Answers
The value of c that satisfies the Mean Value Theorem for this problem are given as follows:
A. [tex]4\sqrt{3}[/tex]
How to obtain the value or values of c?The function for this problem is given as follows:
f(x) = x + 48/x.
The bounds of the interval are given as follows:
a = 3, b = 16.
The derivative of the function is given as follows:
f'(x) = 1 - 48/x².
The numeric value of the derivative at x = c is given as follows:
f'(c) = 1 - 48/c²
The numeric values of the functions at the bounds are given as follows:
f(b) = f(16) = 16 + 48/16 = 19.f(a) = f(3) = 3 + 48/3 = 19.Then the value of c is obtained as follows:
1 - 48/c² = 0/16
1 - 48/c² = 0
48/c² = 1
c² = 48
c = square root of 48.
[tex]c = \sqrt{16 \times 3}[/tex]
c = [tex]4\sqrt{3}[/tex]
Option A, as we have to be reminded that the interval is [3,16], hence the negative root is not considered.
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Related Questions
in general, a change in what causes a movement along a curve in the models we have studied? a change in what causes a shift in the curve?
Answers
In general, a change in the price of the product causes a movement along the demand curve; and a change in production cost and related factors causes a shift in the supply curve.
What is demand curve?The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In a typical representation, the price will appear on the left vertical axis of the graph, and the quantity demanded on the horizontal axis.
What is supply curve?The supply curve is a graphic representation of the relationship between product price and quantity of product which a seller is willing and able to supply. Product price is measured on the vertical axis of the graph, and the quantity of product supplied on the horizontal axis.
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jane will toss a fair coin two times. if you know that the first coin toss resulted in heads, what would the probability be that both coins would land on heads? explain.
Answers
The probability that both coins will land on heads is 50%. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails.
This is because the result of the first coin toss does not influence the outcome of the second coin toss, meaning each toss is an independent event with a 50% chance of landing on heads.The probability that both coins will land on heads is 50%. This is because the result of the first coin toss does not influence the outcome of the second coin toss. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails. This means that the probability of both coins landing on heads is the same as the probability of either coin landing on heads, which is 50%. Therefore, the probability that both coins will land on heads is 50%.
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Find the principal value of cos[pie/2 -sin inverse (1/2)]
Answers
The value of the given expression cos(π/2 - sin⁻¹(1/2)) will be equal to 1/2.
What are Trigonometric functions?The fundamental six functions of trigonometry have a range of numbers as their result and a boundary input value that is the angle of the right triangle.
As per the given information in the question,
cos(π/2 - sin⁻¹(1/2))
Use the formula given below,
cos(π/2 - θ) = sin θ
From the above formula,
sin(sin⁻¹ (1/2))
= 1/2
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Is this a function or not a function?
Image result for vertical line graph
Answers
Answer:
not a function. There cannot be mutiple y-values under one x value.
Step-by-step explanation:
The original quantity is 10 and a quantity is 15 what is the percent increase
Answers
Step-by-step explanation: Pour résoudre ce problème, nous devons trouver le pourcentage d’augmentation entre les deux quantités. Cette augmentation est la différence entre les deux quantités exprimée en pourcentage.
Étape 1 : Calculer la différence entre les deux quantités.
La différence est 15 - 10 = 5.
Étape 2 : Diviser la différence par la quantité originale.
5 / 10 = 0,5
Étape 3 : Multiplier le résultat par 100 pour obtenir le pourcentage.
0,5 x 100 = 50
Conclusion : L’augmentation est de 50 %.
Helppp please I’m confused
Answers
Answer: 55%
the percent of the female participants is: [tex]\frac{121}{121+99}.100=\frac{121}{220}.100=55[/tex] (%)
Step-by-step explanation:
A scale drawing of a rectangular park had a scale of 1 cm = 110 m.
7.4 cm
4.2 cm-
What is the actual area of the park in meters squared?
Answers
The actual area of the park is 376068 meters squared. If A scale drawing of a rectangular park had a scale of 1 cm = 110 m.
Define area of rectangle.The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the product of its length and breadth.
Given
A scale drawing of a rectangular park had a scale of 1 cm = 110 m.
Length of rectangle,
7.4 × 110
814m
Breadth of rectangle,
4.2 × 110
462 m
Area of rectangle
length × breadth
814 ×462
376068
The actual area of the park is 376068 meters squared. If A scale drawing of a rectangular park had a scale of 1 cm = 110 m.
