The area enclosed by the two given curves can be found by calculating the definite integral of the difference between the upper curve and the lower curve.
In this case, the upper curve is y² = 1 - r and the lower curve is y² = x + 1. To find the points of intersection, we can set the two equations equal to each other:
1 - r = x + 1
Simplifying the equation, we get:
r = -x
Now we can set up the integral. Since the curves intersect at r = -x, we need to find the limits of integration in terms of r. We can rewrite the equations as:
r = -y² + 1
r = y² - 1
Setting them equal to each other:
-y² + 1 = y² - 1
2y² = 2
y² = 1
y = ±1
So the limits of integration for y are -1 to 1.
The area can be calculated as:
A = ∫[from -1 to 1] (1 - r) - (x + 1) dy
Simplifying and integrating, we get:
A = ∫[from -1 to 1] 2 - r - x dy
A = ∫[from -1 to 1] 2 - y² + 1 - x dy
A = ∫[from -1 to 1] 3 - y² - x dy
Integrating, we get:
A = [3y - (y³/3) - xy] [from -1 to 1]
A = 2 - (2/3) - 2x
So, the area enclosed by the two given curves is 2 - (2/3) - 2x.
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Graph the line.
y=-5x+4
15 points
Answer:
go up 4 on the y axis and then go up five and to the left 1. Also go to desmos and it will answer all out your graphing question.
Step-by-step explanation:
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helpppp meeeee outttttt pleaseeeee ASAPPPP!!!!
Answer:
\(\boxed{\sf sin\ C =\frac{40}{41}}\)
Step-by-step explanation:
We need to find out the value of sinC using the given triangle . Here we can see that the sides of the triangle are 40 , 41 and 9 .
We know that the ratio of sine is perpendicular to hypontenuse .
\(\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}\)
Here we can see that the side opposite to angle C is 40 , therefore the perpendicular of the triangle is 40. And the side opposite to 90° angle is 41 . So it's the hypontenuse . On using the ratio of sine ,
\(\sf\longrightarrow sinC =\dfrac{ p}{h}\\\\\sf\longrightarrow sin\ C =\dfrac{AB}{AC}\)
Substitute the respective values ,
\(\sf\longrightarrow \boxed{\blue{\sf sin\ C =\dfrac{40}{41}}}\)
Hence the required answer is 40/41.
a.5÷4 divide and show work
Answer:
1.25
Step-by-step explanation:
1.25
THATS THE ANSWER
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From a table of integrals, we know that for ,≠0a,b≠0,
∫cos()=⋅cos()+sin()2+2+.∫eatcos(bt)dt=eat⋅acos(bt)+bsin(bt)a2+b2+C.
Use this antiderivative to compute the following improper integral:
∫[infinity]01cos(3)− = limT→[infinity]∫0[infinity]e1tcos(3t)e−stdt = limT→[infinity] if ≠1s≠1
or
∫[infinity]01cos(3)− = limT→[infinity]∫0[infinity]e1tcos(3t)e−stdt = limT→[infinity] if =1.s=1. help (formulas)
For which values of s do the limits above exist? In other words, what is the domain of the Laplace transform of 1cos(3)e1tcos(3t)?
help (inequalities)
Evaluate the existing limit to compute the Laplace transform of 1cos(3)e1tcos(3t) on the domain you determined in the previous part:
()=L{e^1t cos(3)}=
"From a table of integrals, we know that for \(\(a \neq 0\)\) and \(\(b \neq 0\):\)
\(\[\int \cos(at) \, dt = \frac{1}{a} \cdot \cos(at) + \frac{1}{b} \cdot \sin(bt) + C\]\)
and
\(\[\int e^a t \cos(bt) \, dt = \frac{e^{at}}{a} \cdot \cos(bt) + \frac{b}{a^2 + b^2} \cdot \sin(bt) + C\]\)
Use this antiderivative to compute the following improper integral:
\(\[\int_{-\infty}^{0} \cos(3t) \, dt = \lim_{{T \to \infty}} \int_{0}^{T} e^t \cos(3t) \, e^{-st} \, dt = \lim_{{T \to \infty}} \text{ if } s \neq 1, \, \text{ or } \lim_{{T \to \infty}} \text{ if } s = 1.\]\)
For which values of \(\(s\)\) do the limits above exist? In other words, what is the domain of the Laplace transform of \(\(\frac{1}{\cos(3)} \cdot e^t \cos(3t)\)\)?
Evaluate the existing limit to compute the Laplace transform of on the domain you determined in the previous part:
\(\[L\{e^t \cos(3t)\\).
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Which theorem or postulate proves that △ABC and △DEF are similar?
Select from the drop-down menu to correctly complete the statement.
The two triangles are similar by the ________.
