The given parametric curve x=cost, y=et; 0≤t≤π/2, intersects the line y=1 at t=0, and intersects the line x=0 at t=π/2. Therefore, we need to find the area bounded by the curve and the lines y=1 and x=0, between t=0 and t=π/2. We can use the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. In this case, we need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The final result is A=e-1/2.
The given parametric curve x=cost, y=et; 0≤t≤π/2, intersects the line y=1 at t=0, and intersects the line x=0 at t=π/2. Therefore, we need to find the area bounded by the curve and the lines y=1 and x=0, between t=0 and t=π/2. To do so, we can use the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. In this case, we need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The final result is A=e-1/2.
The area bounded by the parametric curve x=cost, y=et; 0≤t≤π/2, and the lines y=1 and x=0 is e-1/2. This can be found using the formula for area enclosed by a curve given by A=∫(y.dx) from a to b, where y is the function of x. We need to express x in terms of y, so we can use x=arccos(y) and substitute it in the formula. The curve intersects the line y=1 at t=0 and the line x=0 at t=π/2, which defines the boundaries for the integral.
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Micheal measured the distance around the circler swimming pool as apppoximly 108 feet which of the following represents the approximates radius of the circular swimming pool
The radius of the circular swimming pool is 17.20 feet.
What is the radius?The distance round the circular swimming pool is the circumference of the circle.
Radius = circumference / (pi x 2)
108 / (3.14 x2)
108 / 6.28 = 17.20 feet
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The function G(x) = 2-sin(x) is the result of the application of
transformations on the original function F(x) = cos(x). Which of the following options correctly describes the transformations applied to F(x)?
The transformations applied to F(x) is a vertical shift of 2 and a phase shift of π/2.
What are transformations?When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects."
Function transformations are highly useful for graphing functions without having to start from scratch because they allow you to move, extend, compress, or reflect the curve.
The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:Translation,Dilation and Reflection.
The given function F(x)=cos x is transformed to G(x)=2-sin x, by applying a vertical shift of 2 units upwards and a phase shift of π/2.
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Can some please help
Number of rooms left excluding a quarter of 140 is: 105 rooms.
What is a Quarter of a Number?A quarter is one-fourth. A quarter of a number is therefore, one-fourth of that number or 1/4 part of the number.
Therefore, number of rooms cleaned = 1/4(140) = 35.
A quarter of the 140 rooms is: 35.
Number of rooms left for cleaning in the afternoon = 140 - 35
Number of rooms left for cleaning in the afternoon = 105 rooms.
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Diane is filling a candle order for a wedding. She needs 6 large arrangements and 13 small arrangements .The large arrangements each contain 25 candles. The small arrangements each contain 12 candles. How many candles does diane need in all?
Answer:
406 candles in all.
Step-by-step explanation:
She needs 6 large arrangements with 25 candles in each arrangement.
Multiply 25 and 6 to find how much candles for all large arrangements combined.
25*6=150
She also needs 13 small arrangements with 12 candles in each arrangement.
Multiply 13 and 12 to find how much candles for all the small arrangements combined.
13*12=156
Add the answers together to find how many candles in all.
156+150=406.
She needs 406 candles in all.
Hope this helps!
Answer:
306
Step-by-step explanation:
First we find the number of candles needed for each size of arrangement.
Large Arrangements:
6 large arrangements with 25 candles each:
25 × 6 = 150
Small Arrangements:
13 small arrangements with 12 candles each:
13 × 12 = 156
Now we add the results above to find a grand total:
total = 150 + 156 = 306
Solve for X if possible:
5x -4y = 24
x =
Answer:
x=6 because if you multiple 4x6 you get 24
not exactly sure but try
Answer:
it is not possible
Step-by-step explanation:
there are two different variables in one equation, so you cannot solve for one. You would need a system of equations to do that.
you can solve for x in terms of y, which is x = (24+4y)/5 but i dont think thats what the question is asking so the answer is probably just that its not possible
laura goes for a cycle from her house to the post office 4km away work out laura's speed cycling to the post office CORBETTMATHS 2016
ItItItIt takes Laura 15 minutes (0.25 hours) to cycle to the post office.
Speed and timea. It takes Laura 15 minutes (0.25 hours) to cycle to the post office.
b. Speed:
Speed=Distance/Time
Speed=4/0.25
Speed=16 km/hr
c. It takes Laura 20 minutes to cycle to the post office.
d. Time
Time=20 minutes (1/3 hour)
Speed:
Speed=Distance/Time
Speed=4÷1/3
Speed=12 km/hr
Therefore It takes Laura 15 minutes (0.25 hours) to cycle to the post office.
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A family is having a pool built in their backyard. If their yard is rectangular and measures 10x by 10x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built
Answer:
[tex]100x^2-4\pi x^2[/tex]
Also can be said as:
[tex]4x^2(25-\pi )[/tex]
Step-by-step explanation:
The scenario:The question is asking you, "how much is left over."
