The anti derivative of the function eˣ² is eˣ²/2x.
What is defined as the anti derivative?Derivatives are the inverse of antiderivatives. An antiderivative is a function that does the opposite of what a derivative does. There are many antiderivatives of one function, but they all take the shape of a function + an arbitrary constant. Indefinite integrals rely heavily on antiderivatives.An antiderivative, F, of the a function, f, is a function that may be differentiated to get the original function, f. In other words, an antiderivative is defined mathematically as follows: ∫ f(x) dx = F(x) + C, where C is the integration constant.The given function is; eˣ².
To find the anti derivative of the function, integrate the function with respect to x.
Let y = eˣ²
Integration of exponential function remains same but applying the chain rule, the derivative of the power of exponent comes at the denominator.
∫y. dx = ∫eˣ² .dx.
∫eˣ² .dx. = eˣ²/(d/dx)x²
∫eˣ² .dx. = eˣ²/2x
Thus, the anti derivative of the function is found as eˣ²/2x.
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HELPPPPPP
What is the distance between the following points?
Choose 1 answer:
7
9
√65
√80
Using long division, what is 14 divided by 1,726
Can you guys help me with this math question
need help please as soon as possible please
The value of the trigonometric ratio sin C of the given right angle triangle is; A: a/b
How to use Trigonometric ratios?
We know that the three trigonometric ratios of a right angle triangle are given as;
sin θ = opposite/hypotenuse
cos θ = Adjacent/hypotenuse
tan θ = Opposite/Adjacent
Now, from the right angle triangle given to us, if we want to consider the angle C, then we will have the trigonometric ratios as;
sin C = a/b
cos C = c/b
tan C = a/c
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the table shows the number of questions answered incorrectly by each player on a game show.if each missed question is worth "-77" points,what is the change in olive sco due to the incorrect questions?
The change in Oliver's score due to the incorrect questions will be -63.
How to illustrate the information?It should be noted that the table shows the number of questions answered incorrectly by each player on a game show.
It should be noted that based on the information, every question missed is worth -7 points.
Therefore, the change in Oliver's score due to the incorrect questions will be:
= 9 ×-7
= -63
The change is -63.
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find the surface area of the cylinder DO NOT ROUND YOUR ANSWER!!
The surface area of the cylinder is 1733.28 square inches
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the surface area of the cylinder?The shape is given as
Shape = cylinder
Also, we have
Radius, r = 12 inches/2
r = 6 inches
Height, h = 40 inches
The surface area of the cylinder is calculated as
SA = 2πr² + 2πrh
So, we have:
SA = 2 * 3.14 * 6² + 2 * 3.14 * 6 * 40
Evaluate
SA = 1733.28 square inches
Hence, the area is 1733.28 square inches
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WE DO:
C
A bag of fruit contains 6 apples, 3 oranges.2
banana, and 4 pears. Jose will randomly select
one piece of fruit, put it back, and choose
another piece. What is the probability that the
first piece of fruit Jose selects will be an apple
and the second piece of fruit will be an orange?
YOU
M
CO
C
S
Answer:
[tex]\frac{2}{25}[/tex]
Step-by-step explanation:
There are a total of 15 pieces of fruit. For the first selection, we want a apple (6) and the second pick we want and orange (3).
[tex]\frac{6}{15}[/tex] x [tex]\frac{3}{15}[/tex] =
Which is the same as
[tex]\frac{2}{5}[/tex] x [tex]\frac{1}{5}[/tex] if I simplify both fractions which is [tex]\frac{2}{25}[/tex]
What is the pressure when 650N is applied over 40m2?
Answer:
16,25 Pa
Step-by-step explanation:
P=F/A;
650/40 = 16,
The length of the base of a rectangular prism is given as x + 4, and the width of the base is x +2. The height of the rectangular prism is three more than two times the length. Build a function to model the volume of the rectangular prism. (Hint: volume is l•w•h)
guestion 24
determine the size of the angle
mark
The size of the angle marked t is 60 degrees.
We are given an isosceles triangle with one angle as 30 degrees.
