula:
[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}[/tex]
[tex]\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:[/tex]
[tex]\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)[/tex]
[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]
[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}[/tex]
Therefore:
[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x[/tex]
[tex]\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:[/tex]
[tex]\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}[/tex]
Divide both sides by 2:
[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}[/tex]
Rewrite in the same format as the given integral:
[tex]\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]
Differentiation Rules used:
[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\sin(k)$}\\\\If $y=\sin(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=k\cos(kx)$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\cos(k)$}\\\\If $y=\cos(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=-k\sin(kx)$\\\end{minipage}}[/tex]
Integration Rules used:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $e^{kx}$}\\\\$\displaystyle \int e^{kx}\:\text{d}x=\dfrac{1}{k}e^{kx}+\text{C}$\end{minipage}}[/tex]
Related Questions
Express verbal statement in algebraic form.
The cost to rent a sailing boat at Catalina Island is $370 per day
plus $80 for every hour of use. What is the maximum number of
hours the sail boat can be rented for each day, if the rental cost is
not to exceed $1090 per day?
Answers
Answer:
370 + 80x ≤ 1090
Step-by-step explanation:
By using letter variables for the unknown numbers, we can break down the question into mathematical terms:
If the cost is $370 per day and the number of days is unknown, we can substitute the number of days with a placeholder. In this case, it'll be a variable such as x. So the cost can be represented by $370y.
If the cost is $80 per hour and the number of hours is unknown, we can substitute the number of hours with a placeholder. In this case, it'll be a variable such as y. So the cost can be represented by $80x.
The questions asks for the total cost not to exceed $1090 per day. This means that we know that the number of days is 1. We're trying to find the maximum number of hours, so our equation will combine the costs of both day costs and hour costs:
$370 (1 day) + $80 (x hours) ≤ $1090 per day
The symbol is the equal to or less than symbol, meaning the combined total costs is either equal to $1090 or less than it.
To simplify this, we can rewrite it as:
370 + 80x ≤ 1090
Gabrielle's age is three times Mikhail's age. The sum of their ages is 36. What is Mikhail's age?
Answers
Answer:
Gabrielle is 27
Mikhail is 9
Step-by-step explanation:
g = 3m
g + m = 36
since g = 3m we can substitute it in the equation
g + m = 36 as
3m + m = 36
4m = 36
m = 9
3m = 27 which is g
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What is the area of the polygon given below?
Answers
Answer:
340 i am pretty sure
Step-by-step explanation:
PLEASE HELP ME!!!!!!!!!
Answers
Answer:
option 4 and option 3 are the answers respectively
Answer:
[tex] \sqrt{ {2}^{3} } \\ \sqrt{3} \\ .............[/tex]
2 Math questions! Offering the brainliest to who answers
Answers
Answer:
first one L second one D
Step-by-step explanation:
Can someone help me? I’ll give brainliest to whoever gets it right first
Answers
Answer:
72 Degrees
Step-by-step explanation:
We know that its 72 because of VAT, the vertical angle theorem.
Detailed Explanation:
In the figure the given angles are Vertically Opposite Angles. Vertically Opposite Angles are always Equal.
Therefore, x = 72°
find in factord form -9n+n^2=0
Answers
Answer:
n(-9+ n) =0
Step-by-step explanation:
-9n+n^2=0 Kind of use 'reverse distributive' property
n (-9 + n) = 0
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
Answers
Step-by-step explanation:
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
2x+4+5x+25=4x-32+2x-4
7x+29=6x-36
7x-6X=-36-29
X=-65
Answer:
x = -65
Step-by-step explanation:
2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
Distribute:
2(x + 2): 2x + 4
5(x + 5): 5x + 25
=
4(x - 8): 4x - 32
2(x - 2): 2x - 4
Combine like terms:
(2x + 4) + (5x + 25) = (4x - 32) + (2x - 4)
5x + 2x: 7x = 4x + 2x: 6x
4 + 25 = 29 = -32 - 4: -36
7x + 29 = 6x - 36
Now we want to separate like terms,
subtract 29 from both sides
subtract 6x from both sides
7x + 29 - 29 - 6x = 6x - 29 - 6x- 36
7x - 6x = - 29 - 36
x = -65
2. (06.03)
What is the solution to the following system of equations? (2 points)
y = -x2 – 5x − 4
y = -x² + 9x - 18
O (-1,-10)
O (1,-10)
O (-1,10)
(1.10)
Answers
Answer: (1, -10)
Step-by-step explanation:
Since both of the equations are set equal to y, we can conclude that:
[tex]-x^2 -5x-4=-x^2 + 9x-18\\\\-5x-4=9x-18\\ \\ -14x-4=-18\\\\-14x=-14\\\\x=1[/tex]
If x=1, then [tex]y=-(1)^{2}+9(1)-18=-10[/tex]
Thus, the solution is (1, -10)
In AABC, a = 13, b = 14, and c = 18. Find m/A.
