Answer:
[tex]\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx = \frac{e^\bigg{\frac{1}{4}}}{8} - \frac{e^\bigg{\frac{1}{9}}}{8}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringExponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integrals
Definite IntegralsIntegration Constant C
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]
U-Substitution
eˣ Integration: [tex]\displaystyle \int {e^u} \, dx = e^u + C[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for u-substitution.
Set: [tex]\displaystyle u = 4x^{-2}[/tex][u] Differentiate [Derivative Rule - Basic Power Rule]: [tex]\displaystyle du = -8x^{-3} \ dx[/tex][du] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle du = \frac{-8}{x^3} \ dx[/tex]Step 3: Integrate Pt. 2
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^6_4 {\frac{-8}{x^3}e^{4x^{-2}}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{1}{9}}_{\frac{1}{4}} {e^u} \, dx[/tex][Integral] eˣ Integration: [tex]\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx = \frac{-1}{8}(e^u) \bigg| \limits^{\frac{1}{9}}_{\frac{1}{4}}[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx = \frac{-1}{8} \bigg[ -e^\bigg{\frac{1}{9}} \bigg( e^\bigg{\frac{5}{36}} - 1 \bigg) \bigg][/tex]Simplify: [tex]\displaystyle \int\limits^6_4 {\frac{1}{x^3}e^{4x^{-2}}} \, dx = \frac{e^\bigg{\frac{1}{4}}}{8} - \frac{e^\bigg{\frac{1}{9}}}{8}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Y+4=2(x+3) In slope-intercept form
Also can I please have Brainliest?
Only if I'm correct of course.
Your welcome, Loves!
URGENT: WILL MARK BRANIEST, LOOK AT PIC!
Answer:
It gives u answer in picture
Step-by-step explanation:
Free points?
i have to find the area of the shaded region. please helppp!!!!! xksnkskzks
Answer:
9.53 cm2
Step-by-step explanation:
hope it helps
Here is the solution:
not all rational algebraic equations can be expressed in quadratic equations agree disagree defend your answer in at least two sentences
Abby is painting two cubes for an art project.
Cube 1: side length = 3 feet
Cube 2: side length = 2 feet
The surface area of a cube is 6s², where s is the length of one side.
Find the total surface area that Abby will paint.
1. Find the surface area of cube 1. Show your work, and include units with your answer.
2. Find the surface area of cube 2. Show your work, and include units with your answer.
3. What is the total area Abby will paint?
Answer:1: 56. 3 squared is 9, times 6 is 56.2: 24. 2 squared is 4, times 6 is 24.3: 80. 56+24=80
Step-by-step explanation:
1. The surface area of cube 1 is 54 sq ft, the surface area of cube 2 is 24 sq ft, the total area Abby will paint is 78 sq ft
What is a cube?A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.
We are given that Abby is painting two cubes for an art project.
Cube 1: side length = 3 feet
Cube 2: side length = 2 feet
The surface area of a cube = 6s², where s is the length of one side.
1. Each side of cube 1 is
3 feet x 3 feet, = 9
so, each side has an area of 9 square feet.
Then Multiply by 6 sides and the area
6 x 9 = 54
that is 54 square feet.
2. Each side is 2 feet x 2 feet = 4
so, the area of one side is 4 square feet.
Then Multiply by 6 sides and the area
6 x 4 = 24
That is 24 square feet.
3. the total area = 54 + 24 = 78 square feet
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Tommy multiplied 0.24 by 100 to change it to what type of number?
A) percent
B) decimal
C) fraction
D) benchmark percent
16(x+3)=4(x+9)
solve for x
⭐ Respuesta :
Ecuación : 16 (x + 3) = 4 (x + 9)⭐ Resolvemos :
[tex]16(x+3)=4(x+9)\\16x+48=4x+36\\16x-4x=36-48\\12x=-12\\x=-12/12\\\\\boxed{x=-1}[/tex]
⭐ Explicación paso a paso :
16 (x + 3) = 4 (x + 9)
Multiplicamos los paréntesis "16(x+3)" y "4(x+9)"16x + 48 = 4x + 36
Términos semejantes ...16x - 4x = 36 - 48
Restamos respectivamente ...12x = -12
El número 12 multiplicando a "x" pasa a dividir...x = -12 ÷ 12
Dividimos y ya tenemos el resultado!! ^-^ x = -1❤ Ver mas ejemplos : brainly.lat/tarea/29507142 ❤
. William fills 1/3 of a water bottle in 1/6 of a minute. How much time will it
take him to fill the bottle?
Answer:
It will take him
[tex] \frac{1}{2} [/tex]
of a minute to fill the bottle.
Step-by-step explanation:
I'm really not sure this is right but..
we can solve using proportions. Cross-multiply and divide.