We have to find the angle marked t.
Let us name the triangle.
Let the vertex formed by the intersection of two equal sides be A and,
The vertex with 30 degree angle be B and the third vertex be C.
We know that,
AB = AC
Hence,
∠ ABC = ∠ ACB = 30 degrees.
Hence, ∠ BAC = 180 - 30 - 30 = 120 degrees
We know that,
t + ∠ BAC = 180 degrees (supplementary angles)
Hence,
t + 120 = 180
t = 180 - 120
t = 60 degrees
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x2+2x-12=0 vertex form
Taking into account the definition of vertex form, the quadratic function y=x² +2x-12 in vertex form is f(x) = 1(x - +1)² -13
Vertex form of a quadratic functionThe function f(x) = ax²+ bx + c with a, b, c real numbers and a ≠ 0, is a quadratic function expressed in its polynomial form.
The graph of a quadratic function is a curve called a parabola.
Every quadratic function can be expressed by f(x) = a(x - h)² + k
where
"a" is the main coefficient.the ordered pair (h;k) are the coordinates of the vertex of the parabola.The value of -b÷(2a) indicates the value of x or h and replacing this value into the function, you get the value of y or k of the vertex of the function.
Vertex form in this caseIn this case, the quadratic equation y=x² +2x-12, where:
a= 1b= 2c= -12The value of x or h of the vertex is calculated as -2÷(2×1)
Solving: -2÷2= -1
The value of y or k of the vertex of the function is calculated as y=(-1)²+2×(-1) -12
Solving y= -13
Finally, the quadratic function can be expressed in vertex form by f(x) = 1(x - +1)² -13
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Order 81%, 8/9, 0.79, and 9/11 from least the greatest.
Answer:
9/11, 8/9, 0.79, 81%
Step-by-step explanation:
i don't know how to explain but this is pretty much how you'd do it
3) Isaac has 18 coins, all quarters and nickels. The total value of the coins it $3.50.
Determine the number of quarters and the number of nickels that Isaac has.
By using the method subtraction,
1 quarter is 0.25
1 nickel is 0.05
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.
Given that,
Isaac has 18 coins, all quarters and nickels.
The total value of the coins it $3.50.
Let the quarters be x and nickels be y
x+ y= 18
x= 18 - y... equation 1
1 quarter is 0.25
1 nickel is 0.05
So,
0.25x+ 0.05y= 3.50
substitute x value in above equation
0.25(18-y)+0.05 = 3.50
4.5-0.25y+ 0.05 = 3.50
4.55 - 3.50 = 0.25y
1.05= 0.25y
y= 4.2
y in equation 1
x= 18 - y
x= 18-4.2
x= 13.8
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What is the slope of the line that passes
through the points (8,0) and (-4,-8)?
Write your answer in simplest form.
( Someone please help me, I'll mark brainliest )
Answer the question in the photo.
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
find the equation of the line passing through the points (2, 11) and (-8, -18)
y = [ ? ]x + [ ]
i would appreciate the help!
The equation of the line passing through the points (2, 11) and (-8, -18) is y = 29 / 10 x + 26 / 5
How to find the equation of a line?The equation of a line can be express as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through the points (2, 11) and (-8, -18).
Hence,
m = -18 - 11 / -8 - 2
m = - 29 / - 10
m = 29 / 10
Therefore, let's find the y-intercept using (2, 11)
The equation is as follows:
11 = 29 / 10(2) + b
11 = 58 / 10 + b
b = 11 - 58 / 10
b = 110 - 58 / 10
b = 52 / 10 = 26 / 5
Therefore,
y = 29 / 10 x + 26 / 5
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help please. thanks if you do
Answer:
m∠BGF = 80°Step-by-step explanation:
As per diagram, the angles BGC and CGF are marked as congruent.
