Answers
Answer: 0.8284 units²
Step-by-step explanation:
To find the area between curves, we need to use the integral. We can see that both sides of the shaded region are equal to each other. Therefore, we can find the area of one shaded part and multiply it by 2 for the 2 shaded regions. For the integral, we can find the area of the shaded region on the left side, on the interval from 0 to π/4.
Now that we know the integral, we can figure out the function. We do this by subtracting the top curve by the bottom curve. The top curve on the left shaded region, is y=cosx. The bottom curve on the shaded region is y=sinx. Therefore, we will subtract cosx-sinx.
[tex]2\int\limits^\frac{\pi }{4} _0 {cosx-sinx} \, dx[/tex]
Now that we have the integral, we can solve by splitting the integral into 2 separate integrals by the Sum Rule. Let's disregard the multiply by 2 for now, but we will make sure to multiply by 2 at the end.
[tex]\int\limits^\frac{\pi }{4} _0 {cosx} \, dx -\int\limits^\frac{\pi }{4} _0 {sinx} \, dx[/tex]
Now, we can solve each integral separately.
[tex]\int\limits^\frac{\pi }{4} _0 {cosx} \, dx =sinx]^\pi^ /^40[/tex]
*Note: The 0 is at the base of the bracket. I can't find a way to do it in the equation editor, but know that it's there.
[tex]sin(\frac{\pi }{4} )-sin(0)=\frac{\sqrt{2} }{2} -0=\frac{\sqrt{2} }{2}[/tex]
Now, we can find the integral of sinx.
[tex]\int\limits^\frac{\pi }{4} _0 {sinx} \, dx=-cos]^\pi ^/^40[/tex]
*Note: The 0 is at the base of the bracket. I can't find a way to do it in the equation editor, but know that it's there.
[tex]-cos(\frac{\pi }{4} )-(-cos(0))=-\frac{\sqrt{2} }{2} -(-1)=-\frac{\sqrt{2} }{2} +1[/tex]
Now that we have the integral of each integral, we can subtract them, and multiply by 2.
[tex]\frac{\sqrt{2} }{2} -(-\frac{\sqrt{2} }{2} +1)=\sqrt{2}+1[/tex]
[tex]2(\sqrt{2} +1)=0.8284 units^2[/tex]
Related Questions
help with this I don't know how to solve please
Answers
Answer:
The right answer is the first one, 6,245.
Step-by-step explanation:
[tex]EG^2=DG*GF \\ EG^2 = ab\\ EG^2 = 3*13\\ EG^2=39\\ EG=\sqrt{39}[/tex]
[tex]\sqrt{39} = 6,2449... = 6,245[/tex]
pls help me help me help me
Answers
Answer:
C. -3/2
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
We know that line m is perpendicular to line l.
Line l has a slope of 2/3. To find the slope of line m, find the negative reciprocal of 2/3.
Negative: switch the sign
2/3 --> -2/3
Reciprocal: switch the numerator (top number) and denominator (bottom number)
-2/3 --> -3/2
Line m has a slope of -3/2 and C is correct.
Answer:
C
Step-by-step explanation:
perpendicular lines have negative reciprocal slope
Suppose A is a 5times7 matrix. How many pivot columns must A have if its columns span set of real numbers RSuperscript 5? Why?
Answers
Answer:
Five
Step-by-step explanation:
Pivot columns are said to be columns where pivot exist and a pivot exist in the first nonzero entry of each row in a matrix that is in a shape resulting from a Gaussian elimination.
Suppose A = 5 × 7 matrix
So; if A columns span set of real numbers R⁵
The number of pivot columns that A must have must be present in each row. In a 5 × 7 matrix ; we have 5 rows and 7 columns . So , since A must be present in each row, then :
The matrix must have five pivot columns and we can infer that about the statements that "A has a pivot position in every row" and "the columns of A spans R⁵" are logically equivalent.