[tex]\frac{ \frac{1}{3} of \: a \: water \: bottle}{\frac{1}{6} minute} \: = \frac{ \frac{3}{3} of \: a \: water \: bottle}{x} \\ \\ \frac{ \frac{1}{6} }{ \frac{1}{3} } = \frac{ \frac{1}{3} x}{ \frac{1}{3} } \\ \\ \frac{1}{2} = x[/tex]
How many solutions does 7x -10 = 7(x+3)
Answer: The answer to this question is that there is no solution to that problem
Step-by-step explanation:
The sword maker in the cove ordered a special tape to wrap the sword handles with. He knew each sword would need 48 inches of tape. If he ordered 100 feet of tape, will he have enough tape to wrap 28 swords? How much will he have left over or how much more will he need?
Answer:
a) If he ordered 100 feet of tape, will he have enough tape to wrap 28 swords?
No he would not
b) How much will he have left over or how much more will he need?
= He would have 144 inches left over.
Step-by-step explanation:
The sword maker in the cove ordered a special tape to wrap the sword handles with. He knew each sword would need 48 inches of tape. If he ordered 100 feet of tape, will he have enough tape to wrap 28 swords? How much will he have left over or how much more will he need?
From the above question, each sword would need 48 inches of tape
He would need to wrap 28 swords, hence:
1 swords = 48 inches
28 swords = x
x = 28 × 48 inches
= 1344 inches of tapes
Therefore to cover each sword he would need a total of 1344 inches of tape.
He ordered 100 feet of tape
We convert 100 feet to inches
1 foot = 12 inches
100 feet = x
x = 100 × 12 inches
x = 1200 inches
Hence, he ordered 1200 inches of tape.
a) If he ordered 100 feet of tape, will he have enough tape to wrap 28 swords?
100 feet = 1200 inches of tapes
To wrap 28 swords he would need 1344 inches of tape hence, he would not have enough tape to wrap 28 swords.
b) How much will he have left over or how much more will he need?
= 1344 inches - 1200 inches
= 144 inches
He would have 144 inches left over.
HELP ME OMG ILL GIVE YOU BRAINLIEST AND ILL FOLLOW YOU!!!!!!!
Explain in detail with at least two sentences how to represent the sum of z1 and z2 geometrically given that z1 = 8 – I and z2 = -9 + 2i. Then, give the sum 21 + Z2 in rectangular form.
Answer:
Given are two complex numbers as
When we add algebraically, we add the real parts and then add the imaginary parts separately
Hence
Geometrically we draw position vector of both the points. The sum would be resultant of these two vectors.
Step-by-step explanation:
The sum of the complex number in rectangular form is -1 +i
Sum of complex numberComplex numbers are written in the form x + iy
Given the complex numbers expressed as:
z1 = 8 - i
z2 = -9 + 2i
Take the sum
z1 + z2 = (8 - 9) + (-i+2i)
z1 +z2 = -1 + i
Hence the sum of the complex number in rectangular form is -1 +i
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Tell whether the following equation represents or not represents a linear function. 20x + 4y = 8 The equation represents a linear function.
Answer:
— 20x + 4y = 8 The equation represents a linear function.. Add answer+5 pts.
Step-by-step explanation:
How do I do this?
.
.
Answer:
the answer is 4 i believe
Step-by-step explanation:
How do you solve problems involving sequence? Discuss the mathematics concepts and principles applied when solving problems involving sequence
Step-by-step explanation:
Sequence is defined as arrangement f numbers in a specific or defined pattern. Sequence are categorized into
1) Arithmetic
2) Geometric
Arithmetic sequence are characterized by their common difference while Geometric sequence are characterized by their common ratio.
Given a sequance of numbers say;
T1, T2, T3...
The first term "a" of the sequence is T1
Common difference d = T2-T1 =T3-T2
Common ratio = T2/T1 = T3/T2
The formula for calculating nth term of an Arithmetic sequence is expressed as;
Tn = a+(n-1)d
a is the first term
n is the number of terms
d is the common difference
The nth term of a Geometric sequence is expressed as;
Tn = ar^{n-1}
r is the common ratio
Numbers are arranged in a sequence when they follow a predetermined or established pattern. Sequences can be divided into
1) Mathematics
2) Graphitic
Geometric sequences are characterized by their common ratio, whereas arithmetic sequences are distinguished by their common difference.
Suppose a sequence of numbers is given;
T1, T2, T3...
The sequence's initial term "a" is T1.
common distinction d = T2-T1 =T3-T2
T2/T1 Common Ratio T3/T2
The following is the formula for finding the nth term in an arithmetic sequence:
Tn = a+(n-1)d
The first term is a.
The number of terms is n.
d is the typical discrepancy
The nth term of a Geometric sequence is expressed as;
[tex]T_{n} =ar^{n-1}[/tex]
r is the common ratio
To learn more about information Sequence :
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there are 40 boys and 20 girls at the party 35% from boys wearing glasses and 60% girls wearing how many people wearing glasses glasses
Answer:
12 g 14 b
Step-by-step explanation:
.
Is (-1, -9) a solution to the equation y 9x?
