Answer:
[tex]x,y\ could\ be\ any\ real\ numbers[/tex]
Step-by-step explanation:
[tex]As\ a\ linear\ equation\ in\ two\ variable\ has\ infinite\ solutions,\\5x-2y=18, will\ also\ have\ infinite\ solutions\ and\ x\ and\ y\ can\ take\ any\ real\ values.[/tex]
The indefinite integral of ((6e^4x)(e^arctan(3e^4x)))/(1+9e^8x)
Answer:
[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{e^\big{arctan(3e^{4x})}}{2} + 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⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Integration
Integrals[Indefinite Integrals] Integration Constant CIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
U-SolveStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \int {\frac{6e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = 6\int {\frac{e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex]Step 3: integrate Pt. 2
Set variables for u-substitution.
Set u: [tex]\displaystyle u = 4x[/tex][u] Differentiate [Basic Power Rule, Multiplied Constant]: [tex]\displaystyle du = 4 \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{4e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(3e^u) + u}}{1 + 9e^\big{2u}}} \, du[/tex]Step 5: Integrate Pt. 4
Set variables for u-substitution #2.
Set v: [tex]\displaystyle v = 9e^{2u} + 1[/tex] [v] Differentiate [Exponential Differentiation, Chain Rule]: [tex]\displaystyle dv = 18e^{2u} \ du[/tex][v] U-Solve: [tex]\displaystyle u = ln \Big( \frac{\sqrt{v - 1}}{3} \Big)[/tex][dv] U-Solve: [tex]\displaystyle du = \frac{e^{-2u}}{18} \ dv[/tex][U-Solve] Rewrite u: [tex]\displaystyle e^u = \frac{\sqrt{v - 1}}{3}[/tex]Step 6: Integrate Pt. 5
[Integral] U-Solve: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(3(\frac{\sqrt{v - 1}}{3})) + ln(\frac{\sqrt{v - 1}}{3})}}{1 + 9(\frac{\sqrt{v - 1}}{3})^2} \frac{1}{18e^{2u}}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{\sqrt{v - 1}e^\big{arctan(\sqrt{v - 1})}}{3[1 + v - 1]} \frac{1}{18(\frac{\sqrt{v - 1}}{3})^2}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{\sqrt{v - 1}e^\big{arctan(\sqrt{v - 1})}}{3v} \frac{1}{2(v - 1)}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(\sqrt{v - 1})}}{6v\sqrt{v - 1}} \, dv[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{1}{4}\int {\frac{e^\big{arctan(\sqrt{v - 1})}}{v\sqrt{v - 1}} \, dv[/tex]Step 7: Integrate Pt. 6
Set variables for u-substitution #3.
Set z: [tex]\displaystyle z = arctan(\sqrt{v - 1})[/tex][z] Differentiate [Arctrig Differentiation, Chain Rule]: [tex]\displaystyle dz = \frac{1}{2v\sqrt{v - 1}} \ dv[/tex]See attachment for rest of work (would not fit entire answer in answering box).
1. In the first week, he spent $16 on lunches. How much was in his account then?
Answer:
hen he deposited some more money and his account balance was $28.
Step-by-step explanation:
Answer:7
Step-by-step explanation:
Kamama is making a quilt. She started with a hexagon that she loves. If Kamama wants the rest of her hexagons to be congruent, which transformations can
she use?
Please choose all of the transformations that she can use to create a congruent image.
Fun fact: Kamama is a Cherokee name meaning Butterfly.
Reflection
Translation
Dilation
Rotation
Based on the fact that Kamama wants her hexagons to be congruent, the transformations that she can use are:
ReflectionTranslationRotationWhat transformations give congruent shapes?In order to have congruent shapes, there are three transformations that can be used.
Firstly, it is important to note that congruent shapes have the same size and the same shape. They are identical except for their orientation which may be different.
A reflection would create a congruent shape that would have the same size and angles but the orientation should be different. This is the same as a rotation. A translation will often result in congruent shapes that also have the same orientation. This means that Kanama can use any of these transformations.
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y= 1/3 x+2
y = -x-2
Write solution as an ordered pair
Answer: (-3,1)
Step-by-step explanation:
inputting the two equations into a graphing calculator tells us that these two lines intersect at the point (-3,1)
Beinggreat78, you are ~Summoned~
Answer:
B.
Step-by-step explanation:
0.32 > 0.304 > 0.03
Work and answers are provided in the screenshot attached! :)
The area of the figure is
square units.
