Answer:
Starting position of mine shaft is = 10m above ground
but,
it moves in opposite direction so it travels the distance (-350 m ) below the ground.
Total distance covered by mine shaft = 10m - (-350m)
= 10 + 350
= 360m
Now, taken to cover a distance of 6m by it = 1 minute
Time taken to cover a distance of 1m by it = \frac{1}{6\ }\min
Therefore, tie taken to a cover a distance of 360m = \frac{1}{6}\times\ 360\ =\ 60\ \min\ \
60 minutes = 1 hour
thus, in one hour the mine shraft reaches = 350 below the ground
Step-by-step explanation:
[tex] \displaystyle \int \limits_{0}^{ \frac{ \pi}{2} } \tt\tan (x) \ln ( \sin (x))[/tex]
Let [tex]x = \arcsin(y)[/tex], so that
[tex]\sin(x) = y[/tex]
[tex]\tan(x)=\dfrac y{\sqrt{1-y^2}}[/tex]
[tex]dx = \dfrac{dy}{\sqrt{1-y^2}}[/tex]
Then the integral transforms to
[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_{y=\sin(0)}^{y=\sin\left(\frac\pi2\right)} \frac{y}{\sqrt{1-y^2}} \ln(y) \frac{dy}{\sqrt{1-y^2}}[/tex]
[tex]\displaystyle \int_{x=0}^{x=\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy[/tex]
Integrate by parts, taking
[tex]u = \ln(y) \implies du = \dfrac{dy}y[/tex]
[tex]dv = \dfrac{y}{1-y^2} \, dy \implies v = -\dfrac12 \ln|1-y^2|[/tex]
For 0 < y < 1, we have |1 - y²| = 1 - y², so
[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = uv \bigg|_{y\to0^+}^{y\to1^-} + \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]
It's easy to show that uv approaches 0 as y approaches either 0 or 1, so we just have
[tex]\displaystyle \int_0^1 \frac{y}{1-y^2} \ln(y) \, dy = \frac12 \int_0^1 \frac{\ln(1-y^2)}{y} \, dy[/tex]
Recall the Taylor series for ln(1 + y),
[tex]\displaystyle \ln(1+y) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n y^n[/tex]
Replacing y with -y² gives the Taylor series
[tex]\displaystyle \ln(1-y^2) = \sum_{n=1}^\infty \frac{(-1)^{n+1}}n (-y^2)^n = - \sum_{n=1}^\infty \frac1n y^{2n}[/tex]
and replacing ln(1 - y²) in the integral with its series representation gives
[tex]\displaystyle -\frac12 \int_0^1 \frac1y \sum_{n=1}^\infty \frac{y^{2n}}n \, dy = -\frac12 \int_0^1 \sum_{n=1}^\infty \frac{y^{2n-1}}n \, dy[/tex]
Interchanging the integral and sum (see Fubini's theorem) gives
[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy[/tex]
Compute the integral:
[tex]\displaystyle -\frac12 \sum_{n=1}^\infty \frac1n \int_0^1 y^{2n-1} \, dy = -\frac12 \sum_{n=1}^\infty \frac{y^{2n}}{2n^2} \bigg|_0^1 = -\frac14 \sum_{n=1}^\infty \frac1{n^2}[/tex]
and we recognize the famous sum (see Basel's problem),
[tex]\displaystyle \sum_{n=1}^\infty \frac1{n^2} = \frac{\pi^2}6[/tex]
So, the value of our integral is
[tex]\displaystyle \int_0^{\frac\pi2} \tan(x) \ln(\sin(x)) \, dx = \boxed{-\frac{\pi^2}{24}}[/tex]
[tex]\displaystyle \int \limits_{0}^{ \frac{ \pi}{2} } \tt\tan (x) \ln ( \sin (x))\\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin \left( \dfrac{\pi}{2} - x \right) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: I = \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \:2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(x) \right) \: dx + \int^{ \frac{\pi}{2} }_{0} \: \ln \left( cos(x) \right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \right) +\ln\left( cos(x) \right) \: dx }[/tex]
[tex]\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( sin(x) \: cos(x) \right) \: dx } \\ \\\displaystyle\sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \: \ln \left( \dfrac{sin(2x)}{2}\right) \: dx } \\ \\\displaystyle \sf{ \implies \: 2I =\int^{ \frac{\pi}{2} }_{0} \:\ln \left( sin(2x) \right)\:dx-\ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]
Put 2x = t, so,[tex]\displaystyle\sf{ \implies \: 2I = \dfrac{1}{2} \int^{ \pi}_{0} \: \ln \left( sin(t) \right) \:dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\\displaystyle\tt{ \implies \: 2I = \dfrac{1}{2} \cdot2 \int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2) \int^{ \frac{\pi}{2} }_{0} \: dx}[/tex]
[tex]\displaystyle \tt{ \implies \: 2I =\int^{ \frac{\pi}{2}}_{0} \: \ln \left( sin(t) \right) \: dt - \ln(2)\int^{ \frac{\pi}{2} }_{0} \: dx} \\ \\ \displaystyle \tt{ \implies \: 2I = I - \ln(2) \left[x \right] ^{ \frac{\pi}{2} }_{0} } \\ \\ \displaystyle \tt{ \implies \: I = -\ln(2)\left[ \dfrac{\pi}{2} - 0 \right] }[/tex]
[tex]\displaystyle \sf{ \implies \: I = - \dfrac{\pi}{2} \ln(2) }[/tex]