A. AA Similarity Postulate
B. SSS Similarity Theorem
C. SAS Similarity Theorem
Option A. AA Similarity Postulate. The AA Similarity Postulate is a geometric principle that states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
This means that their corresponding sides are in proportion, and the triangles have the same shape, but not necessarily the same size. This postulate is one of the ways to prove the similarity of two triangles. In the case of the given question, if we know that two angles of one triangle are congruent to the two angles of another triangle, then we can use the AA Similarity Postulate to prove that the triangles are similar. This principle is widely used in geometry and helps to establish relationships between different shapes and figures.
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A local publishing company prints a special magazine each month. It has been determined that x magazines can be sold monthly when the price is p = D(x) = 4.600.0006x. The total cost of producing the magazine is C(x) = 0.0005x²+x+4000. Find the marginal profit function
The marginal profit function represents the rate of change of profit with respect to the number of magazines sold. To find the marginal profit function, we need to calculate the derivative of the profit function.
The profit function is given by P(x) = R(x) - C(x), where R(x) is the revenue function and C(x) is the cost function.
The revenue function R(x) is given by R(x) = p(x) * x, where p(x) is the price function.
Given that p(x) = 4.600.0006x, the revenue function becomes R(x) = 4.600.0006x * x = 4.600.0006x².
The cost function is given by C(x) = 0.0005x² + x + 4000.
Now, we can calculate the profit function:
P(x) = R(x) - C(x) = 4.600.0006x² - (0.0005x² + x + 4000)
= 4.5995006x² - x - 4000.
Finally, we can find the marginal profit function by taking the derivative of the profit function:
P'(x) = (d/dx)(4.5995006x² - x - 4000)
= 9.1990012x - 1.
Therefore, the marginal profit function is given by MP(x) = 9.1990012x - 1.
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If the children were to share the juice equally, how much would each child get? Show your work.
Answer:
you are missing part of the question
Step-by-step explanation:
A bird is flying directly above a tree. You are standing 84 feet away from the base of the tree. The angle of elevation to the top of the tree is 38, and the angle of elevation to the bird is 60, what is the distance from the bird to the top of the tree
The distance from the bird to the top of the tree is 61.95 feet.
We have,
Angle of elevation to the top of the tree: 38 degrees.
Angle of elevation to the bird: 60 degrees.
Distance from the base of the tree to your position: 84 feet.
Let the distance from the bird to the top of the tree as 'x'.
Using Trigonometry
tan(38) = height of the tree / 84
height of the tree = tan(38) x 84
and, tan(60) = height of the tree / x
x = height of the tree / tan(60)
Substituting the value of the height of the tree we obtained earlier:
x = (tan(38) x 84) / tan(60)
x ≈ 61.95 feet
Therefore, the distance from the bird to the top of the tree is 61.95 feet.
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b=2-7 solve this question please
Answer:
b=−5
Step-by-step explanation:
Subtract the numbers
b=2−7
b= −5
Answer:
b = -5
Step-by-step explanation:
b = 2 - 7
b = -5
1) 17, 29, 32, 9, 30, 14, 8, 39, 11, 32, 23
Minimum :
Maximum:
Q1:
Q2:
Q3:
Answer:
Minimum: 8
Maximum: 39
Q1: 11
Q2: 23
Q3: 32
Step-by-step explanation:
Set the numbers into numerical order
8 9 11 14 17 23 29 30 32 32 39
Then separate into quarters
[8 9 11] [14 17 23] [29 30 32] 32 39
Which one of the following is a characteristic of the classical approach to probability? Oa. Probabilities are based on outcomes observed from past experiments.Ob. None of the aboveOc. Probabilities are based on opinion.Od. Probabilities assume outcomes of an experiment are equally likely
The characteristic of the classical approach to probability is that the probabilities assume outcomes of an experiment are equally likely , the correct answer is (d) .
The Classical Approach to probability is also known as the "classical method" .
The classical approach is based on the assumption that all outcomes of an experiment are equally likely to occur.
The probability of an event is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
This classical approach is often used in situations where the outcomes of an experiment can be clearly defined and enumerated.
Therefore, the correct statement about Classical Approach is in Option(d).
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The given question is incomplete , the complete question is
Which one of the following is a characteristic of the classical approach to probability?
(a) Probabilities are based on outcomes observed from past experiments.
(b) None of the above.
(c) Probabilities are based on opinion.
(d) Probabilities assume outcomes of an experiment are equally likely.
the normal approximation can be used in a two-sample test of proportions for which one of these sets of values?
The normal approximation can be used in a two-sample test of proportions when the sample sizes are sufficiently large.