In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).
This means your equation to solve this question is:
[tex]x=B-P[/tex]
Step 1:The value of B is the area of the backyard.
We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.
The formula is [tex]B=L*W[/tex], where L is the length and W is the width.
Both the length and width are 10x, so we must plug that into this equation.
We end up getting:
[tex]B=10x*10x[/tex]
Which can be simplified to:
[tex]B=100x^2[/tex]
Step 2:The value of P is the area of the pool.
The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.
The formula is [tex]P=\pi r^2[/tex], where r is the radius.
Plugging in the radius of 2x, we get:
[tex]P=\pi (2x)^2[/tex]
By solving this out, we end up with:
[tex]P=4\pi x^2[/tex]
Step 3:From the scenario, we have the equation:
[tex]x=B-P[/tex]
And from steps 1 and 2, we have the values:
[tex]B=100x^2[/tex] and [tex]P=4\pi x^2[/tex]
Now we just plug those values in to get:
[tex]x=100x^2-4\pi x^2[/tex]
And finally, the amount of the backyard remaining is:
[tex]100x^2-4\pi x^2[/tex]
Different format:This answer may be simplified to:
[tex]4x^2(25-\pi )[/tex]
Line a is purpendicular to line b. if the slope of line a is 7 than what is the slope of line b
The slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.
According to the question,
Line 'a' is perpendicular to the line 'b'. If the slope of the line 'a' is 7.
The condition of slopes if two lines are perpendicular m₁ m₂ = -1
(7)(m₂) = -1
m₂ = -1/7
Hence, the slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.
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Which of the following matches the graph of f (x) = 2(x + 1)2(x – 1)(x – 2)?
The graph that matches the function f(x) = 2(x – 1)2(x + 1)(x + 2) is shown in the attached file
How to draw the graph of a Polynomial?A function assigns the value of each element of one set to the other specific element of another set.
We want to draw the graph of the function f(x) = 2(x – 1)2(x + 1)(x + 2). Using relevant coordinates input into the function and the generated output, the graph of the given function is as attached below.
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What do these values indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?
Because the sample statistic centers around a different value than the population parameter, the sample mean absolute deviation is a biased estimator of the population mean absolute deviation.
Reason Behind a Biased Estimator
The expected value (average) of all the sample absolute deviations must match the population absolute deviation in order for the absolute deviation to function as an unbiased estimator. It does not, however, which makes the values of sample mean absolute deviation behave as a biased estimator.
Brief Description of Sample Mean Absolute Deviation
The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection. It is a statistical summary of statistical variability or dispersion.
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Make w subject of formula
C=(4+w)/(w+3)
Answer:
Step by Step Solution
More Icon
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
c-((4+w)/(w+3))=0
STEP
1
:
4 + w
Simplify —————
w + 3
Equation at the end of step
1
:
(w + 4)
c - ——————— = 0
w + 3
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using (w+3) as the denominator :
c c • (w + 3)
c = — = ———————————
1 (w + 3)
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
c • (w+3) - ((w+4)) cw + 3c - w - 4
——————————————————— = ———————————————
1 • (w+3) 1 • (w + 3)
Equation at the end of step
2
:
cw + 3c - w - 4
——————————————— = 0
w + 3
STEP
3
:
When a fraction equals zero :
3.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
cw+3c-w-4
————————— • w+3 = 0 • w+3
(w+3)
Now, on the left hand side, the w+3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
cw+3c-w-4 = 0
Solving a Single Variable Equation:
3.2 Solve cw+3cw-4 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
Answer:
w = (4 - 3C)/(C - 1).
Step-by-step explanation:
C=(4+w)/(w+3)
Multiply both sides of the formula by w+3:-
C(w + 3) = 4 + w
Cw + 3C = 4 + w
Cw - w = 4 - 3C
w(C - 1) = 4 - 3C
w = (4 - 3C)/(C - 1).
You must write your answer in fully simplified form.
2t= -12
Answer:
t=-6
Step-by-step explanation:
what is the area for the green square?
Based on the polynomial remainder theorem, what is the value of the function when x=−5?
f(x)=x^4+12x^3+30x^2−12x+70
Answer:
5.
Step-by-step explanation:
f(x)=x^4+12x^3+30x^2−12x+70
The remainder theorem says that f(a) is the value of f(x) when f(x) is divided by (x - a).
So when a = -5 f(a) will be 5.
Answer is 5.
if m<0 and b>0,the graph of y=max+b does not pass through which quadrant
Answer:are u sure its not y=mx+b? And it doesn’t pass thru 1 im pretty sure
Step-by-step explanation:
Answer: Quadrant III
Explanation:
Let's pick example values for m and b
I'll go for m = -2 and b = 5. Anything works as long as m is negative and b is positive.