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Describe how to write 4x^2 + 8x - 10 = 0 in vertex form
Answers
Answer:
(2x + 1)^2 = 7
Step-by-step explanation:
To write the quadratic equation 4x^2 + 8x - 10 = 0 in vertex form, we need to first complete the square. To do this, we need to add and subtract the same value to the quadratic term and the linear term so that the resulting quadratic has the form (x - h)^2 = k.
In this case, we need to add and subtract the square of half of the coefficient of the linear term, which is 8/2 = 4. This gives us the equation:
4x^2 + 8x + 4 - 4 - 10 = 0
This simplifies to 4(x^2 + 2x + 1) - 14 = 0, which can be rewritten as (2x + 1)^2 - 7 = 0.
To put this in vertex form, we need to rewrite the right side of the equation as a perfect square, so we add 7 to both sides to get (2x + 1)^2 = 7.
Then, we take the square root of both sides to get 2x + 1 = ±√7. We can then solve for x to get x = -1/2 ± √7/2.
Therefore, the equation 4x^2 + 8x - 10 = 0 can be written in vertex form as (2x + 1)^2 = 7.
If C is the line segment from (5,4) to, (0,0), find the value of the line integral:
Answers
The value of line integral of the line segment from (5,4) to, (0,0) is 90.
Given that C is the line segment from (5,4) to (0,0):-
So, our first task is to calculate the line segment
After calculating the line segment, we will be able to calculate the line integral
We know that the equation of line is -
y - y1 = (y1 - y2)/ (x1 - x2) * (x - x1)
So now,
y - 0 = (4 - 0)/ (5 - 0) * (x - 0)
y = 4/5 x
5x - 4y = 0 -----------> (1)
A line integral is used to calculate the area covered by that line
c1 = ∫₀⁴ 5x dx ------> (2)
c2 = ∫₀⁵ -4y dy -----> (3)
c1 = [ 5 x²/2 ]₀⁴ = 5 * ( 4² - 0)/2 = 40
c2= [ -4 y²/2 ]₀⁵ = -4 * ( 5² - 0)/2 = 50
The value of the line integral: c1 + c2 = 40 + 50 = 90
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Help me out please !!!!!!!!
Answers
Answer: 3 boxes
Step-by-step explanation:
she has 3 stuffed animals left and its not manditory to fill a box so you would put the threee remaining into one box
7. find and describe a case in which the land surface of an area in the u.s. has subsided due to groundwater withdrawal. if possible, give an estimate of how many feet the land surface subsided.
Answers
an instance where a region's u.s. land surface has changed subsided due to groundwater withdrawal. The land surface in the Central Valley has subsided by as much as 30 feet in distance some areas due to unsustainable groundwater withdrawals.
The most famous case of land subsidence due to groundwater withdrawal in the United States is the Central Valley of California. The land surface in the Central Valley has subsided by as much as 30 feet distance in some areas due to unsustainable groundwater withdrawals. In addition to land subsidence, the unsustainable withdrawals have caused significant groundwater depletion, surface water contamination, and reduced agricultural productivity.
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the null hypothesis claims that the proportion of community college students who work full-time is 0.45. the alternative hypothesis is that this proportion is greater than 0.45. which sample proportion will have the smallest p-value?
Answers
The sample proportion will have the smallest p-value is for Z=3 that can be calculated by taking comparisons between Z=1,2 and 3.
Null hypothesis H0= P=0.45
Alternative hypothesis H1= P>0.45
The null hypothesis assumes that any form of distinction among the selected traits which you see in a fixed of records is because of chance. For example, if the predicted income for the playing recreation are truely same to 0, then any distinction among the common income withinside the records and 0 is because of chance.
H=1000, x1=500, x2=600 and x3=700
P1= x1/h=500/1000=0.5
P2=x2/h=600/1000=0.6
P3=x3/h=700/1000=0.7
Z1=P1-P/(P(1-P)/h)61/2 = 0.5-0.45/(0.45*0.55/1000)^1/2 = 0.32
P-value for Z1=P(Z1>0.32)=0.37748
Z2=P2-P/(P(1-P)/h)61/2 = 0.6-0.45/(0.45*0.55/1000)^1/2 = 0.95
P-value for Z2=P(Z2>0.95)=0.17106
Z3=P3-P/(P(1-P)/h)61/2 = 0.7-0.45/(0.45*0.55/1000)^1/2 = 1.59
P-value for Z3=P(Z3>0.95)=0.055917
Thus, the smallest P-value will be for Z3.