The rule of thumb is that each sample should have at least 10 successes and 10 failures. When these conditions are met, the sampling distribution of the difference in sample proportions can be approximated by a normal distribution with a mean equal to the difference in population proportions and a standard deviation calculated from the sample proportions. This approximation allows us to calculate probabilities and make inferences using the standard normal distribution. It is important to note that this approximation may not be accurate for small sample sizes, in which case exact methods such as the Fisher's exact test should be used instead. In summary, the normal approximation can be used in a two-sample test of proportions when the sample sizes are large enough and the conditions are met.
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Please Help!! i can’t fail this!!
Melissa orders 4 books for $5.95 each. The total shipping cost on her order is $3.50.
How can Melissa find the total cost of her order and the shipping?
A. Add $5.95 and $3.50. Then, multiply the sum by 4.
B. Multiply $3.50 by 4. Then, add the product to $5.95.
C. Multiply $5.95 by 4. Then, add the product to $3.50.
D. Multiply $5.95 by 4. Then, multiply the product by $3.50.
Answer:
C: Multiply $5.95 by 4. Then, add the product to $3.50.
Answer:c
Step-by-step explanation:
help me out please
(geometry)
Answer:
x = 17
Step-by-step explanation:
The angles are same side interior angles and they will add to 180 when the lines are parallel
6x+8 + 4x+2 = 180
10x+10 = 180
Subtract 10 from each side
10x+10-10 =180-10
10x = 170
Divide by 10
10x/10 = 170/10
x = 17
Answer:
x = 17
Step-by-step explanation:
Theorem:
If two lines are cut by a transversal such that same-side interior angles are supplementary, then the lines are parallel.
For the lines to be parallel, the sum of 6x + 8 and 4x + 2 must equal 180.
6x + 8 + 4x + 2 = 180
10x + 10 = 180
10x = 170
x = 17
Find measure of angle NPI
5. Find the length of DE if D is between points Cand E, CD= 6.5 centimeters, and CE = 13.8 centimeters. 6. Find the length of XZ. 4x + 3
Answer:
\(cd = 6.5cm \\ ce = 13.8cm \\ de = ce - cd \\ de= 13.8cm - 6.5cm \\ de = 10.3cm\)
The subtraction between CE and CD is the length of DE
How do you find the number of distinguishable permutations of the group of letters: A, A, G, E, E, E, M?
In order to find the number of distinguishable permutations of the group of letters A, A, G, E, E, E, M, we can use the following formula:
The number of permutations = n! / (n1! n2! ... nk!), where n is the total number of objects to be arranged, and n1, n2, ..., nk are the numbers of objects that are identical to one another.
For this problem, we have 7 letters with 2 A's, 3 E's, and 1 G and 1 M letter.
Using the formula above, we can find the number of distinguishable permutations: 7! / (2! 3! 1! 1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (3 × 2 × 1) × (1 × 1) × (1 × 1)] = 2520
Therefore, there are 2520 distinguishable permutations of the group of letters A, A, G, E, E, E, M.
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1/5 times 8 =? help please asap
Answer:
8/5 aka 1.6
Step-by-step explanation:
What is the value of x in the equation 1/4(4 + x) = 4/3
The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.
Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:
1/4(4 + x) = 4/3
4 * 1/4(4 + x) = 4 * 4/3
Simplifying:
4 + x = 16/3
Subtract 4 from both sides of the equation:
4 + x - 4 = 16/3 - 4
Simplifying:
x = 16/3 - 12/3
x = 4/3
A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.
Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.
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I need help with shifting functions
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g(x) = h(x - 7) + 5
The plus 5 on the outside of the brackets represents the graph moving up by 5 units
The minus 7 on the inside of the brackets represents the graph moving right by 7 units.
Note: When it is on the inside of the brackets, you would do the opposite of what it suggests.
Normally, minus 7 would mean the graph shifts to the left, however, it means the opposite in this case.
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Suppose that f(x)=x^2 and g(x)=-2/3 x^2 which statement best compares the graph of g)x) with the graph of f(x)?
The graph of g(x) is the graph of f(x) stretched vertically and reflected over the axis.
The correct option is C.
We can compare the graphs of two functions f(x)=x² and g(x)=-2/3 x² by determining their vertices, domain, range, axis of symmetry, and shape of the graphs. The vertex of f(x)=x² is at the origin (0,0), which means that the parabola opens upward and is symmetrical around the y-axis.
The domain is all real numbers, and the range is y≥0. The axis of symmetry is the y-axis. On the other hand, the vertex of g(x)=-2/3 x² is also at the origin, and it opens downward. It is also symmetrical around the y-axis. The domain is all real numbers, and the range is y≤0.
The axis of symmetry is the y-axis, just like f(x).It is important to remember that g(x) is the negative of f(x), which indicates that g(x) is reflected across the x-axis. Furthermore, the stretch factor is 2/3, which makes the graph of g(x) flatter than the graph of f(x) and it is stretched vertically and reflects over x axis(option c).