_____________________☞︎︎︎Apologies,if incorrect.
pleasle help with math problem
Answer: 12
I am not sure what you need help with exactly but
3 ÷ 1/4 = 12
Reason: 3 ×4/1 = 12 3×4= 12/1 take off the 1 and the answer is 12
why 4/1 you would find the reciprocal of 1/4 and the reciprocal of 1/4 is 4/1 or just 4 you dont need the 1 but if you cant handle your math problem without the 1 you can use it but always remember to take out the 1 in your final answer.
I really hopes this helps you.
Find the measure of <2
Answer:
<2 = 28°
Step-by-step explanation:
3y+ 53 = 7y -55 (Corresponding angles)
collect like terms
-4y= -108
y= 27°
3y-53 = 28
<2 =28° (Alternating angles ; 2 parallel lines)
(-8,-5) after a translation right 1 units and down 5 units?
jelp pls with 2 work pps brainly
Answer:
The underline one is 40.
Missing numbers. 35, 40 45, 50, 55, 60, 65, 70.
Step-by-step explanation:
Add 5 rule
Answer:
5. The tens place.
6. 35, 40, 45, 50, 55, 60, 65.... (And so on)
Step-by-step explanation:
Hoped this helped.
(x + 1)(x - 1)
I dont understand this could any1 help me
Answer:
x^2-1
Step-by-step explanation:
you must use the distributive property
first you do x•x=x^2,
then you do x•1 and x•-1 to get x and -x and those cancel out,
the you do 1•-1=-1, then you put it together to get x^2-1
Step-by-step explanation:
It's a factored form of the quadratic equation
[tex] {x}^{2} - 1[/tex]
in the form of [tex] {ax}^{2} + bx + c[/tex]
in which a = 1, b = 0, c = 1.
1) A very lucrative savings account earns 2.8% annual interest, compounded monthly. It is currently worth $10,427.39. How much was it worth a year and a half ago?
926+729299277=5289+83783
1 pts
Compute the total amount accumulated if you invested $850 for 4 years at 2.4% compounded
semiannually. Round your answer to the nearest cent and include '$' in your response.
9514 1404 393
Answer:
$935.11
Step-by-step explanation:
The amount is given by the formula ...
A = P(1 +r/n)^(nt) . . . P invested at rate r for t years compounded n per year
A = $850(1 +0.024/2)^(2·4) = $935.11
The amount accumulated will be $935.11 after 4 years.
what is -4 3/4 = x - 1 1/5
Answer:
12.95 or in fraction form 259/20Step-by-step explanation:
Do you want to know how to write the decimal number 12.95 as a fraction?
Here we will show you step-by-step how to convert 12.95 so you can write it as a fraction.
You can take any number, such as 12.95, and write a 1 as the denominator to make it a fraction and keep the same value, like this:
12.95 / 1
To get rid of the decimal point in the numerator, we count the numbers after the decimal in 12.95, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by 100 to get the following fraction:
1295 / 100
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of 1295 and 100 is 5. When we divide the numerator and denominator by 5, we get the following:
259 / 20
Therefore, 12.95 as a fraction is as follows:
259 / 20
The homeowners association for a residential community is selecting a committee of 7. There are 24 candidates for positions. How many possible committees can be formed?
Answer: 168
Step-by-step explanation:
Times the two numbers together to get the combinations.
