The integration is as follow
[tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex] = 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C[tex]\int\limits {33 sec^5 (x)} \, dx[/tex] = 33/4 tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + CWhat is Integration?Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.
Given:
first, [tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex]
= [tex]\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx[/tex]
let [tex]e^{4x}[/tex] = z
4[tex]e^{4x}[/tex] dx = dz
= 1/4 [tex]\int\limits {dz / \sqrt{19} ^2 -z^2} \,[/tex]
= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C
= 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C
Second,
[tex]\int\limits {33 sec^5 (x)} \, dx[/tex]
= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]
= 33/4 tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]
= 33/4 tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C
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find the area of the triangle below 5.4 m 9 m 4.5 m 7.5 m
Answer:i think is it 1640.25
Step-by-step explanation:
Using the slot method and multiple cases, calculate the probability that you would roll 3 sixes with four standard dice.
Answer:
[tex]Pr = \frac{1}{216}[/tex]
Step-by-step explanation:
The sample space of a single dice is:
[tex]S = \{1,2,3,4,5,6\}[/tex]
[tex]n(S) = 6[/tex]
Required:
The probability of rolling 3 sixes
In a sample space of a roll of die, we have:
[tex]n(6) = 1[/tex]
In a roll of dice, the probability of rolling a 6 is:
[tex]P(6) = \frac{n(6)}{n(S)}[/tex]
[tex]P(6) = \frac{1}{6}[/tex]
In 3 rolls, the probability is:
[tex]Pr = P(6)^3[/tex]
[tex]Pr = [\frac{1}{6}]^3[/tex]
[tex]Pr = \frac{1}{216}[/tex]
Find the area of a regular pentagon with a side of 10 cm. and an apothem of 4 cm.
Answer:100
Step-by-step explanation:perimeter times apothem divided by two
A rectangle has the dimensions shown. The area of the rectangle would be represented by which type of expression? linear expression quadratic expression exponential expression rational expression
Answer:
rational expression
Step-by-step explanation:
Answer:
it's quadratic
Step-by-step explanation:
The area of a sector with a radius of 22 yards is 89.45 square yards. Calculate the approximate angle of the sector
Answer:
0.3696 radian
21.178°
Step-by-step explanation:
Given :
Radius, r = 22 yards
Area of Sector = 89.45 yd²
Approximate angle of the sector :
Area of Sector = 1/2 * θ * r²
89.45 = 1/2 * θ * 22²
89.45 = 0.5 * 484 * θ
89.45 = 242θ
θ = 89.45 / 242
θ = 0.3696 radian
Radian to degree
0.3696 * 180 / π = 21.178°
Convert the units of capacity.
10 pt = ___ ___ qt
Answer:
6.00475
Step-by-step explanation:
What is the least positive integer such that it is a multiple of 16 and the product of its digits is a multiple of 12?
Answer:
24
Step-by-step explanation:
Multiples of 16 are [tex]16,32,48,64,80,...[/tex]
Find product of each of the multiple of 16 until a number is obtained, the product of whose digits is a multiple of 12.
[tex]16=1(6)=6\\32=3(2)=6\\48=4(8)=32\\64=6(4)=24[/tex]
Here, 24 is a multiple of 12.
So,
24 is the least positive integer such that it is a multiple of 16 and the product of its digits is a multiple of 12.
Please help!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Quadrilateral A'B'C'D'A
A, prime, B, prime, C, prime, D, prime is the image of quadrilateral ABCD , A B, C, D under a dilation with a scale factor of 4.
What is the length of segment \overline{C'D'}
ill really like the help.
Thank you.
Answer:
41 I think
Step-by-step explanation:
I looked it up for you!
Can somebody who knows how to do this plz help answer these questions correctly (only if u done this before) thx :3
WILL MARK BRAINLEST WHOEVER ANSWERS FIRST :DDDD
Step-by-step explanation:
angle b = 25° ( vertically opposite)
angle a = 155° ( linear pair)
angle c = 155 ( vertically opposite)
angle a and c are vertically opposite angles
Create and solve a 2 step with subtraction and multiplication Also, x = 9
Answer:
x - 4(x - 2) = -37
x - 4x + 8 = -37
-5x = -37 - 8
-5x = -45
x = 9
the sum of a number x and 7 is 35
dont need answer
Answer:
28
Step-by-step explanation:
x + 7 = 35
subtract 7
x = 28
please help!
AABC ~ AQRS
Find the missing side length, n.
5
R
12.5
n
Q
10
B
5
2
A
4
C
n = [?]
Using the property of similar triangles, we found that the value of n is 5.
This is the length of the side RQ.
What are similar triangles?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are similar. Similar figures are described as items with the same shape but varying sizes, such as two or more figures. Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.
The given triangles are both right triangles.
So they can be considered similar triangles.
One of the properties of similar triangles is that the ratio of corresponding sides is always equal.
Then we can write for the given triangles,
BA/RQ = AC/QS
2/n = 4/10
n = 2 * 10 / 4 = 5
Therefore using the property of similar triangles, we found that the value of n is 5.
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What's the distance between (–4, 3) and (4, 3)? Question 7 options: A) 11 units B) –8 units C) 14 units D) 8 units
Answer:
it is 8 unit .because distance will not be negative.As it is scalar .