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Using the intermediate value theorem find the value of c such that f(c)=m. F(x)=x^2-x+11 on (2,11), m=31
Answer: The Intermediate Value Theorem states that if a function is continuous on a closed interval and takes on two different values at the endpoints of the interval, then it must take on all values between those two endpoints.
Given the function f(x) = x^2 - x + 11 and the interval (2, 11), we know that f(2) = 2^2 - 2 + 11 = 13 and f(11) = 11^2 - 11 + 11 = 121. And we want to find the value of c such that f(c) = 31.
Since 31 is between 13 and 121 and the function f(x) is continuous on the interval (2, 11), we can conclude that by the Intermediate Value Theorem, there exists a value c in the interval (2, 11) such that f(c) = 31. To find the specific value of c, we would have to perform further calculations or use a root-finding method.
Step-by-step explanation:
the empirical rule assumes that the distribution of data follows a normal curve. group startstrue or false
The statement "The empirical rule assumes that the distribution of data follows a normal curve." is True.
The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This implies that the distribution of data follows a normal curve.
A normal distribution is a type of probability distribution that follows a symmetrical bell-shaped curve. It is also known as the Gaussian distribution and is a continuous probability distribution. The normal distribution is defined by its mean, which is the average of the values, and its standard deviation, which is a measure of the spread of the values from the mean.
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Fraction A 5/6 , Fraction B 3/4 ........
What is the numerator of Fraction A?
What is the denominator of Fraction B?
What is the denominator of Fraction A?
Answer: A = 5
B = 4
C = 6
Jermaine and Josh observed an anthill for their science project. They observed that an ant moved 45.0 millimeters (mm) in 85.0 seconds (s). How fast was the ant moving?
Answer:
Velocity =displacement/time
Distance covered is 45mm which is 0.045m or 0.45cm but the displacement is very small so use mm instead. Time taken (t) to cover the distance is 85s. V=45/85
V=0.53mm/s
Step-by-step explanation:
(20 POINTS TO ANSWER PLEASE CORRECTLY) In Mr. Henry’s math classroom, there are 15 girls and a total of 26 students. Part B: Write the ratio of boys to girls in the form a:b. SHOW YOUR WORK OR EXPLAIN YOUR REASONING.
Answer:
15:26. Hope this helps!
There are 15 girls and 26 boys so simply but the lower number berfore the higher number.
if N is 1/8 as much as 16, what does N equal?
Background:
"As much as" means that two quantities are being compared and is a keyword for division.
Procedure:
\(N=\frac{16}{8}=2\)Answer: 2
Mike hiked to a lake in 5.5 hours at an average rate of 4 1/5miles per hour. Pedro hiked the same distance at a rate of 4 3/5 miles per hour. How long did it take Pedro to reach the lake? Round to the hundredths place.
Answer:
Step-by-step explanation:
{4 1/5 =4.2 and 4 3/5 = 4.6}
Mike's hiking Distance = Pedro's hiking Distance
3.5 Hours *4.2 Miles/ hour = Pedro's Hiking Time *4.6 miles/ hours
Bye Have a Good Day!!! I answered your Question For you I'm A Smart Helper and Good at School But If anyone needs me to help them with sum just reply to my comment ok Bye.Please help!! If f (x) = e^x sin x, then f’ (x) =
Answer:
\( f'(x) = {e}^{x}( \sin x + \cos x ) \)
Step-by-step explanation:
\(f(x) = {e}^{x} \sin x \\ \\ f'(x) = \sin x \frac{d}{dx} {e}^{x} + {e}^{x} \frac{d}{dx} \sin x \\ \\ f'(x) = \sin x \: {e}^{x} +{e}^{x} \cos x \\ \\ f'(x) = {e}^{x}( \sin x + \cos x ) \)
1 individuals in a tetrahybrid cross is AaB-bCcDd. Assuming independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes?
1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.
2. AABBCcDD: This genotype can be produced in two ways:
a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.
The probability of this happening is = 1/128.
b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.
3. The probability of this happening is 1/32.
AaBbCcDd : The probability of this happening is 1/256.
4. aaBBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is 1/128.
b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is 1/32.
To solve this problem, we need to use the principles of probability and Punnett squares.
For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.
Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:
A | A | a | a
---|-----|-----|----
B | B | b | b
---|-----|-----|----
C | C | c | c
---|-----|-----|----
D | D | d | d
Each box in the Punnett square represents a possible combination of alleles from the two parents.
For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.
We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.
AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.
The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.
AABBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.
The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)
b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)
AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).
The probability of this happening is \((1/2)^8 = 1/256.\)
aaBBCcDD - This genotype can be produced in two ways:
a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)
b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.
The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)
Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.
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