Complete the square in the denominator to get
tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1
… = (tan(t ) + 7)² - 1
Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes
[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = 2 \int \frac{\mathrm du}{u^2-1}[/tex]
Separate the integrand into partial fractions:
[tex]\dfrac1{u^2-1} = \dfrac12 \left(\dfrac1{u-1}-\dfrac1{u+1}\right)[/tex]
Then we get
[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = \int \left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm du \\\\ =\ln|u-1|-\ln|u+1| + C \\\\ = \ln\left|\frac{u-1}{u+1}\right|+C \\\\ = \boxed{\ln\left|\frac{\tan(t)+6}{\tan(t)+8}\right|+C}[/tex]
The perimeter of a rectangular garden is 120 feet The garden is two times as long as it’s why the system of equation can be used to find the width in the length what is the length
Answer:
Step-by-step explanation:
Garden is two times as long as it is wide.
L = 2W
Perimeter is 120 feet
2L + 2W = 120
L +W = 60
(2W) + W = 60
3W = 60
W = 20 feet
L = 2W = 40 feet
The length of a shoe is 25 centimeters. How long is the shoe in meters? (Note: 1 meter = 100 centimeters). pls help
Answer:
0.25meters
As 100cm=1metre
so, 25cm=25/100meter
=0.25metre
Step-by-step explanation:
If you like my answer than please mark me brainliest
The answer is 0.25 meters
linear equation 7x+25=9
Answer:
x = -16/7
Step-by-step explanation:
7x+25=9
Subtract 25 from each side
7x+25-25=9-25
7x = -16
Divide each side by 7
7x/7 = -16/7
x = -16/7
Answer:
[tex]7x + 25 = 9 \\ 7x = 9 - 25 \\ 7x = - 16 \\ x = \frac{ - 16}{7} \\ x = - 2.29[/tex]
Step-by-step explanation:
I hope it helped U
stay safe stay happy
What is the product of these two binomials?
(x2 - 5)(2x - 1)
Select the correct answer.
o 2x3 - x2 + 10x - 5
O 2x3 - x2 - 10x-5
o 2x3 - x2 - 10x + 5
o 2x3 - x2 + 10x + 5
Answer:
2x³ - x² - 10x + 5
Step-by-step explanation:
Use FOIL method.
(x² - 5) (2x - 1) = x²*2x +(x²)*(-1) + (-5)*(2x) + (-5)*(-1)
= 2x³ - x² - 10x + 5
The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
Answer:
f^-1 (-15) = -6
f^-1(4) + f(9) = 0
Step-by-step explanation:
f^-1 (-15) =
Look where the output is -15 and find the x value ( x=-6)
Since where are using the inverse function, the input becomes the output and the output and the output becomes the input
f^-1 (-15) = -6
f^-1 (4) = -11 (inverse function)
f(9) = 11 ( regular function)
f^-1(4) + f(9) = -11+11 = 0
PLEASE HELP
4/9w = -8
Show your work in details if you can, I have a hard time understanding this.
[tex] \begin{cases}\large\bf{\blue{ \implies}} \tt \: \frac{4}{9} \sf \: w \: = \: - 8 \\ \\ \large\bf{\blue{ \implies}} \tt \: \frac{4 \sf \: w}{9} \: = \: 8 \\ \\ \large\bf{\blue{ \implies}} \tt 4 \sf \: w \: = \: 9 \: \times \: 8 \\ \\ \large\bf{\blue{ \implies}} \tt 4 \sf \: w \: = \: 72 \\ \\ \large\bf{\blue{ \implies}} \tt \sf \: w \: = \: \cancel\frac{72}{4} \\ \\ \large\bf{\blue{ \implies}} \tt \sf \: w \: = \: 18 \end{cases}[/tex]
please help me asap!!!!!
Answer:
392
Step-by-step explanation:
1.49×10⁸/3.8×10⁵ = 392
PLease help me multiply and divide these two fraction problems I don't understand at all.
Multiply:
4(−5 2/3)
Divide:
−5/8÷12
Answer:
I am not so sure but I am assuming-5 2/3 to be mixed fraction so improper fraction wud be -17/3
now 4*- 17/3 = 68/3
now divide -5/8 ÷ 12
so u must know the rule that if division we can multiply by reciprocal
so -5/(8*12) = -5/96
hope that helps
In 2014, the population of Ohio was 11.59 million people. One-hundred years earlier the population was 5.109 million people. Using scientific notation, how much did the population grow over the hundred-year span?
The answer is the population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]
Given that in 2014, the population of people in Ohio = [tex]11.59[/tex] million
Also given that One-hundred years earlier of the year 1914, the population = [tex]5.109[/tex] million people
One-hundred years earlier in the year 2014 = 2014 [tex]- 100[/tex] years
One-hundred years earlier in the year 2014 = Year 1914
The scientific notation of the year 2014 population is [tex]11.59*(10)^6[/tex]
The scientific notation of the year 1914 population is [tex]5.109*(10)^6[/tex]
How much did the population grow over the hundred-year span?