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how many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 11?
Answers
We need to start by choosing some 10 integers so that we can ensure that when they are divided by 11, at least two of the integers will give the same remainder.
The following is the explanation:
If you divide a number by 11, the answer will be a fraction. There are 11 remainders which might occur, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
If for example we choose one number and divide it by 11, there is a chance that the remainder may be any of the 11 (0 reminders 1). Therefore, if we choose 10 numbers, we will have the opportunity to pick 10 unique remainders, ranging from 0 to 10.
In conclusion, if we select one more integer, that is we pick 10 integers, then at least two of them would have the same remainder since there are only 10 remainders.
Because of this, we need to choose 10 numbers such that we can guarantee that at least two of them will provide the same remainder when they are divided by 11.
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Why do we need to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number?
Answers
The statement would no longer be true if you did not flip the signs.
Example: 1 < x < 2 multiplied by (-1) equals -2 < x < -1, because you can't have a number that is greater than -1, and less than -2 at the same time.
I the ytem of equation conitent and independent conitent and dependent or inconitent
Answers
The system of linear equations, y = 2x + 4 ;
2y = x + 6 has a unique solution and it is a consistent system of linear equations.
What is linear System of Equations and it's solution?An ordered pair that satisfies all equations of the system is the solution of the system. A system of linear equations can have one solution, no solution, or an infinite number of solutions. The systems of equations can be classified according to the number of solutions. If a system has at least one i.e unique solution, it is called consistent. We have, the system of equations is
y = 2x + 4 => 2x - y + 4 = 0 --(1)
2y = x + 2 => x - 2y + 6 = 0 --(2)
Comparing the equation (1) with a₁x + b₁y + c₁=0
and equation(2) with a₂x + b₂y + c₂=0
We get, a₁ = 2 , a₂= 1 , b₁ = -1 , c₁= 4 , b₂= -2 , c₂ = 2
Now, compute the ratio of coefficients of variables .
a₁/a₂ = 2/1 , b₁/b₂ = -1/-2 = 1/2 , c₁/c₂= 4/6 = 2/3
=> a1/a2 ≠ b1/b2 ,
here, both lines are intersect at a point and a unique solution exist for pair of linear equations. In such a case , the pair of linear equations is said to be consistent. Thus, system is consistent.
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Complete question:
Is the system of equation is consistent and
independent consistent and dependent or inconsistent?
y = 2x + 4 , 2y = x + 6
which of the following statement is false ? (a)a triangle has three sides. (b) a triangle has three vertices.(c)a triangle has three angles.(d) a triangle has two diagonals
Answers
Answer: D
Step-by-step explanation:
Answer:D
Step-by-step explanation: A triangle has no diagonals
sinxcosx = 1/2cosx
Solve for x.
Answers
Answer:
[tex]x=\dfrac{1}{2} \pi + 2\pi n[/tex]
[tex]x=\dfrac{3}{2}\pi +2 \pi n[/tex]
[tex]x=\dfrac{1}{6}\pi+2 \pi n[/tex]
[tex]x=\dfrac{5}{6}\pi+2 \pi n[/tex]
Step-by-step explanation:
Given trigonometric equation:
[tex]\sin x \cos x &= \dfrac{1}{2} \cos x[/tex]
Rearrange the equation so that it equals zero:
[tex]\begin{aligned}\sin x \cos x &= \dfrac{1}{2} \cos x\\2 \sin x \cos x &= \cos x\\2 \sin x \cos x - \cos x &=0\\ \cos x (2 \sin x - 1)&=0\end{aligned}[/tex]
Apply the zero-product property.
Case 1
[tex]\begin{aligned}\cos x &=0\\x&=\cos^{-1}(0)\\x&=\dfrac{1}{2} \pi +2\pi n, \; \dfrac{3}{2}\pi +2 \pi n\end{aligned}[/tex]
Case 2
[tex]\begin{aligned}2\sin x - 1& = 0\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\x&=\sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{1}{6} \pi+2 \pi n, \; \dfrac{5}{6} \pi +2 \pi n\end{aligned}[/tex]
a pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle. is the perimeter of the pentagon greater than 26 centimeters?
Answers
the perimeter of the pentagon greater than 26 centimeters is given by
23.51
Given that a pentagon with 5 sides of equal length and 5 interior angles of equal measure is inscribed in a circle
The circle has area of 16 pi sq cm.