Let f(x) = −4(0.25)^x. The graph of g(x) = f(x)+k is shown below. Identify the value of k. k=
Answers
Which equation represents the line passing through points A and C on the graph below? On a coordinate plane, point A is at (2, 3), point B is at (negative 2, 1), point C is at (negative 4, negative 3), and point D is at (4, negative 5). y= negative x minus 1 y = negative x + 1 y = x minus 1 y = x + 1
Answers
The equation that represents the line that passes through the points A and C is y = x + 1
What is a linear equation?A linear equation is an equation that has a constant rate or slope, and is represented by a straight line
The points are given as:
(x,y) = (2,3) and (-4,-3)
Calculate the slope, m using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{-3 -3}{-4 - 2}[/tex]
Evaluate
m = 1
The equation is then calculated as:
y = m *(x - x1) + y1
So, we have:
y = 1 * (x - 2) + 3
Evaluate
y = x - 2 + 3
This gives
y = x + 1
Hence, the equation that represents the line that passes through the points A and C is y = x + 1
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ2
Answer:
y = x + 1
Step-by-step explanation:
Edge2020
In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. Compute the sample mean, standard mean, standard deviation and variance of the data:1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8 Mean = ???Variance = ???Standard Deviation= ???
Answers
Answer:
Mean = 3.12, Variance = 3.324, Standard deviation = 1.8232
Step-by-step explanation:
Total number of students = 10 students.
Given data, 1.1, 5.2, 3.6, 5.0, 4.8, 1.8, 2.2, 5.2, 1.5, 0.8
To find the mean, at first we have to take the sum of all given data and then divide with the number of students.
Let the data is X, = 1.1, + 5.2, + 3.6, + 5.0, + 4.8, + 1.8, + 2.2, + 5.2, + 1.5, + 0.8 = 31.2
Mean = 31.2 / 10 = 3.12
[tex]\text{Standard deviation, S} = \sqrt{\frac{\sum x^{2} - \left [ (\sum x)^{2}/n \right ]}{n-1}} \\S = 1.8232 \\\rm The \ Variance = S^{2} = 3.324[/tex]
Chloe has a budget of $800 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume?
Answers
Answer:
$42.10
Step-by-step explanation:
Assuming that she did not yet buy a costume for herself, 800 dollars divided among 18 people plus herself is equal to $42.10 maximum per person.
Answer:
44.44
Step-by-step explanation:
800 didvided by 18.
Find (f - g) (4)
f(x) = 4x - 3
g(x) = x^3+2x
a) 59
b) 85
c)-59
d) 285
Answers
Explanation:
F(x) = 4x -3
f(4) = 4(4) - 3 = 13
g(x) = x^3 + 2x
g(4) = 4^3 + 2(4) = 64 + 8 = 72
(F - g)(4) = 13 - 72 = -59
. Jayvon bakes two small circular cakes that are 8 inches across their widest point and 3 inches high. He removes the cake from the pans to frost them. Jayvon would like a consistent quarter-inch deep layer of frosting. How many cubic inches of frosting does he need for the cakes if he wants to frost only the top and sides of each cake
Answers
Answer:
20π in³ or 62.832 in³
Step-by-step explanation:
The surface area for each cake is given by:
[tex]S=\pi r^2+2\pi rh[/tex]
Where 'r' is the radius of each cake (4 inches), and 'h' is the height of each cake (3 inches). Since there are two cakes, the total surface area is:
[tex]A=2*(\pi r^2+2\pi rh)\\A=2*(\pi 4^2+2\pi*4*3)\\A=80\pi\ in^2[/tex]
If Jayvon wants a consistent quarter-inch deep layer of frosting covering the surface of the cakes, the volume of frosting required is:
[tex]V=80\pi *0.25\\V=20\pi\ in^3 = 62.832\ in^3[/tex]
He needs 20π in³ or 62.832 in³ of frosting.
The oblique pyramid has a square base. What is the volume of the pyramid? 2.5 cm3 5 cm3 6 cm3 7.5 cm3
Answers
Take a look at the attachment below. It fills in for the attachment that wasn't provided in the question -
An oblique pyramid is one that has a top not aligned with the base. Due to this, the height of the pyramid connects with two vertices at its ends to form a right angle present outside the pyramid, knowing that it is always perpendicular to the base. There is no difference between the calculations of the volume of an oblique pyramid and a pyramid however -
[tex]\\Base Area = 2 cm * 2 cm = 4 cm^2,\\Volume ( Pyramid ) = 1 / 3 * ( Base Area ) * ( Height ),\\Volume = 1 / 3 * ( 4 ) * ( 3.75 ),\\-------------------------\\Volume = 5 cm^3[/tex]
And thus, you're solution is 5 cm^3, or in other words option b!