It gives us:
∠BGC ≅ ∠CGF or7x - 2 = 8x - 8Solve it for x:
8x - 7x = 8 - 2x = 6Find the angle measures:
m∠BGC = m∠CGF = 7*6 - 2 = 42 - 2 = 40To find the measure of ∠BGF consider the angle addition:
m∠BGF = ∠BGC + ∠CGFm∠BGF = 40 + 40 = 80PLEASE help ill give brainliest
Answer:
A = 73°
Step-by-step explanation:
angle A + angle B = 180°
[tex](6x-35)+(3x+53) = 180[/tex]
[tex]6x+3x-35+53=180[/tex]
[tex]9x+18=180[/tex]
[tex]x=\frac{180-18}{9}[/tex]
[tex]x=18[/tex]
Angle A = 6(18) - 35 = 108 - 35 = 73°
Angle B = 3(18) + 53 = 54 + 53 = 107°
73 + 107 = 180
Hope this helps
what is 5/3 x 1 x 3 in a fraction
First, any number multiplied by 1 yields the result of itself
Therefore, we can rewrite it as 5/3 x 3.
We do the multiplication : 5/3 x 3 = 5/3 x 3/1 = (5x3)/(3x1) = 15/3 = 5.
Rewrite 5 as 5/1 for a fraction result.
a container is in the shape of a square based prism with base measurement of 3m and the height is 5m. The top and bottom are made of steel and the sides are made of aluminum. If steel costs $2.95/m^ and aluminum costs $1.57/m^, how much would it cost to make the container?
The cost for making the container if steel costs $2.95/m and aluminum costs $1.57/m is $28. 27
How to determine the cost of the containerBased on the information given, we have that;
The base of the square prism is measured 3mThe height of the square prism is measured 5mWe also have the following deductions;
Steel was used for the top and bottom are both made of steelAluminum was used for the sides of the square prismThe properties of a square prism include;
Opposite sides are parallel Opposite sides are parallelOpposite sides are equalOpposite angles are equal The diagonals of the prism divide each otherThe cost for aluminum = 10($1.57)
Multiply the values by expanding the
The cost for aluminum = $10. 57
The cost for steel = 6($2.95)
Multiply through, we have;
The cost for steel = $17. 7
Total cost for the container = Cost of steel + cost of aluminum
Total cost for the container = $10. 57 + $17. 7
Total cost for the container = $28. 27
Thus, the value of the cost is $28. 27
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HELP ANSWER ASAP!! WILL GIVE BRAINLIEST!
Please give description and how to do problem ! NO LINKS !!!
Just answer questions 12 and 13 !
Answer:
Step-by-step explanation:
12. We have : angle ABF = angle ABE + angle FBE = 2(w+11) + angle FBE = 8w - 6
-> angle ABE = 8w - 6 - [2(w+11)] = 8w - 6 - 2w - 22 = 6w - 28.
13. As we can see, angle EBA and angle EBC is a linear pair, therefore they're supplementary angles, adding up to 180.
-> 3r + 10 + 2r - 20 = 180
5r - 10 = 180
r = 38.
So, angle EBF = 2r - 20 = 76 - 20 = 56.
(pls just don't blur the question next time cause im very confused why the 2 angles are marked equal)
PLEASE HELP I AM GROUNDED AND MY MOM IS FURIOUS WITH MY GRADE
Answer:
p = 11, I hope this helps and I hope you can improve your grade.
Step-by-step explanation:
Adjacent Angles = 90 degrees, or a right angle.
90 = (5p + 7) + (3p - 5)
1. Subtract the numbers
90 = 5p + 2 + 3p
2. Combine Like Terms
90 = 5p + 2 + 3p
90 = 8p + 2
3. Subtract 2 from both sides
90 - 2 = 8p + 2 - 2
88 = 8p
4. Divided 8 from both sides
88/8 = 8p/8
p = 11
The zurn family ate at a restaurant that was having 15% discount on that day .Their meal costs 64.75,and they left a 20% tip .What is the total cost of the meal? (Note: the tip applies to the total cost of the meal before the discount was applied)
The total cost of the meal is 66.045
Given,
The cost of the meal = 64.75
The discount given on that day = 15%
The tip given by Zurn family = 20%
We have to find the total cost of the meal.
First we have to find the total cost including tip before discount is added.