Hence radius of circle = 4 cm
The pengagon each side would be a chord of equal length subtending angle 72 at the centre.
visualize the triangle made by one side of pentagon with centre. This is isosceles with angles 72, 54 and 54
Use sine angle for this triangle.
, where R = radius =4 and s = side of pentagon.
s= 4.702
Perimeter = 5s = 23.5114 cm
Perimeter not greater than 26 cm.
If origin is at the centre then two vertices would be (4,0) (4cos 72, 4sin72),(4cos 144, 4 sin 144) and so on.
Longest diagonal = distance between (4,0) and (4cos 144, 4 sin 144)
= (-3.236, 2.351) and (4,0)
=7.608
Yes greater than 8 cm
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Sarah is 148 centimeters tall. How tall is Sarah in inches? Round to the nearest tenth inch.
Answers
Answer:
58.3
Step-by-step explanation:
divide the length value by 2.54
58.2677
Answer:
58,3 inches
Step-by-step explanation:
1 inch = 2.54 cm
[tex]148 \: cm \:*\:\frac{1\:inch}{2.54\: cm} = 58,267716535433070866141732283465\\\\148\: cm=58,3 \:inches[/tex]
44 out of 60 as a persentage
Answers
Answer: 73.3%
Step-by-step explanation:
take 44 and divide it by 60
44/60 = 0.0733 repeating
move the decimal place to the right twice
0.0733 --> 73.3%
What is the domain of this function?
Answers
Answer:
all real numbers
Step-by-step explanation:
the graph continues to the left and to the right because there are arrows
what is the probability that if 7 letters are typed, no letters are repeated? write your answer in decimal form, rounded to the nearest thousandth. the probability that no letters are repeated is .
Answers
The probability that no letters are repeated is 0.0015, rounded to the nearest thousandth.
The probability that no letters are repeated is calculated using the formula P = n! / (r^n * (n-r)!)
, where n is the total number of letters and r is the number of each letter.
The numbers here are n = 7 and r = 1.
This means the probability of no letters being repeated is 7! / (1^7 * 6!) = 0.0015.
This can be rounded to the nearest thousandth, giving the answer of 0.0015.
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Julie is given the data point (6, 7) as a point on the profit equation that she must create. Her boss mentioned that the last equation that
they used was y = 2x+3. If Julie wants to write the new equation that is parallel to the old equation, what would her new equation look
like?
y=6x+7
y=2x-5
Answers
y=2x+7. In order to create an equation that is parallel to the old equation, Julie must make sure that her new equation has the same slope as the old equation. The slope of the old equation is 2, so Julie's new equation should also have a slope of 2. Additionally, she must make sure that the y-intercept of her new equation is the same as the given data point, which is (6, 7). Therefore, the new equation should be in the form y = 2x + b, where b is the y-intercept. Plugging in the values from the given data point, we get y = 2x + 7. This equation is parallel to the old equation and passes through the given data point, so it is the correct answer.
Answer:
The answer to the question is that the new equation that is parallel to the old equation and passes through the point (6, 7) is y = 2x - 5.
Step-by-step explanation:
To create an equation that is parallel to the old equation, you need to use the same slope. This means that your new equation should be y = 2x + b, where b is a constant. Since the point (6, 7) is on the new equation, you can plug those values into the equation to find b.
The temperature at 4pm is 43 degrees. Throughout the night it steadily falls 6 degrees.
What is the rate of change in this situation?
Answers
Answer:
The rate of change in this situation is 6 degrees per hour.
Step-by-step explanation:
The rate of change in this situation is -6 degrees per hour. To find this, we need to divide the change in temperature by the amount of time over which the change occurs. In this case, the temperature falls from 43 degrees to 43-6=<<43-6=37>>37 degrees, so the change in temperature is 43-37=<<43-37=6>>6 degrees. Since the temperature falls over the course of one night, the rate of change is 6 degrees / 1 night = -6 degrees per hour.
Use the drawing tools to graph the line that represents the equation 2y = -4x + 6.
Drawing Tools
Select
Point
Click on the Graph to
place a Point.
Line
Show Instructions
-8
4
-6
-4
-2
4-
2-
-2-
-4-
-6
2
4
6
8
Answers
If it is a line that does go through 0,0 then it is NOT PROPORTIONAL
Dilate the line segment by a scale factor of 2 with a center of dilation at the origin. Draw the dilated segment on the provided graph.