Growth of the population from 1914-2014 = [tex]11.59*(10)^6 - 5.109*(10)^6[/tex]
Growth of the population from 1914-2014 = [tex]6.481*(10)^6[/tex]
Conclusion: The population grew over the hundred-year span by [tex]6.481*(10)^6[/tex]
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PLEASE I HAVE AN HOUR Why might you use the distributive property to simplify 3(30-2)
Nasa is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before the launch and has a diameter of 4.7 feet. What is the total weight in pounds?
Answer:
Step-by-step explanation:
Determine the pattern for the following sequence and find the next two terms: 1, -2,4,-8, ...
Answer:
Answer:×(-2)
Answer:×(-2)Step-by-step explanation:
-2/1 = -2
4/-2 = -2
-8/2 = -2
Next two: 16, -32
The figure to the right shows the graphs of the cost and revenue functions for a
company that manufactures and sells small radios. The solid red line represents the
revenue function, R(x) = 55x; the dashed blue line represents the cost function,
C(x) = 15,000 + 30x. Use the formulas to find R(300) - C(300). Describe what this means for the company
(Type integers or decimals.)
R(300) - C(300) = ???
which represents a $ ???
loss for the company
B. R(300) - C(300) = ??
which represents a ??
gain for the company
From the formula R(300) - C(300) we understand that is loss of 7500 for the company.
The given functions are R(x) = 55x and C(x) = 15,000 + 30x.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is R(300) - C(300).
Now, R(300) = 55 × 300 = 16500
C(300) = 15,000 + 30 × 300
=15,000 + 9000
= 24,000
Now, R(300) - C(300) = 16500-24000
= -7,500
Therefore, from the formula R(300) - C(300) we understand that is loss of 7500 for the company.
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solve it quickly. l follow you make brainlaist. first solve so l
[tex]5 \frac{2}{3} + 3 \frac{1}{5} \\ \frac{17}{3} + \frac{16}{5} \\ \frac{(17 \times 5) + (16\times 3)}{5 \times 3} \\ \frac{85 + 48}{15} \\ \frac{133}{15} = 8\frac{13}{15} [/tex]
HELP MEEEE FAST PLZ
MY MOM THINKS IM SMART BUT I DON'T GET THIS AHHHH HELP
Answer:
10
Step-by-step explanation:
-3 = 7 - 10
-3 = -3
Translate the verbal phrase "three less than three times a number w into an expression.
Answer:
3w - 3
Step-by-step explanation:
A company makes cylindrical crackers that have a cylindrical hole in the middle.
The diameter of the entire cracker is 16\text{ mm}16 mm16, start text, space, m, m, end text, the diameter of the hole is 8\text{ mm}8 mm8, start text, space, m, m, end text, and the cracker is 18\text{ mm}18 mm18, start text, space, m, m, end text long.
What is the volume of the material used in each cracker?
Round to the nearest cubic millimeter.
Answer:
Its 2714
Step-by-step explanation:
Khan Academy
The volume of the material that would be needed for each cylindrical cracker is approximately: 2,714 mm³ mm³.
What is the Volume of a Cylinder?Volume of a cylinder = πr²h
The volume of the material used for each cylindrical cracker = Volume of entire cylindrical cracker - volume of cylindrical hole
Radius of entire cracker (r) = 16/2 = 8 mm
Height (h) = 18 mm
Volume of the entire cracker = π(8²)(18) ≈ 3,619 mm³
Radius of hole (r) = 8/2 = 4 mm
Height (h) = 18 mm
Volume of the entire cracker = π(4²)(18) ≈ 905 mm³
The volume of the material used for each cylindrical cracker = 3,619 - 905 = 2,714 mm³
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Solve for X and show your work and explain please
Answer: x = 45
Step-by-step explanation:
Given
(2/3)x + 4 = (4/5)x - 2
Add 2 on both sides
(2/3)x + 4 + 2 = (4/5)x - 2 + 2
(2/3)x + 6 = (4/5)x
Subtract (2/3)x on both sides
(2/3)x + 6 - (2/3)x = (4/5)x - (2/3)x
6 = (12/15)x - (10/15)x
6 = (2/15)x
Divide 2/15 on both sides
6 / (2/15) = (2/15)x / (2/15)
[tex]\boxed{x=45}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
x = 45
Step-by-step explanation:
2/3 x + 4 = 4/5x - 2 Add 2 to both sides
2/3 x + 4 + 2 = 4/5x Combine
2/3x + 6 = 4/5x Subtract 2/3 x from both sides.
6 = 4/5x - 2/3 x Multiply both sides by 15
6*15 = 4/5 x * 15 - 2/3x * 15
6*15 = 12x - 10x Combine the left and right
90 = 2x Divide by 2
x = 45
Let's see if it works.
LHS = 2/3 * 45 + 4
LHS = 2*15 + 4
LHS = 30 + 4
LHS = 34
RHS
Right hand side = 4/5 * 45 - 2
RHS = 36 - 2
RHS = 34 which is the same as the LHS
PLEASE HELP MATH
Find the interquartile range of the data shown on the box-and-whisker plot below.