HHHHEEEEEEELLLLPPPPPPP !!!!!!
Answer:
C
Step-by-step explanation:
Mike has a fish tank in the shape of a rectangular prism with dimesions of 6 feet by 5 feet by 3 feet. He has a canister that he uses to fill up the fish tank that is in the shape of a cylinder with a diameter of 2 feet and a height of 4 feet. How many tiems will he need to fil up the canister to fill up the tank?
Answer:
7 times
Step-by-step explanation:
To answer this question :
1. the volume of the rectangular prism has to b determined
2. the volume of the cannister has to be determined
3. divide the volume of the rectangular prism by the volume of the cannister
Volume of the rectangular prism = Width X Height X Length = 6 x 5 x 3 = 90ft³
Volume of a cylinder = πr²h
where
h = height
π = 3.14
Diameter = 2r
radius = 2/2 = 1 feet
3.14 x 1 x 4 = 12.56 feet
90 / 12.56 = 7.2 times
Approximating to the nearest whole number gives 7 times
If the acceleration is 600m/s/s and the mass is 300kg, calculate the force? *
Answer:
600 m/s2 ×300 kg = 180000 kg.m/s2
Answer:
180000Kgm/s2
Step-by-step explanation:
Force is the product of mass and acceleration. So F=MA
F=600 x 300
F=180000
Please help!
An isosceles triangle has base angles that each measure 34°. Which of the following equations could be used to find x, the measure of the third angle of this isosceles triangle in degrees?
A. 34 + x = 180
B. 68 + x = 180
C. 68 + 2x = 180
D. 34 + 2x = 180
Elvis and $74 .50 a month.. how much does he earn to the nearest one penny.
A. in a year
B. in a week
C. in a day
Answer:
Part A
12 months a year means
%74.5 x 12 = $894
Part B
4 weeks in a month means
$74.5 ÷ 4 = $18.625
But rounded to the nearest penny. . .
$18.62
because in the thousandths place was a 5 and you round up when there is a 5 or above
Part C
We will go with 31 days in a month, but I will also do 30 for you
$74.5 ÷ 30 = $2.48333
But rounded to the nearest penny. . .
$2.48
because you round down when there is anything less than a 4
$74.5 ÷ 31 = $2.40322580645
But rounded to the nearest penny. . .
$2.40
because you round down when there is anything less than a 4
(5g2+6g-10)
-(6b2+2g+9)
Answer:
look at given picture
Step-by-step explanation:
there is complete soln
Adding & subtracting decimals word problems
Answer:
7.17 km
Step-by-step explanation:
please like my answer and brainliest me......huhu
solve for x
Need help with this last question
Answer:
x = 8
Step-by-step explanation:
2(78°) = 20x - 4
156 = 20x - 4
add 4 to each side of the equation:
160 = 20x
divide both sides by 20:
x = 8
The Valley Central School District ordered 300 bagels for their spring faculty breakfast. They want 65% of the bagels to be plain. How many plain bagels should they order?
PLS HELP ASAP
Answer:
The answer to your question is 195
Which method would be the most efficient way to solve the method : substitution method, Eliminating method or equal value 3x+y=1 4x+y=2
Answer:
Eliminating method
Step-by-step explanation:
For the given situation i.e.
3x + y = 1
And,
4x + y = 2
Here we use the elimination to determine the value of x and y
So,
3x + y = 1
4x + y = 2
- - -
-x = -1
x = 1
Now put the value of x in any of the above equation
So,
3 + y = 1
y = -2
brown hair (H) is dominant to blond hair (h). Two hybrid parents have 4 kids. what is the likelihood that their kids will be hybrids as well? (this is punnett square)
Answer:
50 %
Step-by-step explanation:
Solve for x
(3x-15) & (2x+7)
Answer:
for the first one X=-5
for the second one it's a fraction so look at the picture
HELP ME I WILL MARK BRAINLIEST
Answer:
The answer is 1/15
I hope it helps
24 > 6 + 3y = ____
image of question included
Answer:
Step-by-step explanation:
24 > 6 + 3y
Bringing like terms on one side
24 - 6 > 3y
18 > 3y
18/3 > y
6 > y
Option C 6 is the correct answer
Help p please:)......
A corporation is under orders to reduce the time office workers spend filling out their TPS reports. Previously the average time spent on the TPS report was 6.3 hours. In order to test whether the time to fill out the TPS report has been reduced, a sample of 48 office workers was randomly chosen, and their completion times recorded. The mean completion time for their TPS reports was 5.7 hours with a standard deviation of 1.8 hours. In order to test that the time to complete the TPS report has been reduced, state the appropriate null and alternative hypotheses.
Answer:
The null hypothesis, H₀ is that the mean completion time for the TPS report remains at the duration of 6.3 hours
The alternative hypothesis, H₁ is that the mean completion time for the TPS report is less than 6.3 hours
Step-by-step explanation:
The given parameters are;
The average time spent on the TPS report = 6.3 hours
The number of workers in the sample used for the test = 48 office workers
The mean completion time of the TPS report for the sample = 5.7 hours
The test aim; To find out whether the mean time required to fill out the TPS report has been reduced
The null hypothesis, is H₀; μ = 6.3 hours
The alternative hypothesis, H₁; μ < 6.3 hours