24x7=168
Possible number of committees formed is equals to 3.
What is number?
" Number is defined as the arithmetic value which represents the count of any given quantity."
According to the question,
Total number of candidates for positions = 24
Number of candidate selected for 1 committee = 7
Total possible number of committees = [tex]\frac{24}{7}[/tex]
= 3.428
≈ 3 committees (approximate)
As one committee is formed by 7 candidates , it can not be in decimals or fractions.
Hence, possible number of committees formed is equals to 3.
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solve the system of equations by graphing.
3x + y = -4
x - 2y = -6
Answer:
(-2,2)
Step-by-step explanation:
Which of the statements about the picture below are true? Check all that apply.
A. F is the circumcenter of the triangle.
B. F is the incenter of the triangle.
C. F is the point of concurrency of the perpendicular bisectors of the sides of the triangle.
D. F is the point of concurrency of the angle bisectors of the angles of the triangle.
E. F is equidistant from the angles of the triangle.
F. F is equidistant from the three sides of the triangle.
Answer:
Below
Step-by-step explanation:
The following are true:
B. F is the incenter.
D. F is the point of concurrency of the angle bisectors of the angles of the
F. F is equidistant from the three sides of the triangle.
The following statements are true:
B. F is the incenter.
D. F is the point of concurrency of the angle bisectors of the angles of the
F. F is equidistant from the three sides of the triangle.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ. It has three connected vertices.
The circumcenter of a triangle is measured from the point at which the perpendicular bisectors of its sides cross.
The incenter of a triangle is the point at which the triangle's three internal angle bisectors meet.
Thus, the following statements are true:
B. F is the incenter.
D. F is the point of concurrency of the angle bisectors of the angles of the
F. F is equidistant from the three sides of the triangle.
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4(x - 4) + 2x -10 and what the answer
Answer:
Expression: 6x - 26. Equation: 3
Step-by-step explanation:
EXPRESSION
4x - 16 + 2x - 10
6x - 26
EQUATION 1
4x - 16 = 2x - 10 (Seems reasonable. Sorry if this isn't it)
4x = 2x + 6
2x = 6
x = 3
EQUATION 2
4x - 16 + 2x = - 10
6x - 16= -10
6x = 6
x = 1
Plz help me well mark brainliest! Only if correct!.
Answer:
[tex]6(\frac{5}{6}x+\frac{2}{3}) =-9(6)[/tex][tex]5x- -58[/tex][tex]5x+4=-54[/tex]Step-by-step explanation:
Hope this helps!
Describe an example in which two variables are strongly correlated, but changes in one do not cause changes in the other.
Just because 2 things are related doesn't mean they will both be changed when one thing happens. For example steak and candy, just because they are both food doesn't mean they taste the same or interact with each other.
pls pls help!!! brainliest!!
Chris got a new cell phone and wanted to download some music. The graph shows the storage on his cell phone as a function of
-intercept in terms of this problem.
A. The x-intercept shows that he can download 53 songs before running out of storage on his phone
B. The x-intercept shows that he started with 16 songs downloaded before adding more.
C. The x-intercept shows that he has 53 GB of storage on his phone.
D. The x-intercept shows that he can download 16 songs before running out of storage on his phone.
Answer: the answer is A. The x-intercept shows that he can download 53 songs before running out of storage on his phone
Step-by-step explanation:
Chris got a new cell phone and wanted to download some music. The graph shows the storage on his cell phone as a function of
-intercept in terms of this problem.
A. The x-intercept shows that he can download 53 songs before running out of storage on his phone
B. The x-intercept shows that he started with 16 songs downloaded before adding more.
C. The x-intercept shows that he has 53 GB of storage on his phone.
D. The x-intercept shows that he can download 16 songs before running out of storage on his phone.
Whats the area and the perimeter of this shape. show calculations
Answer:
The answer is 15 cm
Step-by-step explanation:
as one square is 1 cm and there are 15 squares used for this shape then it is 15 cm
Productivity gains are an important factor in the expenditure model because
A. companies can “squeeze” workers more than normal
B. it shifts the AD curve to the left
C. the investments made are cheaper and allows companies to
D. it shifts the AS curve to the right
Answer:
A
Step-by-step explanation:
companies can squeeze workers more than normal
simplify the expression (b+3)+(2b-2)
Answer:
if you meant (b+3)+(2^b-2), the answer is b+1+2^b
Step-by-step explanation:
but if you meant (b+3)+(2b-2), the aanswer is 3b+1
Answer:
3b+1
Step-by-step explanation:
(b+3)+(2b-2)
b+3+2b-2
3-2
b+1+2b
b+2b
3b+1
124/72 simplified is?