B
A
39.5
с
b
a
Answers
Answer:
Step-by-step explanation:
Using the Law of Cosines,
[tex]a^{2}=b^2 + c^2 - 2bc \cos A\\\\13^{2}=14^{2}+18^{2}-2(14)(18) \cos A\\\\-351=-504 \cos A\\\\\cos A=\frac{351}{504}\\\\A=\boxed{\cos^{-1} \left(\frac{351}{504} \right)}[/tex]
Darrel divided 8,675 by 87. His work is shown below
Which answer choice correctly identifies the error Darrel made when dividing?
a b c or d?
Answers
see attachment:
Please state the equation of the line in standard form
Answers
Answer:
See below
Step-by-step explanation:
Slope = rise / run
from 0,-1 to 1.5 , 0
this is 1 / 1.5 = 2/3
y xis intercept = -1
y = 2/3 x -1 Slope intercept form
2/3 x - y = 1 another form
2x - 3y = 3 Standard form (I think this is 'standard form' ....yah?)
p + (-q) - 2 = ? When p = -3 and q = 5
Answers
Answer:
= -10
Step-by-step explanation:
p + (-q) - 2 = x
if:
p = -3
q = 5
then:
-3 + (-5) - 2 = x
we know that:
+(-) = -
then:
-3 +(-5) - 2 = -3 - 5 - 2 = x
x = -10
The value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have given an expression:
= P + (-q) - 2
Plug p = -3
q = 5
= -3 + (-5) - 2
= -3 - 5 - 2
= -10
Thus, the value of the expression p + (-q) - 2 is -10 if the p = -3 and q = 5 the answer is -10.
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MATH: Inverse function, 10 pts for your help!
Answers
The inverse of g(5) and the inverse of h(x) are 2 and [tex]h^{-1}=\frac{-x-13}{4}[/tex] respectively
Inverse of a function
Given the following coordinates and function
g = {(-6, -5), (2, 5), (5,6), (6,9)}
The inverse of "g" is determined by switching the coordinates to have:
g^-1(x) = {(-5, -6), (5, 2), (6, 5), (9,6)}
Since the value of the y-coordinate when x = 5 is 2, hence g^-1(5) = 2
Given the function expressed as:
h(x) = -4x - 13
y = -4x - 13
Replace y with x
x = -4y - 13
4y = -x - 13
y = (-x-13)/4
[tex]h^{-1}=\frac{-x-13}{4}[/tex]
Determine the composite function [tex](hoh^{-1})(-1)[/tex]
h(h(x)) = h(-4x-13)
h(h(x)) =[tex]\frac{-(-4x-13)-13}{4} \\[/tex]
[tex]h(h(x))=\frac{4x}{4} \\h(h(x)) = x\\h(h(-1)) = -1[/tex]
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A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area of 135 square units.
Part A Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B What is the perimeter of the expanded rectangle?
Answers
The equation to model the above scenario is [tex]x^{2}[/tex] +22x - 23 = 0
The perimeter of the expanded rectangle is 48 units
What is a rectangle?A rectangle is a quadrilateral with its 4 angles 90°
Analysis:
First rectangle:
length = 10 + x
width = x
Second rectangle:
length = x + 14
width = x + 8
Area of expanded rectangle = 135 square unit
(x+8)(x+14) = 135
[tex]x^{2}[/tex] + 8x + 14x + 112 = 135
[tex]x^{2}[/tex] + 8x + 14x -23 = 0
[tex]x^{2}[/tex] + 22x -23 = 0
[tex]x^{2}[/tex] + 23x - x - 23 = 0
(x-1)(x+23) = 0
Therefore x = 1
Expanded length = 1+14 = 15
Expanded width = 1+8 = 9
Perimeter = 2(9+15) = 48 units
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Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)
2. Jay Smith deposited $5,000 into an annuity due at the beginning of each quarter for 3 years at 6%
compounded quarterly.
Answers
Answer:
value: $66,184.15interest: $6,184.15Step-by-step explanation:
The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.
__
formulaThe formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...
FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148
FV ≈ 66,184.15
calculatorThe attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.
__
a)The future value of the annuity due is $66,184.15.
b)The total interest earned is the difference between the total of deposits and the future value:
$66,184.15 -(12)(5000) = 6,184.15
A total of $6,184.15 in interest was earned by the annuity.
On a walk through the woods, Mr. Finley saw 16 blue jays and 25 purple finches. Write the ratio of finches to blue jays three different ways.
Answers
Answer:
25:16
50:32
100:64
Step-by-step explanation:
what are the solutions in the following equations?
Answers
Answer: (0, -6) and (1, -5)
Step-by-step explanation:
If [tex]x-y=6[/tex], then [tex]y=x-6[/tex]. Substituting this into the second equation,
[tex]x-6=x^{2}-6\\\\x^{2}-x=0\\\\x(x-1)=0\\\\x=0, 1[/tex]
If x=0, y=-6.
If x=1, y=-5.
So, the solutions are (0, -6) and (1, -5)
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.1 years, and standard deviation of 0.6 years.
If you randomly purchase one item, what is the probability it will last longer than 2 years?
Answers
The probability will last longer than 2 years will be 3.3%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
First let us calculate the z score using the formula:
[tex]z = \dfrac{(x- \mu)} { s}[/tex]
where x = 2, u is the mean = 3.1 years, and s is the standard deviation
[tex]z =\dfrac{ (2 - 3.1) }{ 0.6}[/tex]
z = -1.83
From the standard probability tables, the p-value at z = -1.83 is:
P = 0.033 = 3.3%
Therefore the probability that will last longer than 2 years will be 3.3%.
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A uniform density curve goes from negative 5 to positive 1.
What would the height need to be for this curve to be a density curve?
Negative one-sixth
One-sixth
One-fifth
1
Picture posted below
Answers
Answer: Choice B) One-sixth
In other words, the fraction 1/6
===========================================================
Explanation:
The base, aka horizontal component, is 6 units long. Count out the spaces from -5 to 1 to get a result of 6.
Or you could subtract and use absolute value in either of these two ways
|A - B| = |-5 - 1| = |-6| = 6|B - A| = |1 - (-5)| = |1 + 5| = |6| = 6Where A = -5 and B = 1 are the endpoints mentioned. Absolute value is used to ensure the result of the subtraction isn't negative. Negative distance on a number line doesn't make sense.
----------
However you determine the base, we'll multiply it by the unknown height which we'll call h. This leads to the area of the rectangle. The area is 6h.
Rule: The area under a probability density curve must always be 1.
So the area 6h must be 1 which helps us see that...
6h = 1
h = 1/6
Divide both sides by 6 to isolate h fully.
Answer:
B
Step-by-step explanation:
I keep putting in the formula but I keep getting the answer wrong
Answers
Answer:
314 in² (nearest whole number)
Step-by-step explanation:
Radius of a regular polygon: The distance from the center of the polygon to any vertex. The radius of a hexagon is equal to the length of one side.
Therefore, from inspection of the given diagram:
radius = 11 in ⇒ side length = 11 inTo find the area of a regular polygon, we first need to calculate the apothem. The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.
[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]
where:
s = length of one siden = number of sidesGiven:
s = 11 inn = 6Substitute the given values into the formula and solve for a:
[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]
Area of a Regular Polygon
[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]
where:
n = number of sidess = length of one sidea = apothemGiven:
n = 6s = 11[tex]\textsf{a}=\dfrac{11\sqrt{3}}{2}[/tex]Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]
[tex]\implies \sf A=314.3672216...[/tex]
[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]
0 1 3 6 10 what goes after 10?
Answers
Answer:
15
Step-by-step explanation:
0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
Line l has a slope of 2/3 The line through which of the following pair of points is perpendicular to l?
Answers
We conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.
The line through which of the following pair of points is perpendicular to l?Remember that two lines are perpendicular only if the slope of one of the lines is equal to the opposite of the inverse of the slope of the other line.
So, if line l has the slope 2/3.
Then the perpendicular lines have a slope equal to -3/2.
Now, remember that if a line goes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So here we just need to find two points (x₁, y₁) and (x₂, y₂) such that the slope is equal to -3/2.
If we define (x₁, y₁) = (0, 0), then the other point must be:
[tex]a = \frac{y_2 - 0}{x_2 - 0} = -3/2\\\\y_2/x_2 = -3/2[/tex]
Then we can write the other point as (2, -3).
So we conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.