We go from y = mx+b to y = -2x+5
Plot this graph as shown below. The line passes through quadrants I, II, and IV. Only quadrant III is not touched at all.
Wen Sam got a puppy from the shelter, it weighed 20.5Ibs. The puppy gain%30 of its original weight in the first month that Sam had him. How much did the puppy weight after the first month?
The weight of the puppy after the first month as described is; 26.65lbs.
What is the weight of the puppy?Since, it follows from the task content that the initial weight of the puppy is; 20.5lbs and it gained 30% of this after 1 month, it follows that the weight of the puppy after one month is;
Weight = 20.5lbs × 130% = 26.65lbs.
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In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is _____. Group of answer choices 21 22 23 24
If the sample size of population is 24 then the number of degrees of freedom for reading the t value is 23 which is option c.
Given sample size of 24,mean 23.
We have to determine the number of degrees of freedom which will be used to find the critical values of t.
Degree of freedom is the number of values in the final calculation of a statistic that are free to vary means that can change their values in the formula of calculating t.
t=(X-μ)/s/[tex]\sqrt{n}[/tex]
where X is sample mean ,
μ is hypothsised population mean
s is sample standard deviation
n is sample size.
Degree of freedom=n-1
In this question n is 24 so the degree of freedom =24-1=23.
Hence the number of degrees of freedom for reading the t value is 23.
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. sipho buys a car for r169 000. he pays a deposit of 15% and then makes monthly installments of 1% of the leftover amount for 9 years. i) what amount must sipho pay for the deposit? ii) what is the monthly payment that sipho makes? iii) how much does sipho pay in total for the car?
The amount for the deposit is $25350, monthly payment is $1436.5 and the total amount that Sipho pays is $178492.
Given price of car $169000, deposit of 15%, monthly installments being 1% of left over price and number of years be 9 years.
We have to find the amount of deposit, monthly installments and the total amount paid by Sipho.
We have been told that deposit is 15% of total amount. So the deposit will be 15%*169000=$25350.
Monthly installment is 1% of the left over amount.
left amount=169000-25350=$143650.
Monthly installment being =143650*1/100
=$1436.5
Total amount paid by Sipho=deposit +installment amount * numberof installments
Number of installments=12*9
=108
Total amount=25350+1436.5*108
=25350+155142
=$178492
Hence deposit is $25350, monthly payment being $1436.5, total amount be $178492.
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which of the following best describes this graph
x² - 4x + 4 is the graphed parabola, so the correct option is D.
Which equation is the graphed one?
On the graph, we can see a parabola that opens upwards (then the leading coefficient is positive), and has a vertex at the point (2, 0).
Also, we can see that the y-intercept is y = 4, that means that the constant term of the parabola is 4.
The only option with a constant term equal to 4 is the last option:
y = (x - 2)*(x - 2) = x² - 4x + 4
So that is the graphed parabola.
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How did the temperature change it increased by 50% and then it decreased by 33 1/3%
There is no change in the temperature.
What is temperature?A temperature is a physical number that describes how hot matter is, or it can be used to calculate the average translational kinetic energy per atom or molecule in a system. It is the measurable fraction of matter's molar thermal energy; a temperature difference allows heat transfer to take place, as energy transfers from a hotter body to a colder body.To find how much temperature is changed:
Let, 'F' be the temperature.
Temperature decreased by [tex]33\frac{1}{3}[/tex]%.
F × (1-.33333) = Temperature increases by 50%.
(F × (1-.33333)(1.50)) = F = No net change, right back to the original temperature F.
Therefore, there is no change in the temperature.
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please help solve for n. 5/15 = n/21 a. n = 35 b. n = 7 c. n = 5 d. n = 90
Answer:
b. n = 7
Step-by-step explanation:
You want to solve the proportion ...
5/15 = n/21
This is most easily done by multiplying by the inverse of the coefficient of the variable:
(21/1)(5/15) = (21/1)(n/21)
7 = n . . . . . . . . . simplify
__
Additional comment
The math is a little easier if you simplify 5/15 to 1/3. Then, n = 21/3 = 7.
How do you find the interior angle of a triangle given the external angle of 125°
Answer:
<x = 55 degrees
<y = 55 degrees
<z = 70 degrees
Step-by-step explanation:
The 125 degree angle and x are supplementary since they form a straight line, which means that their degrees add up to 180. To find x, the interior angle, we must subtract 125 from 180.
180 - 125 = 55
Angle x is 55 degrees. Since the sides opposite x and y are marked with lines, they are congruent, and since the sides are congruent, the angles must be, too. So, y is also 55 degrees.
Finally, the angles in any triangle add up to 180 degrees. To find z, we must subtract the values of x and y from 180.
180 - 55 - 55 = 70, so z is 70 degrees.