Answer:
80 square units
Step-by-step explanation:
The figure given can be decomposed to have two trapezoids of equal dimensions and a rectangle.
Area of the figure = (2*area of a trapezoid) + (area of a rectangle)
Area of the 2 trapezoids:
Area of the two trapezoid = 2(½(a + b)*h)
Where,
a = 2 + 6 + 2 = 10 units
b = 6 units
h = 2 units
Plug in the values:
Area of the two trapezoid = 2(½(10 + 6)*2)
= 2(½(16)*2)
Area = 32 units²
Area of the rectangle:
Area = length × width
Length = 8 units
Width = 6 units
Area = 8 × 6 = 48 units²
✔️Area of the figure = 32 + 48 = 80 units²
Notes: Factorial function (symbols: !) says to multiply all whole numbers from our chosen number down to 1
Answer:
ggg if fdrsyviinoiv fcvui I tzhvii u u y
Please show me the work!
Answer:
9/2π cm/s
Step-by-step explanation:
Volume of the spherical balloon V= 4/3πr³
Rate of change of volume dV/dt = dV/dr * dr/dt
dV/dr = 3(4/3πr²)
dV/dr = 4πr²
dV/dr = 4π(2)²
dV/dr = 16π
If V = 72cm²/s
72 = 16π*dr/dt
dr/dt = 72/16π
dr/dt = 9/2π cm/s
Hence the radius is changing at 9/2π cm/s
.The values of x and y vary directly, and mul
when x = 48, y = 36. Find the value of x when
y = 18
Step-by-step explanation:
In the general scenario we find thaf x exceeds y by 12. If they vary directly it means even though the values x and y change they will always have the constant different 12
x=y+12
:. x=18+12
x=30
I HOPE THIS HELPS
Find the percent of decrease. Round the percent to the neares
amount of decrease: 20 pounds
original amount: 80 pounds
Answer:
75% decrease
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/algebra/percentage-decrease-calculator.php?v_1=80&v_2=20&action=solve
When using the quotient rule of exponents, you must _____
coefficients and _____
the exponents.
Answer:
When multiplying exponents of the same base, add the exponents. When dividing exponents of the same base, subtract the exponents. When raising a power to a power, multiply the powers.
Step-by-step explanation:
50 POINTS!!!!
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
y=-16x^2+212x+139
The cost of a gallon of orange juice is $3,50, What is the maximum number of containers you can buy for $15
A magazine survey of a five-year period considered 100 featured actors. The
table to the right shows the "worst" ten actors, in terms of how much their
films returned per dollar that the actor earned.
The set of actors with at least a return of $7.50 are {H, J, K}
What are the set of actors?The actors that would be included in this set include actors that earn an amount equal to $7.50 or an amount greater than $7.50.
A set can be described as a collection of objects whose elements are fixed and cannot be changed. Thus, elements in this set would include those who earn more than or equal to $7.50.
To write a set in a roster form, the elements in the set are written in a row within curly brackets or braces - { }. The elements in the set are then separated by commas.
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What is the base when the expression (-1.5)2 • (3.2)5 is written as a single power of 5?
we can rewrite:
(-1.5)²*(3.2)⁵ = 3.76⁵
The new base of the expression is 3.76
What is the new base of the expression?Here we have the expression:
(-1.5)²*(3.2)⁵
And we want to write this as a single expression with a power of 5.
First we can rewrite:
(-1.5)² = x⁵
x = (-1.5)^(2/5)
Then the new base of the expression will be:
x*3.2
(-1.5)^(2/5)*3.2 = 3.76
Then we can rewrite:
(-1.5)²*(3.2)⁵ = 3.76⁵
The new base of the expression is 3.76
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Help help help ! :)
Which equation’s line is steeper and explain how you know
The equation's line that is steeper is y = 3x + 7
Slope of a lineFrom the question, we are to determine which of the given equations' line is steeper
The given equations are
y = 3x + 7
and
y = (1/2)x + 9
First, we will compare the equations to the form of an equation of a straight line
The equation of a straight line is of the form
y = mx + c
Where m is the slope
and c is the y intercept
Thus,
The slope of the equation, y = 3x + 7, is 3
and
The slope of the equation, y = (1/2)x + 9, is 1/2
NOTE: The higher the slope of a line, the steeper the line
Hence, the equation's line that is steeper is y = 3x + 7
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what is the result if you decrease the sum of 78.932 and 721.832 by 389.823 pls
Answer:
410.941
Step-by-step explanation:
2. Complete the truth table for the statement S ^ P.
S P S ^ P T T T F F T F F
Answer:
Step-by-step explanation:
Find the slope of the line from the table.