Answer:
The answer is B
Step-by-step explanation:
The number of large cracks in a length of pavement along a certain street has a Poisson distribution with a mean of 1 crack per 100 ft. a. What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement
Answers
Answer:
6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Poisson distribution with a mean of 1 crack per 100 ft.
So [tex]\mu = \frac{ft}{100}[/tex], in which ft is the length of the pavement.
What is the probability that there will be exactly 8 cracks in a 500 ft length of pavement
500ft, so [tex]\mu = \frac{500}{100} = 5[/tex]
This is P(X = 8).
[tex]P(X = 8) = \frac{e^{-5}*5^{8}}{(8)!} = 0.0653[/tex]
6.53% probability that there will be exactly 8 cracks in a 500 ft length of pavement
c. Find the price of 16 shirts if 5 costs GH¢80
Answers
Answer:
16 shirts = GH¢256
Step-by-step explanation:
If 5 shirts cost GH¢80
Let's determine the price of 16 shirts by cross multiplying the values
This method of evaluating answers is one of the essential methods .
It's just Making sure that the values within each side of the wall to symbol crosses each other.
But one shirt = GH¢80/5
one shirt = GH¢16
So
5 shirts= GH¢80
16 shirts = (16 shirts * GH¢80)/5 shirts
16 shirts = GH¢1280/5
16 shirts = GGH256
What is the slope of the function, represented by the table of values below?
Answers
Answer:
C. -2
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Simply use 2 xy values and plug them into the formula:
m = (-4 - 0)/(5 - 3)
m = -4/2
m = -2
Answer:
-2
Step-by-step explanation:
Since we have two points we can use the slope formula
m = (y2-y1)/(x2-x1)
= (10-6)/(-2-0)
=4/-2
-2
The graph of f(x) = 4x3 – 13x2 + 9x + 2 is shown below. On a coordinate plane, a function is shown. The function starts from the bottom of quadrant 3 and goes up through the x-axis at (0, negative 0.25) and then through the y-axis at (0, 2). It then starts to curve down at (0.5, 4) until it reaches (1.75, negative 0.5). It then curves up and crosses the x-axis at (2, 0) and goes up approaching x = 3. How many roots of f(x) are rational numbers? 0 1 2 3
Answers
Answer:
3
Step-by-step explanation:
f(x) = 4x^3 – 13x^2 + 9x + 2
This looks complicated but all we need to find are the Roots
We are looking for when y=0
So given each part of the information, we can label how many times it happens
The function starts from the bottom of quadrant 3: Starts lower left
and goes up through the x-axis at (0, negative 0.25) : This is ONE ROOT
and then through the y-axis at (0, 2). : It's now on the 2nd quartile
It then starts to curve down at (0.5, 4): It's moving towards y=0
until it reaches (1.75, negative 0.5).: It has now passed y=o and there are TWO ROOTS
It then curves up and crosses the x-axis at (2, 0) and goes up approaching x = 3: It has passed y=0 again, so there are THREE ROOTS
This polynomial function has 3 ROOTS
Answer:
The first for the graph is crosses and then it is touches for the second.
Step-by-step explanation:
Find all solutions to the equation.
7 sin2x - 14 sin x + 2 = -5
If yall can help me for Pre-Calc, that would be great.
-Thanks.
Answers
If the equation is
[tex]7\sin^2x-14\sin x+2=-5[/tex]
then rewrite the equation as
[tex]7\sin^2x-14\sin x+7=0[/tex]
Divide boths sides by 7:
[tex]\sin^2x-2\sin x+1=0[/tex]
Since [tex]x^2-2x+1=(x-1)^2[/tex], we can factorize this as
[tex](\sin x-1)^2=0[/tex]
Now solve for x :
[tex]\sin x-1=0[/tex]
[tex]\sin x=1[/tex]
[tex]\implies\boxed{x=\dfrac\pi2+2n\pi}[/tex]
where n is any integer.
If you meant sin(2x) instead, I'm not sure there's a simple way to get a solution...
how many are 4 x 4 ?