Brainliest, please :)
❄Hi there,
the external angle & the interior angle form a linear pair, which means, if you add these angles together, you'll arrive at 180°.
Using this knowledge let's set up an equation and find x:
[tex]\triangleright \ \sf{125+x=180}[/tex]. We let x be the desired angle.
[tex]\triangleright \ \sf{x=180-125=55}[/tex]
So the interior angle is [tex]\angle\sf{55}\textdegree[/tex].
❄
I know only one answer whats the other one help me image-
Answer:
A. 4(4a + 18)
B. 8(2a + 9)
Step-by-step explanation:
We know that :
16a = 4×4×a
72 = 4×18
Then
16a + 72 = 4×(4a) + 4×(18)
= 4 × (4a + 18)
On the other hand,
16a = 8×2×a
72 = 8×9
Then
16a + 72 = 8×(2a) + 8×(9)
= 8 × (2a + 9)
If a car manufacturer purchases new labor saving technology for its assembly line we would not expect
If a car manufacturer purchases new labour saving technology for its assembly line then we would not expect the production to be declined,wastage of time and money.
Given that a car manufacturer purchases a new labour saving technology.
We have to write the expectation that the car manufacturer would not make after buying such a technology.
We know that improvement of technology means abolition old technology and adoption of new and improved technology.
The advantages of new technology is:
1) It provides a competitive advantage over the competitor,
2) It increases the production,
3) It saves cost of the company,
4) It saves time also.
If a car manufacturer purchases new labour saving technology for its assembly line then he would not expect the production to be declined, wastage of time and money.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour he works.
Scenario 2: At a local bakery, one box of donuts costs $5. Two boxes of donuts cost $10.
Consider the two scenarios given above. Can you write an equation to represent each situation? What would the graphs of these equations look like? Can you think of a situation that would result in a similar equation?
Describe a scenario that would result in an equation similar to the equations for Scenarios 1 and 2. Post your scenario and the corresponding equation to the discussions area.
Answer:
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour(h) he works. And ammount of money can be (m)
considering theres no like first hour pay or something then it would be
Equation: m = 8h
Scenario 2: At a local bakery, one box of doughnuts(b) costs $5(c). Two boxes of doughnuts cost $10.
Equation: c = 5b where b is the ammount of doughnut boxes and c is the cost
Scenario 1a: Jim goes to the gym for 10 hours(h) It costed him $20(c) for those 10 hours.
Equation: c = 2h
Scenario 1b: Kayla goes to a for a ride on her bike and traveled 15 miles(m) and was out for 30 minutes. (t)
Equation: t = 2m
I don’t get this either please save me from this ahhhhhh
Answer:
y=
[tex] - \frac{x {}^{2} + 8x + 16 }{2} - 7[/tex]
Step-by-step explanation:
calculate the product, use (a+b)^2=a^2+2ab+b^2
An airplane rises at an angle of 12 degrees with the ground. About how high, in feet will the plane be above the ground when it has traveled 500 yards fromt he airport horizontally? Round your answer to the nearest foot.
In a 10-year period, Bakersfield, CA population grew from 558,000 to 718,000. What is the percentage of increase? (Round to the nearest tenth of a percent)
The percent increase to the nearest tenth is 22.2%
Calculating percent increasePercent increase is the percent it takes from a value to change from its initial value
Given the following
Initial value = 558,000
Final value = 718,000.
Determine the percent increase
% increase = (718,000-558000)/718,000 * 100
% increase = 160000/718000 * 100
% increase = 22.2%
Hence the percent increase to the nearest tenth is 22.2%
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The ratio of dogs to cats in a shelter is 9:15.if the total number of cats and dogs is 96.how many dogs are there?
There are 36 dogs in the shelter.
How to find the total number of dogs in the shelter?The ratio of dogs to cats in the shelter is given as 9:15.
The total number of dogs and cats is given as 96.
Let the constant of proportionality be x.
The total number of dogs is 9x and the total number of cats is 15x.
This means that:
9x + 15x = 96
24x = 96
x = 4.
The total number of dogs in the shelter = 9 × 4
= 36
Therefore, we have found that there are 36 dogs in the shelter.
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The positive integers $1,$ $2,$ $3,$ $\dots$ are listed in order. What is the $1000^{\rm th}$ positive integer with an odd number of digits
There are 9 positive integers with 1 digit (1 - 9).
There are 90 integers with 2 digits (10 - 99).
There are 900 integers with 3 digits (100 - 999).
There are 9000 integers with 4 digits (1000 - 9999).
And so on. It stands to reason that there are [tex]9\times10^{n-1}[/tex] integers with [tex]n[/tex] digits.
Now,
1000 = 9 + 900 + 91
so the 1000th positive integer with an odd number of digits is the 91th number with 3 digits, which is 190.