Click on a fool to begin drawing.
Drawing Tools
Select
Point
Une Segment
16-
14--
12-
10-
8-
Delote
10
12
Undo
14
16
Reset
Answers
Please find attached the drawing of the image of the segment following a dilation by a scale factor of 2 with the center at the origin, created with MS Word.
What is a dilation transformation?A dilation transformation is one in which the size of the object is increased (or decreases) proportionately by a factor known as the scale factor of dilation.
The center of dilation is the origin, which is the point (0, 0)
The coordinates of points on the line segment are; (5, 5) and (0, 0)
Therefore, the line segment to be dilated passes through the center of dilation
The image of the segment to be dilated also will pass through the center of dilation, which is the origin or the point (0, 0)
The dilation of the segment by a scale factor of 2 has a point at the origin (0, 0), the second point is therefor at the point (2× 5, 2 × 5) = (10, 10)
The coordinates of the image of the segment following a dilation are therefore; (0, 0), and (10, 10)
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A, B and C are interior angles of a triangle ABC. Show that
(i) sin (B+C/2) = cos (A/2)
(ii) if angle A= 90°, then find the value of tan (B+C/2)
Answers
Answer:
ok i can do it if u want then see my m.s.g
The required solutions to the given triangle ABC below as:
(i) sin (B+C/2) = cos (A/2)
(ii) if angle A= 90°, then the value of tan (B+C/2) is is undefined.
What are Interior Angles?Interior angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles.
Given that A, B, and C are interior angles of a triangle ABC.
To solve the question, we would consider trigonometric ratios of complementary angles.
sin (90° - θ) = cosθ
We know that for ΔABC,
∠A + ∠B + ∠C = 180° (Angle sum property of triangle)
∠B + ∠C = 180° - ∠A
On dividing both sides by 2, we get,
(∠B + ∠C)/2 = (180° - ∠A)/2
(∠B + ∠C)/2 = 90° - ∠A/2
Applying sine angles on both sides:
sin {(∠B + ∠C)/2} = sin (90° - ∠A/2)
Since, sin (90° - θ) = cos θ, we get
sin (∠B + ∠C)/2 = cos A/2
(ii) if angle A= 90°, then find the value of tan (B+C/2)
If cos A/2 = 0 so ∠A = 90°
sin (∠B + ∠C)/2 = cos A/2 = 0
tan (B+C/2) = ∞
Thus, the value of tan (B+C/2) is undefined.
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Please helppp I’m giving brainlyest
Answers
Answer:
B
Step-by-step explanation:
the shape will reflect b
consider the proposed proof that all real numbers are equal to 0 below. which is the first line that contains an error?
Answers
A. Let x be a real number,B. Add x to both sides of the equation, then C. x - x = 0,D. Therefore, x = 0
A. Let x be a real number - This step states that we are selecting a real number for which we will prove that it is equal to 0. This step does not contain an error.
B. Subtract x from both sides of the equation - This step does not contain an error as it is the first step in the process of proving that the real number is equal to 0.
C. x - x = 0 - This step contains an error, as it doesn't provide enough information to prove that the real number is equal to 0.
D. Therefore, x = 0 - This step also contains an error, as it assumes that the proof is correct without providing any evidence.
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Would you rather receive a 3% raise followed by a 9% raise or a 9% followed by a 3%
Answers
It is better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
What is the percentage increase?
The concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original.
It is generally better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
This is because the percentage raise you receive is applied to your current salary. If you receive a 3% raise first, your salary will be higher when you receive the 9% raise, so the 9% raise will be applied to a higher base salary. This means that you will receive a larger increase in salary overall if you receive the 9% raise first.
For example, let's say you are currently making $50,000 per year. If you receive a 3% raise followed by a 9% raise, your salary would increase to $51,500 after the first raise and then to $56,365 after the second raise, for a total increase of $6,365.
On the other hand, if you receive a 9% raise followed by a 3% raise, your salary would increase to $54,500 after the first raise and then to $56,365 after the second raise, for a total increase of $5,865.
In this example, you would receive a larger increase in salary overall if you received the 9% raise first. This is because the 9% raise is applied to a lower base salary, resulting in a larger increase in salary overall.
Of course, the actual amount of the raise will depend on your current salary and the percentage of the raise. In general, though, it is usually better to receive a larger percentage raise first, followed by a smaller percentage raise.
Hence, It is better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
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