Answer:
Yes if the equation is Y= 9X
Step-by-step explanation:
-9= 9×-1 ---} -9 = -9
microzooplankton is _____ compared to macrozooplankton
a) smaller
b) bigger
c) faster
d) brighter in color
btw yes i put it on math because i feel like more people do math more
a ) smaller is correct answer
What is the point-slope form of an equation passing through (0, -5) with a 5 points
slope of 2? *
Answer:
y=2x-5
Step-by-step explanation:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]x_{1}=0, y_{1}=-5\\[/tex], and m=2
[tex]y-(-5)=2(x-0)[/tex], -(-5)-Two negatives make it positive, and you distribute the 2
[tex]y+5=2x[/tex], you now subtract 5 to get y by itself to get your answer of
[tex]y=2x-5[/tex]
*NOTE* (0,-5) is the y-intercept, so you could have used the linear equation of y=mx+b, m=2, and b(y-intercept)=-5
giving you y=2x-5
At Saturday night’s football game there were 18 less fans than half the fans at Friday night’s game. There were “x” fans at Friday’s game. Write an expression to represent the number of fans at Saturday’s game.
This can be expressed in this form:
1/2x - 18.
8x27 using distributive property and mental math
Answer:
216
Step-by-step explanation:
8×20=160 and 8×7=56 160+56=216 idky u told me to do it in my head but i did so ya
What is the exact solution to the equation 4^5x=3^(x-2)
list the steps to get the answer
Answer: x = -0.377
Step-by-step explanation:
We have the equation:
4^(5*x) = 3^(x - 2)
Now we can use the fact that:
Ln(A^x) = x*Ln(A)
Then we can apply Ln(.) to both sides of the equation to get:
Ln(4^(5*x)) = Ln(3^(x - 2))
(5*x)*Ln(4) = (x - 2)*Ln(3)
(5*x)*Ln(4) - x*Ln(3) = -2*Ln(3)
x*(5*Ln(4) - Ln(3)) = -2*Ln(3)
x = -2*Ln(3)/(5*Ln(4) - Ln(3)) = -0.377
15 POINTS PLEASE HELP!
Answer:
buddy...u weren't able to attach it properly...
Step-by-step explanation:
u may type it out in the comments...
how can we use a number line to help calculate elapsed time
the sum of the measurement of the angles of a triangle equals 180 degrees what is the measure of the missing angle.
Answer:
108.9
Step-by-step explanation:
180-(30.3+40.8)
180-71.1
108.9
Johnny's Towing Company charges a one-time towing fee of $50, plus $20 per day
that they keep each car.
If Johnny changes his one-time towing fee to $75, describe how the graph of his
function would change.
Solve the equation 2 + 4.7 = -9.3.
Answer: positive then greater than
Step-by-step explanation:
please solve due soon
Answer:
5
Step-by-step explanation:
5+5(0)
The graph shows a line and two similar triangles. On a coordinate plane, a line goes through (0, 3) and (6, 11). A small triangle has a rise of 4 and run of 3. What is the equation of the line? y = 3 x + 3 y = three-fourths x + 3 y = four-thirds x + 3 y = 4 x + 3
Answer:
i think that the answer is the first equation
Step-by-step explanation:
The equation of the line passing through the points (0, 3) and (6, 11) is:
y = (4/3)x + 3.
Option C is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
To find the equation of the line passing through the points (0, 3) and (6, 11).
We can use the slope-intercept form of a linear equation,
which is y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we can find the slope of the line by using the formula:
[tex]m = (y_2 - y_1) / (x_2 - x_1)[/tex]
where
[tex](x_1, y_1) = (0, 3)\\(x_2, y_2) = (6, 11).[/tex]
So,
m = (11 - 3) / (6 - 0) = 8/6 = 4/3
The slope of the line is 4/3.
Next,
We can use the point-slope form of a linear equation to write the equation of the line in terms of one of the points and the slope:
[tex]y - y_1 = m(x - x_1)[/tex]
Choosing the point (0, 3), we get:
y - 3 = (4/3)(x - 0)
Simplifying and solving for y, we get:
y = (4/3)x + 3
Therefore,
The equation of the line passing through the points (0, 3) and (6, 11) is:
y = (4/3)x + 3.
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it is any equation in the form f of x = ax to the second power + bx + c where a b and c are real numbers and a not equal to zero . is t a linear equation, quadratic,rational
Answer:
The answer to this depends on the accuracy of the way this is transcribed. If the value on the left side of the equals sign is indeed x, then it would be a rational equation. If it is meant to be another scalar value though, then this would be a quadratic equation.
Step-by-step explanation:
This depends on the what is on the other side of the equals sign. If it is a scalar value, then you are guaranteed a proper quadratic equation. In the example given though:
[tex]x = ax^2 + bx + c[/tex]
This is not actually true. In this example, we can divide both sides by x, giving us a very different equation:
[tex]x = ax^2 + bx + c\\1 = ax + b + c/x\\ax + c/x = 1b[/tex]
and this equation actually a rational one.
all my points! PLZ help me on this and explain ur answer plzz