Answer:
31/18
Step-by-step explanation:
the ratio of collectible pennants kyle owns to pennants that yasmine owns is 3:2 yasmine has 36 pennants . How will the ratio of kyles pennants to yasmines pennants change if they both sell half of their pennants Explain
Answer:
If they both sell half then Kyle would have 1.5:1 and Yasmine would have 18 pennants.
Step-by-step explanation:
It will change because if they both sell half, they would have to multiply by .05 or divide by 2 because that is half of something.
3/2 or 3*0.5 = 1.5
2/2 or 2*0.5 = 1
36/2 or 36*0.5 = 18
So Kyle would have 1.5:1 pennants left and Yasmine would have 18 pennants left.
Where , the distance between the points ( a, c) and ( b, c) is ( ) units
Answer:
I would love to help but there is no upload. Would you mind creating a new question with a picture or data of the graph
Step-by-step explanation:
A desk is 39 inches wide. What is the width in yards
Answer:
1.0833 yd
Step-by-step explanation:
Inches Yards
37" 1.0278 yd
38" 1.0556 yd
39" 1.0833 yd
40" 1.1111 yd
Have a great day! :D
Leonard conducts a study to see if the number of hawks in a park affects the number
of squirrels. What is the response variable in this study?
A.The number of hawks in the park
B.The number of squirrels in the park
In the experiment, the response variable is the dependent variable, or the measured variable.
The response variable in the study is; B. The number of squirrels in the parkReasons:
The study Leonard conducts is a study to determine if the number of
hawks located in the park affects the number of squirrels in the park.
The response variable is the variable of the experimental result, which is
the dependent or output variable obtained by manipulating the input
variable.
In the experiment conducted by Leonard, the variable that is being
manipulated, which is the input variable is the number of hawks in the park
The variable that is being measured, which is the output variable or the
response variable, is; B. the number squirrels in the park.
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Solve 2x-1/4 + x/3 = 2
Step-by-step explanation:
=> 2x-1/4 + x/3 = 2
=> 3(2x-1) +4x / 12 = 2
=> 6x -3 + 4x = 24
=> 10x = 27
=> x = 2.7
Answer:
x = 27/28
Step-by-step explanation:
Solve 2x-1/4 + x/3 = 2
2x - 1/4 + x/3 = 2
2x + (-1/4) + 1/3x = 2
(2x + 1/3x) + (-1/4) = 2
7/3x + (-1/4) = 2
7/3x = 9/4
3/7 * 7/3x = 3/4 * 9/4
x = 27/28
---------------------
check
2 * 27/28 - 1/4 + 27/28 *1/3 = 2
2 = 2
the answer is good
What will be the velocity of a when it travels 300 min 30 second?with explanation.
Write the ratio:
0.26
to
0.52
as a fraction in lowest terms.
Answer:
[tex] \frac{13}{50} to \: \frac{12}{25} [/tex]
Plx = 3 + 5x+2
Degree
Leading coefficient
Turning Points
End
Behavior of the
Graph
Answer:
cost of renting from company A
C = 15 + 2.30x
cost of renting from company B
C = 22 + 1.90x
equate both the equations
15 + 2.30x = 22 + 1.90x
2.30x - 1.90x = 22-15
0.4x = 7
x = 7/0.4 = 17.5
At 17.5 miles, cost will be equal.
Answer: 17.5 miles
Judy is looking to buy a textbook. The book normally costs $75.82, but it is on sale for 35% below
the regular cost. How much will the book cost before taxes if Judy is to buy it while it is on sale?
Round to the nearest cent.
Answer:
$49.28 is the sale cost.
Step-by-step explanation:
0.35 x 75.82 = 26.537
75.82 - 26.537
= 49.283 and round
The selling cost of the book will be equal to $49.28.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Judy is looking to buy a textbook. The book normally costs $75.82, but it is on sale for 35% below the regular cost.
The selling cost of the book will be calculated as,
Selling Cost = 0.35 x 75.82 = 26.537
Selling Cost = 75.82 - 26.537
Selling Cost = 49.283
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Graph the original function by indicating how the more basic function has ben shifted, reflected, stretched, or compressed