That is,
120% of 64.75
= 64.75 × 120/100
= 6.475 × 12
= 77.7
Here, the total cost including tips before discount is 77.7
Now, we have to deduct the discount.
100 - 15 = 85
That is,
85% of 77.7 will be the total cost of the meal
= 77.7 × 85/100
= 6604.5 / 100
= 66.045
Therefore, the total cost of the meal is 66.045
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graph the line y=-3x+b if its graph goes through the given point A(-2,4)
The graph of the linear equation, y = -3x - 2, that passes through (-2, 4) is shown in the attachment below.
How to Graph The Line of a Linear Equation?The linear equation of a line is expressed in slope-intercept form as y = mx + b. The y-intercept of the line, which is the point where the line intercepts the y-axis, is represented as "b" in the equation.
The slope is represented as "m".
Given that the line, y = -3x + b passes through the point A(-2, 4), find the value of the y-intercept of the line, b, by substituting x = -2 and y = 4 into y = -3x + b:
4 = -3(-2) + b
4 = 6 + b
4 - 6 = 6 + b - 6
-2 = b
b = -2
Substitute b = -2 into the equation:
y = -3x - 2
The graph of y = -3x - 2 is given in the attachment.
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(c) A total of 1800 students attend St. John's College. The ratio
of teachers to students is 1:25.
(i) How many teachers are there at the college.
Three-quarters of the students own laptop computers.
(ii) How many students DO NOT own laptop computers?
Answer: the number of teachers are 14.4 and the amount of students that don’t own laptops of 5400
Step-by-step explanation:
sold for missing side length when necessary round to nearest tenth.
Answer: missing side length = 12.5
Step-by-step explanation:
1. Identify what equation to use
there are 2 side lengths, and no Pythagorean triples present therefore using the Pythagorean theorem a^2+b^2=c^2 would be a good approach
2. plug in numbers
knowing the missing side length is the hypotonus we can plug 6 and 11 for a and b: 6^2+11^2=c^2
3. Solve equation
6^2+11^2=c^2
36+121=c^2
157=c^2
12.52=c | to cancel square (^2) you must square root the number
12.5=c | round
Is 5/8 a reciprocals
Answer:8/5
Step-by-step explanation:
TO find the reciprocal, divide 1 1 by the number given
1/(5/8)
=8/5
Last night, Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael. If Dayja read 84 pages, how many pages did Luis, Dayja, and Michael read all together?
The pages read by Luis, Dayja and Michael read all together is 252.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
The conditions is,
Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael.
Total pages read by Dayja = 84
Now,
Since, Luis read 75% more pages than Dayja.
So, The pages for Luis = 75% of 84
= 75/100 × 84
= 6,300 / 100
= 63
Thus, Pages for Luis = 84 + 63
= 147
And, Number of pages read by Michael = 84 - 63
= 21
Thus, Number of pages read by Michael = 21
So, Total number of pages read by Luis, Dayja and Michael all together is;
= 84 + 147 + 21
= 252
Therefore,
The pages read by Luis, Dayja and Michael read all together is 252.
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astronomers estimate that there are about 10 to the power of 11 galaxics in the universe and that each galexy contains about 10 to the power of 11 stars about how many stars are there in the universe
Answer:
10^22
Step-by-step explanation:
= (10^11)(10^11) -> the bases are the same, add the exponents
= 10^22
Two values of v satisfy the equation |2v- 13| +6 = 9. What is the sum of these values?
Answer: v = 8, 5; The sum of these values would be 13.
∣2v − 13∣ + 6 = 9
Combine like terms, utilizing the properties of equality. Do not forget to follow the order of operations!
∣2v − 13∣ + 6 = 9
Subtract 6 from both sides of the equation.
∣2v − 13∣ = 3
Consider the definition of absolute value (distance from the number zero); the absolute value of x and -x would both be x.
2v − 13 = 3
2v − 13 = −3
Add 13 to both sides of the equation.
2v = 16
2v = 10
Divide both sides of the equation by 2.
v = 8
v = 5
Add the sum of the values.
8 + 5 = 13