The primitive function for [tex]f(x) = 4e^{2x} + e^{-x}[/tex] is given by it's indefinite integral.
To calculate it, recall:
[tex]\frac{d}{dx}e^{ax}=ae^{ax}[/tex]
[tex]\int c f(x)dx = c\int f(x)dx[/tex]
Let's begin
[tex]\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1} + c\\[/tex]
[tex]F(x) = 2e^{2x}-e^{-x} +c[/tex]
To find the costant, we just need to use the fact that [tex]F(0)=2[/tex]
[tex]F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3[/tex]
Therefore,
[tex]\boxed{F(x) = 2e^{2x} - e^{-x} -3 }[/tex]
Write 60% as a
fraction in lowest terms.
?]
Enter
Copyright © 2003 - 2020 Acellus Corporation. All Rights Reserved.
Answer:
The answer is three fiths
Write the expression 8⋅ y ⋅ y ⋅ y ⋅ y using exponents.
Answer:
8^4 8 to the fourth power
Step-by-step explanation:
Answer:
8 * y^4
Step-by-step explanation:
There are not like terms so you can't combine
y^4 = because there are 4 sets of y's
Which of the following is equivalent to 17g2 – 2g2?
Answer:
whichever equation equals =15g2
Step-by-step explanation:
Answer:
(17 – 2)g ^2
Step-by-step explanation:
What is the correct equation to solve for x? Help
Answer:
tan (46°) = 17/x
Step-by-step explanation:
tan (46°) = 17/x
Answer:
tan(46) = 17/x
Step-by-step explanation:
The tangent of an angle is opposite over adjacent, so the tangent of 46 is 17/x, not x/17. Also, sin(46) = opposite/hypotenuse and cos(46) = adjacent/hypotenuse, but we aren’t given the hypotenuse. Therefore, the answer has to be tan(46) = 17/x.
The diagram shown can be used to prove the Pythagorean theorem. Which statement is TRUE about the diagram?
es »
A)
The areas of the two rectangles are not equal.
B)
The diagonal of each rectangle is the hypotenuse of a triangle.
0
The area of the red square is represented by ab.
D)
The area of the blue square is represented by a² + b2
Answer:
Step-by-step explanation:
the answer is c
The sum of two numbers is 61, the difference is 31. What are the numbers?
Answer:
2x = 92
x = 46
For the next number:
y = 61 - 46
y = 15
Have a great day!
Answer:
Step-by-step explanation:
For the First Number you would:
1. 2x = 92
2. x = 46
For the second number you would :
1. y = 61 - 46
2. y = 15
In the figure below, lines p and s are parallel.
Answer:
c
Step-by-step explanation:
i used a calculator (they never lie)
Answer:
22
Step-by-step explanation:
60+6x-12= 180
6x = 180 -48
x= 132/6= 22
Can someone help with this please?
Answer:
y = x - 3
Step-by-step explanation:
From the table attached,
Scatter plot given in the graph is correct.
Let the equation of the line passing from a point (x', y') is,
y - y' = m(x - x')
m = slope
Slope of the line passing through two points [tex](x_2,y_2)[/tex] and [tex](x_1,y_1)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through the points (11, 8) and (12, 9) will be,
m = [tex]\frac{(9-8)}{(12-11)} =1[/tex]
Therefore, equation of the line passing through (11, 8) will be,
y - 8 = 1(x - 11)
y = x - 11 + 8
y = x - 3
What is the product? [3 6 1 2 4 0 0 6 2] x [2 0 1]
Answer:
361,240,062 X 201= [72609252462]
Step-by-step explanation:
The product of the matrices is given below.
[tex]\begin{bmatrix}6 & 0 & 3\\4 &0 & 2\\0&0&0\end{bmatrix}[/tex]
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]\rm a_{ij}[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.
The matrices are given below.
[tex]\begin{bmatrix}3 & 6 & 1\\ 2 & 4 & 0\\ 0 & 6 & 2\end{bmatrix} \text{and} \begin{bmatrix}2 & 0 & 1\\ \end{bmatrix}[/tex]
The product of the matrices will be
[tex]\begin{bmatrix}3 & 6 & 1\\ 2 & 4 & 0\\ 0 & 6 & 2\end{bmatrix} \times \begin{bmatrix}2 & 0 & 1\\ \end{bmatrix} = \begin{bmatrix}6 & 0 & 3\\4 &0 & 2\\0&0&0\end{bmatrix}[/tex]
Thus, the product of the matrices is given below.
[tex]\begin{bmatrix}6 & 0 & 3\\4 &0 & 2\\0&0&0\end{bmatrix}[/tex]
More about the matrix link is given below.
https://brainly.com/question/9967572
#SPJ5
The graphs below have the same shapes what is the equation of the blue graph
Mr. Smith marked up the price of his sofa by 15%. If the sofa originally cost $399, what is the new sale price?