Answers
Answer:
16
Step-by-step explanation:
Scientists want to test a new pair of running shoes. A speed test is performed with two separate groups of participants. The treatment group will wear the new pair of running shoes, while the control group will not. It is believed that age and height may affect speed. Which of the following would be most effective in controlling the confounding variables, such as age and height, in this study?
a. A completely randomized design experiment
b. A longitudinal observational study
c. A retrospective observational study
d. A matched-pair design experiment
Answers
Answer:
a. A completely randomized design experiment
Step-by-step Explanation:
An experiment that is completely randomised is practically an effective way of controlling and reducing the influence of the confounding variables in a research study, especially when you have a sample that is large enough.
Randomisation will ensure that both the group that will wear the new shoe (treatment group) and the group that will not wear the new shoe (control group) will have averagely the same values for age and height. This will eliminate the chances of these confounding variables of correlating with the independent variable in the study, as there would be no difference, in terms of characteristics, between both groups.
6th grade math help me please :))
Answers
Answer:
The answer is option D.
3u + 1 + 7y
All the terms here are different and cannot be combined
Hope this helps you
Given
f(x) = 2x2 + 1
and
g(x) = 3x - 5
find the following.
f-g
Answers
Answer:
The answer is
2x² - 3x + 6Step-by-step explanation:
f(x) = 2x² + 1
g(x) = 3x - 5
To find f - g(x) subtract g(x) from f(x)
That's
f-g(x) = 2x² + 1 - (3x - 5)
= 2x² + 1 - 3x + 5
= 2x² - 3x + 6
Hope this helps you
Kathy wants to buy a camera with an original price of $389. The camera is on sale with a 33% discount. What is the amount of discount?
Answers
Answer:
$128.37
Step-by-step explanation:
Find 33% of 389:
389(0.33) = 128.37
The amount of the discount is $128.37
pleasssssseeeeeeeeeeeeeeeeeeee
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
0.5 = 1/2 and the rectangle with 3 cubes shaded in
0.6 = 60/100 and circle with three parts shaded in
0.8 = Rectangle with 8 cubes shaded and 4/5
▹ Step-by-Step Explanation
You can convert the fractions into decimals, and count the shaded parts for the shaded images.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Consider the following set of sample data: (34, 32, 34, 32, 40, 37, 31, 31, 29, 27). We're interested in using this data to test a null hypothesis about the population mean. Which of the following statements are true?
I. Assuming this represents a random sample from the population, the sample mean is an unbiased estimator of the population mean.
II. Because they're robust, t procedures are justified in this case.
III. We'd use zprocedures here, since we're interested in the population mean.
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
Answers
Answer:
Option I and II
Step-by-step explanation:
I. Assuming this represents a random sample from the population, the sample mean is an unbiased estimator of the population mean.
II. Because they're robust, t procedures are justified in this case.
The t procedures are utilized because they are used as a hypothesis testing tool, which allows for testing of an hypothesis applicable to a population where in this case we are testing the null hypothesis about the population mean.
Help me please!!! Thank you
Answers
Answer:
AD = 23
Step-by-step explanation:
The weights of steers in a herd are distributed normally. The standard deviation is 300lbs and the mean steer weight is 1100lbs. Find the probability that the weight of a randomly selected steer is between 920 and 1730lbs round to four decimal places.
Answers
Answer:
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(920≤ x≤1730) = 0.7078
Step-by-step explanation:
Step(i):-
Given mean of the Population = 1100 lbs
Standard deviation of the Population = 300 lbs
Let 'X' be the random variable in Normal distribution
Let x₁ = 920
[tex]Z = \frac{x-mean}{S.D} = \frac{920-1100}{300} = - 0.6[/tex]
Let x₂ = 1730
[tex]Z = \frac{x-mean}{S.D} = \frac{1730-1100}{300} = 2.1[/tex]
Step(ii)
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(x₁≤ x≤x₂) = P(Z₁≤ Z≤ Z₂)
= P(-0.6 ≤Z≤2.1)
= P(Z≤2.1) - P(Z≤-0.6)
= 0.5 + A(2.1) - (0.5 - A(-0.6)
= A(2.1) +A(0.6) (∵A(-0.6) = A(0.6)
= 0.4821 + 0.2257
= 0.7078
Conclusion:-
The probability that the weight of a randomly selected steer is between 920 and 1730 lbs
P(920≤ x≤1730) = 0.7078
Answer:
0.7975
Step-by-step explanation:
A heavy rope, 30 ft long, weighs 0.4 lb/ft and hangs over the edge of a building 80 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.How much work W is done in pulling half the rope to the top of the building
Answers
Answer:
180 fb*lb
45 ft*lb
Step-by-step explanation:
We have that the work is equal to:
W = F * d
but when the force is constant and in this case, it is changing.
therefore it would be:
[tex]W = \int\limits^b_ a {F(x)} \, dx[/tex]
Where a = 0 and b = 30.