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In(2e^9) in logarithmic expression
I’m having trouble with all of the “In” section and very confused
Answers
In logarithmic form, we get In(2e^9)= ln(2)+9.
LogarithmsWe define the logarithm as the power to which any number must be raised to get few other values.Exponentiation is the reverse process of logarithm.We are given,
ln(2[tex]e^{9}[/tex])
We know that, ln(ab) = ln(a) + ln(b)
So we get,
ln(2[tex]e^{9}[/tex]) = ln(2)+ln([tex]e^{9}[/tex])
Since ln(m^n)=n ln(m)
And ln(e)= 1, we will get,
ln(2[tex]e^{9}[/tex]) = ln(2) +9 ln(e)
= ln(2) +9
Hence, the logarithmic form, we get In(2e^9)= ln(2)+9.
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Hi. how can i Find the *number* of terms of a finite geometric sequence?
r= .75
a= 40
sum= 280
Answers
We have to use the formula [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex] to find the number of terms of a finite geometric sequence.
If a be the first term of a finite sequence, r be the common ratio between consecutive terms and n be the number of terms.
So, we have to use the formula of sum of sequence and then calculate it to reduce the equation to find the value of number of terms, that is n.
Then, Sum of the sequence (Sn) = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
Here, in the given problem,
Sum(Sn) = 280, First term of the sequence(a) = 40, Common ratio(r) = 0.75
So, Sn = [tex]\frac{a(1-r^{n}) }{1-r}[/tex]
⇒ [tex]1-r^{n} =\frac{S_{n}(1-r) }{a}[/tex]
⇒ [tex]r^{n} =1+\frac{S_{n}(1-r) }{a}[/tex]
⇒ [tex]n = log_{r} (1+\frac{S_{n}(1-r) }{a})[/tex]
Now you have to put the values and get the number of terms.
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25. (01.05)
Given the point (2, 3) and the slope of 4, find y when x = 22. (1 point)
I 78
O83
O88
091
Answers
Answer: 83
Step-by-step explanation:
The equation of the line in point-slope form is
[tex]y-3=4(x-2)[/tex]
Substituting in x = 22,
y - 3 = 4(22-2) [substitution]y -3 = 80 [simplify right hand side]y = 83 [add 3 to both sides]On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y <2/3x + 3
y > 3/2x + 3
y > 2/3x + 3
y < 3/2x + 3
Answers
Answer:
The correct linear inequality is y<2/3x+3
Step-by-step explanation:
Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols
In the graph, the grey region corresponds to the region non-allowed by inequality. We see that for x=0, y is allowed to be only less than 3: this means that the correct inequality must be in the form y<mx+3, so only the 1st option or the 4th option.
In order to choose the correct option, we should find the value of m, the slope of the line in the graph. This slope can be found by calculating the variation of y divided by the variation of x:
m=dy/dx
Choosing for example the points x=0 (which corresponds to y=3) and x=3 , we find
So, the equation of the line is y=2/3x+3
and so the correct inequality is
y<2/3x+3
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Fig. R24 shows a flower vase whose circular base is parallel to its circular top.
Use the dimensions in the figure to calculate the curved surface area of the flower vase
Answers
Answer:
operant conditioning and schedules of reinforcement
Solve for all values of y
in simplest form.
∣y−12∣=16
Answers
Answer:
[tex]y=-4; y=28[/tex]
Step-by-step explanation:
The way I like to think about it, with absolute value meaning the distance is
"find which number are 16 apart from 12". Which means 28 (to the right) or -4 (to the left).
More formally, applying the definition of absolute value,
[tex]|y-12|=16 \leftrightarrow y-12=\pm16\\y-12=-16 \rightarrow y=-4\\y-12=+16 \rightarrow y=28[/tex]
x2y, for x = 3 and y = 6
Answers
Answer:
12
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ASSUMING}[/tex]
[tex]\mathsf{x^{2y}}[/tex]
[tex]\huge\textbf{IF SO, FOLLOW THESE STEPS TO}\\\huge\textbf{SOLVE FOR YOUR RESULT}[/tex]
[tex]\mathsf{x^{2y}}\\\mathsf{= 3^{2(6)}}\\\mathsf{= 3^{2\times6}}\\\mathsf{= 3^{12}}\\\mathsf{= 3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3\times3}\\\mathsf{= 9\times9\times9\times9\times9\times9}\\\mathsf{= 81\times81\times81}\\\mathsf{= 6,561\times81}\\\mathsf{= 531,441}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{531,441}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]