X
1
4
7
10
у
7
5
3
1
1
Find the area of a rectangle with a length of 17 centimeters and a width of 6 centimeters.
Answer:
102 cm ²
Step-by-step explanation:
Write the equation for line L in point-slope form and slope-intercept form
L is perpendicular to y=2x
The equation of the line in slope intercept form is y = - 1 / 2 x - 5
The equation of the line in point slope form is (y + 4) = - 1 / 2 (x + 2)
How to represent equation in slope intercept form and point slope form?
The equation in a slope intercept form is represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the equation of the line L in slope intercept form.
The line L is perpendicular to y = 2x
Hence,
m₁m₂ = -1
2m₂ = -1
m₂ = -1 / 2
Therefore,
y = - 1 / 2 x + b
let's find b using (-2, -4)
-4 = - 1 / 2 (-2) + b
b = -4 - 1
b = -5
Hence, the equation of the line in slope intercept form is as follows:
y = - 1 / 2 x - 5
The equation of the line in point slope form is represented as follows:
(y - y₁) = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinatesTherefore, using (-2, -4),
(y + 4) = - 1 / 2 (x + 2)
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Pleaseee help me on this question
Answer:
B
Step-by-step explanation:
For every 1 liter of water, 0.07 kilograms of salt must be added. They are asking for 0.5 liters of water, which is half of 1 liter. So therefore, they need half of 0.07 kilograms of salt, which is 0.035 kilograms
Answer:
0.035 kg.
Step-by-step explanation:
0.5 liter is 1/2 liter
0.07kilograms / 2 = 0.035kg
What is the value of x in the equation 2x +3y = 36, when y=6?
O9
O 27
O 36
Answer:
x=9
Step-by-step explanation:
Substitution and solving
[tex]2x+3y=36\\2x+3(6)=36\\2x+18=36\\2x+18-18=36-18\\36/2=2x/2\\x=9[/tex]
At age 30 you deposit $150 at the end of each month into an IRA that pays 4% interest compounded monthly. In the previous question, we found that the value of the annuity at age 65 would be $137,059.64. How much interest did you earn?
According to the given statement the interest that we earn is
= $74,059 . 64
What Is an Annuity's Present Value?The present value of an annuity seems to be the current worth of future annuity payments based on a predetermined rate of return, as well as discount rate. The higher the discount rate, the smaller the annuity's present value.
According to the given data:monthly payment is 150
at the age = 30
interest rate = 4
till age of = 65
At age 65, the annuity would be worth $137,059.64.
We only need to determine the amount of interest. = ?
for monthly payments, we need to take n, which equals 12 points now total interest. determined by future value. Substitute minus p m t multiplied by n multiplied by t for all values now.
the amount of interest = deposited amount x year x no of year invested
= 150 x 12x(65-30)
present value = 63000
At age 65, the annuity would be worth $137,059.64.
We know that the interest is = balance - capital
= 137,059.64 - 63000
= $74,059 . 64
According to the given statement the interest that we earn is
= $74,059 . 64
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Need help pls help thanks
Answer:
your right
Step-by-step explanation:
25% discount for AED 4000
Answer:
The 25% discount on AED 4000 will be: 1000 AED
Step-by-step explanation:
Given
The amount = 4000Discount = 25%In order to determine a 25% discount on the amount AED 4000, all we need means is to multiply 25/100 or (0.25) by 4000.
i.e
Discount amount = 25% of 4000
= 25/100 × 4000
= 0.25 × 4000
= 1000 AED
Thus, the 25% discount on AED 4000 will be: 1000 AED
after eating La Huerta your subtotal was 25.72$ you want to leave a 15% tip. 15% as a decimal is
four hundred thirty-seven
ten-thousandths in decimal form
Answer:
0.0437
Step-by-step explanation:
I can't really explain this one
Answer:
.0437
Step-by-step explanation:
the 4 is in the hundreds spot, the 37 is in the thousands and ten thousandths
can anyone help me ?
Answer: i think u got it write its that one
Step-by-step explanation:
Some one please help
I have attached the question
Answer:
a number question's answer is a power 2. and is c power 1