Answer:
457.8
Step-by-step explanation:
There are 4 red apples and 3 green apples. How many red and green apples are there?
Answer:
7
Step-by-step explanation:
Just add them together...
what is the domain and range
Answer:
domain = x value
range = y value
Step-by-step explanation:
domain = x value
range = y value
In a scale drawing 1/2 inch represents 3 feet. If the same scale is used, how many inches will be needed to represent 24 feet?
2 inches
4 inches
8 inches
12 inches
PLS HELPPP!!!!!
its due soon, and mainly its asking for verbal
One factor of x^2 + 5x - 24 is?
Answer:
(x-3)(x+8)
Step-by-step explanation:
Answer:
(x-3)(x+8) take your pick
t is -40°F on a cold night in the North Pole. When the sun is out the next day, it is -5°F. What is the difference in temperatures?
Answer:
because at 40 its still warm but really cold but in -5 its cold wherever you go even in the warmest blanket
Step-by-step explanation:
How much acetic acid is in a 15-liter container of acetic acid and water that is marked 40% acetic acid?
The solution is 40% acetic acid.
Multiply the amount of the solution by 40%:
15 liters x 0.40 = 6 liters
There is 6 liters of acetic acid
The last 40 boat rentals at a boat rental company were 22 sunfish, 10 kayaks, and 8 rowboats.
I WILL GIVE BRAINLIEST AND POINTS
Which input value produces the same output value for
the two functions on the graph?
O X=-3
Ox=-2
Ox=-1
Ox=3
The required, x=-2 is the input value that produces the same output value for the two functions on the graph. Option B is correct.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
The statement "x = -2 input value produces the same output value for the two functions on the graph" means that if you plug in x = -2 into both functions, you will get the same output value for both of them. In other words, the two functions intersect at the point (-2, y), where y is the common output value for x = -2.
The graph of the two functions intersecting at the point (-2, 1), where the x-coordinate is -2 and the y-coordinate is the common output value for both functions. This means that if you draw a vertical line at x = -2, it will intersect the graph at the point (-2, 1) for both functions. Therefore, x = -2 is a vertical line of symmetry for the two functions at the point (-2, 1).
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ7
8 1/2 - 6 1/4 please subtract
Answer:
2.25
Step-by-step explanation:
8.5-6.25
(8-6)+(0.5-0.25)
2+0.25
2.25
Answer:
2.25 or 9/4 is the answer
Hope this helps
Solve the inequality for x.
–3x + 6 –3
D) x > –7
You bought a house in 1963 for $56,000. Since then, you have increased the value 6% per year. What is the value of your house in 2017?
Answer:
244,160
Step-by-step explanation:
Lots a Loot Bank charges a monthly service fee and a fee per check, and the chart below shows your total monthly fees in relation to the number of checks issued per month.
Answer:
Monthly service fee is like the fixed cost which is basically the y-value where graph crosses the y-axis.
From graph we see that graph crosses at 1 on y-axis so monthly service fee according to sample graph = $1
Now the per check fee works like slope of the line.
To find the slope we need two points so find any two points on the graph of line. I'm using points (1,0) and (4,3)
now slope can be found using formula
Hence per check fee will be $0.5 as per attached sample graph.
You can use same technique for the original graph given with this question.
Step-by-step explanation:
Answer:
A monthly service fee of 0.50 and a per-check fee of 0.50
Step-by-step explanation:
Carys calculates The total amount E, in dollars, that she earns for working h hours using the equation E=10h.
How many dollars does carys earn per hour?
write the ratio as a fraction in simplest form.
56 days to 5 weeks
Answer: 8 weeks
Step-by-step explanation:
Solve for a.
a+(−4)=−13
Answer:
a+(−4)=−13
a - 4 = - 13
a = -13 + 4
a = -9
hope it helps!
Answer: The value of a is -9.
Step-by-step explanation;
Step 1. Negative times positive is negative. a - 4 = -13.
Step 2. Add four to both sides. a - 4 + a = -13 + 4.
Step 3. Simplify. a = -9.
The radius of a circle can be found by dividing the circumference of the circle by 6.28. What is the radius of a circle that has a circumference of 17.27 feet?
0.36 ft
2.75 ft
10.99 ft
2.58 ft
Answer:
2.75 ft
Step-by-step explanation:
Answer:
2.75
Step-by-step explanation:
I do not understand how you can do this without more information.
Answer:
Step-by-step explanation:
I think you are correct. The bottom of the drawing has to have a width or someway of finding it. Also the breakup of the height needs some sort of clue where that breakup occurs. I think you likely have to ask your instructor.
A recipe for chicken noodle soup is shown.
How many servings could you make if you had 3/4 cup of diced onion?
Answer:
is there answer choices? if not im just guessing so dont take my word for it but i would say 8.5 servings.