Answer:
Step-by-step explanation:
to find an interquartile range of the data in order to proceed with it.
ans:
53 + 1 = 54
57 - 3 = 54
24 + 30 = 54
29 + 25 = 54
The interquartile range of the data shown on the box-and-whisker plot will be 29.
How to find the interquartile range?IQR(inter quartile range) is the difference between third and first quartile.
Usually, we use interquartile range along with two quartiles Q1 and Q3 to get the anomalies.
Those values who lie below Q1 - 1.5 xIQR or above Q3 + 1.5 xIQR are called anomalies.
But since in the case when these things are not obtainable, we check manually which point is lying away from mean or outside of usual range etc.
In order to find an interquartile range of the data in order to proceed with it.
In the box-and-whisker plot given:
Upper quartile = 54
Lower quartile = 25
Interquartile range (IQR)
54 - 25 = 29
Therefore, the interquartile range of the data shown on the box-and-whisker plot will be 29.
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In the picture below, which lines are lines of symmetry for the figure?
A. 1 and 3
B. only 1
C. only 3
D. 2 and 4
Answer:
It's option C. only 3
Step-by-step explanation:
A line of symmetry is a line which will cut any shape in exactly half. In your given picture, only line 3 is symmetrical because if you were to fold the shape after you cut it in half, both halves would match and be equal.
Given: △PST, Area of △PST=71.24 PS=15, Pt=13 Find: m∠P (Please help!!!)
Answer:
46.94 degrees (approx)
Step-by-step explanation:
I need help! I will give brainliest, if correct!
For a certain value of $k$, the system
x + y + 3z = 10,
-4x + 3y + 5z = 7,
kx + z = 3
has no solutions. What is this value of k?
kx + z = 3 means z = 3 - kx. Substitute this into the first two equations:
x + y + 3 (3 - kx) = 10 ==> (1 - 3k) x + y = 1
-4x + 3y + 5 (3 - kx) = 7 ==> (-4 - 5k) x + 3y = -8
Multiply through the first equation by -3 :
-3 ((1 - 3k) x + y) = -3 (1) ==> (-3 + 9k) x - 3y = -3
Add this to the second equation to eliminate y :
((-3 + 9k) x - 3y) + ((-4 - 5k) x + 3y) = -3 + (-8)
(-7 + 4k) x = -11
Normally, you would solve for x by dividing both sides by -7 + 4k. But you can't do that if this turns out to be equal to 0, which happens for
-7 + 4k = 0 ==> k = 7/4
Answer:
k = 7/4
Step-by-step explanation:
how do I do this?????????????????????????????
If 1/2 of a loaf of brown bread costs R6,how much will 2 halves cost
Step-by-step explanation:
1/2 is equal to R6.
So 2 halves mean R6+R6=R12
Or
R6×2= R12
Answer:R12
please solve regression equation
Step-by-step explanation:
can't c please type the question..
Emma spent 4 and one-half days planting her garden. Her brother spent 2 Over 9 as much time as Emma did. How many days did her brother spend planting his garden?
Answer: 1 day
Step-by-step explanation:
i took the test lol...
Is this a function graph help
Answer:
This is not a function graph as no variables are present.
Belinda wants to invest in an option that would help to increase your investment value by the greatest amount in 20 years. Will there be any significant can difference in the value of Belinda‘s investment after 20 years if she uses option two over option one? Explain your answer, and show the investment value after 20 years for each option.
Step-by-step explanation:
Part A, Option 1 is a exponential function while option is a linear equation.
Part B, Let y=b*a^(x) be the function for option 1. At x=1, y=1100 and at x=2, y=1210. 1100=b*a and 1210=b*a^2. Dividing them both we get, b=1.1 and a=1000. y=1000*(1.1)^(x). For option 2, it's a linear equation with a function y(x)=1000+100x.
The 20 year difference would be immense. With option 1, Belinda will get $6727.5 whereas with option 2, they will end up with $3000
Find the surface area?
Answer:
Surface area of prism is 48km^2
The diameter of a cone is 34 ft. the height is 16 ft what is the volume in cubic ft?
Answer:
4842.24 cubic feet
Step-by-step explanation:
Use the formula for the volume of a cone, V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
The diameter of the cone is 34 ft, so the radius is 17 ft.
Plug in the radius and height into the formula, and solve for the volume:
V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
V = [tex]\pi[/tex](17)²[tex]\frac{16}{3}[/tex]
V = [tex]\pi[/tex](289)[tex]\frac{16}{3}[/tex]
V = 4842.24
So, the volume of the cone is 4842.24 cubic feet
Answer:
4,841.32 ft³.
Step-by-step explanation:
Let’s assume that this is a right circular cone and that the radius of the cone is r.
For our problem, r = (1/2)d = (1/2)34 = 17.
The volume of the cone is:
V = (1/3)pi r^2 h, where r is the radius and h is the height.
So, V = (1/3)pi(17^2)16 = 4,841.32 ft³.