F (x) = 0.4 * x
Therefore, we replace and we would be left with:
[tex]W = \int\limits^b_a {0.4*x} \, dx[/tex]
We integrate and we have:
W = 0.4 / 2 * x ^ 2
W = 0.2 * (x ^ 2) from 0 to 30, we replace:
W = 0.2 * (30 ^ 2) - 0.2 * (0 ^ 2)
W = 180 ft * lb
Now in the second part it is the same, but the integral would be from 0 to 15.
we replace:
W = 0.2 * (15 ^ 2) - 0.2 * (0 ^ 2)
W = 45 ft * lb
Following are the calculation to the given value:
Given:
[tex]length= 30 \ ft\\\\mass= 0.4 \ \frac{lb}{ft}\\\\edge= 80 \ ft \\\\[/tex]
To find:
work=?
Solution:
Using formula:
[tex]\to W=fd[/tex]
[tex]\to W=\int^{30}_{0} 0.4 \ x\ dx\\\\[/tex]
[tex]= [0.4 \ \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{4}{10} \times \frac{x^2}{2}]^{30}_{0} \\\\= [\frac{2}{10} \times x^2]^{30}_{0} \\\\= [\frac{1}{5} \times x^2]^{30}_{0} \\\\= [\frac{x^2}{5}]^{30}_{0} \\\\= [\frac{30^2}{5}- 0] \\\\= [\frac{900}{5}] \\\\=180[/tex]
Therefore, the final answer is "[tex]180\ \frac{ lb}{ft}[/tex]".
Learn more:
brainly.com/question/15333493
Find the sum. A. 4x2 – x – 5 B. 10x2 + 7x – 5 C. –10x2 + 7x + 11 D. 4x2 + x – 11
Answers
Answer:
A
Step-by-step explanation:
7x² - 4x - 8 - [ -3x² - 3x - 3]
In subtraction, flip the sign of all terms in the minuend
7x² - 4x - 8
3x² + 3x + 3
4x² - x - 5
the polynomial p(x)=x^3-7x-6 has a known factor of (x+1) rewrite p(x) as a product of linear factors p(x)=
Answers
Answer:(x+1)(x+2)(x-3)
Because..
Explain how you found the volume of the rectangular prism with a hole through it. Explain how you found the volume of the rectangular prism with a hole through it.
Answers
Answer:
Step-by-step explanation:
We khow that the volume of a prism the product of the base and the height
We have a hole inside it so we must khow what is the geometrical form of this whole to calculate its volum then substract from the total volume
Sample Answer:
I found the volume of the large rectangular prism. Then I found the volume of the small rectangular prism. I subtracted the volume of the smaller prism from the volume of the larger prism.
The area of this parallelogram is 120 ft2 find the value of h
Answers
Answer: 6
Step-by-step explanation:
A=bh plus 120 for A and 20 for B
120=20b
/20 divide by 20 each side
H=6
Weekly sales of bagels at the local bakery are as follows: Week Sales 1 400 2 370 3 420 4 380 5 410 6 430 7 400 8 What is the forecast for week 8 using weighted moving averages with the weights 0.6, 0.3, 0.1
Answers
Answer:
410 bagels
Step-by-step explanation:
If the weights of the moving averages are 0.6, 0.3, 0.1. We will determine the forecast for week 8 using week seven's sales with a 0.6 weight, week six's sales with a 0.3 weight, and week five's sales with a 0.1 weight:
[tex]S_8=0.6S_7+0.3S_6+0.1S_5\\S_8=0.6*400+0.3*430+0.1*410\\S_8=410\ bagels[/tex]
The forecast for week 8 is 410 bagels.