The required sets of all real and satisfying numbers are:
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
What are sets?Sets are groups of clearly defined objects or elements in mathematics.
A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
The empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset, and infinite set are the various types of sets.
Now, solve for (x^2 + 3x - 1)^2 = 9:
To make this true, either
x^2 + 3x - 1 = 3 or x^2 + 3x - 1 = -3
x^2 + 3x - 4 = 0, x^2 + 3x + 2 = 0
(x + 4) ( x - 1) = 0, (x + 1) ( x + 2) = 0
x = -4, x= 1, x = -1, x = -2
Therefore, we have five potential intervals to test.
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
Therefore, the required sets of all real and satisfying numbers are:
(-∞ , -4) , (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)
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Let Fx = 2X^2 - 6x + 4 and g(x) 4 cos 1/4 Let R be the region bounded by the graphs of f and g, as shown in the figure above.(a) Find the area of R.(b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y 4.(c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a square. Write, but do not evaluate, an integral expression that gives the volume of the solid.
The area of R can be calculated using the definite integral of the function y = 2x^2 -6x +4 and between g(x ) = cos1/4 and x = 4.
The integral expression is ∫(2x^2)-6x+4dx = ∫e^u du = e^u + C = e^(2x-x^2) + C. Evaluating the integral between x = 0 and x = 1 gives the area of R as e^2 - 1.
(b) The area of S can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1, minus the integral of the function y = 1 between x = 0 and x = 1. The integral expression for S is ∫e^(2x-x^2)dx - ∫1dx = ∫e^u du - x = e^u + C - x = e^(2x-x^2) + C - x. Evaluating the integral between x = 0 and x = 1 gives the area of S as e^2 - 1 - 1.
(c) The volume of the solid generated when R is rotated about the horizontal line y = 1 can be found using the integral expression ∫2πx(e^(2x-x^2) - 1)dx. This expression represents the area of the circular cross-sections of the solid multiplied by 2πx, which is the circumference of the circle. When evaluated between x = 0 and x = 1, this integral gives the volume of the solid generated when R is rotated about the horizontal line y = 1.
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The distanse between Toronto and sudbury is 418km. Terry leaves Sudbury on his motocycle and drives 310km towards Toronto. Damon leaves Toronto at the same time on his motocycle and drives 303km toward Sudbury. How far apart are Terry and Damon?
Using mathematical operations, the distance that differentiates Terry and Damon is 7 kilometers.
What are mathematical operations?Mathematical operations are the computation of values using mathematical operands (÷, ×, +, -, etc), and mathematical operators like addition, subtraction, division, and multiplication.
In this situation, we use the subtraction operation to determine the difference or the distance between Terry and Damon.
The total distance between Toronto and Sudbury = 418 km
The distance covered by Terry from Sudbury to Toronto = 310 km
The length yet to be covered by Terry = 108 km (418 - 310)
The distance covered by Damon from Toronto to Sudbury = 303 km
The length remaining for Damon = 115 km (418 - 303)
The distance apart between Damon and Terry = 7 km (115 - 108)
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Lizzy made 10 cups of strawberry jam and divided the jam equally among 6 containers. How much jam went into each container?
Answer:
1 2/3 went in each container
Step-by-step explanation:
10 divided by 6 is 1.666666666677777777777 which equals to 1 2/3 multiply it by 6 and you will get 10.
consider a sample with data values of 10, 20,12 ,17 , and 16 . round your answers to the nearest whole number
16 is Median a sample with data values .
What is the mathematical median?
The middle number, or median, is obtained by sorting all of the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).
Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.
Mean = Total of values/ Total number of observations
Total of values = 10+20+12+17+16 = 75
Total number of observations = 5
Mean = 75/5 = 15
Median:
Arrange in ascending order = 10, 12,16,17,20
Median = [n+1] / 2
N = number of observation = 5
Median = [5+1]/2 = 3rd observation
Median = 16
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What is the answer for this equation 2n+3-5n+6
Reason:
The like terms 2n and -5n combine to -3n. In other words, 2n-5n = -3n
The other pair of like terms 3 and 6 combine to 3+6 = 9
The melting point of an unknown solid is determined to be 42.0°C. What is this temperature on the
Fahrenheit and Kelvin scales?
°F
K
The temperature on the Fahrenheit scale is 107.6°F and Kelvin scale is 315.15K. The solution has been obtained by unit conversion.
What is unit conversion?
The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, instead of using hours to represent time, you might use minutes, or you could use feet instead of miles to express distance. Measurements are frequently offered in one set of units, like feet, but are required in another set, like chains.
We are given the melting point of an unknown solid to be 42.0°C.
For converting the given temperature in Fahrenheit, we use the given formula:
⇒(Temperature in Celsius × 9/5) + 32 = Temperature in Fahrenheit
So,
⇒(42°C × 9/5) + 32 = x°F
⇒(42°C × 9/5) + 32 = 107.6°F
Now, for converting the given temperature in Kelvin, we use the given formula:
⇒Temperature in Celsius + 273.15 = Temperature in Kelvin
This is because 0°C = 273.15 K
So, 42°C + 273.15 = 315.15K
Hence, the temperature on the Fahrenheit scale is 107.6°F and Kelvin scale is 315.15K.
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Draw rectangle HIJK, if HI = 3x + 7 and JK = 6x − 11,
find the value of x.
pls i need it
Answer:
x = 6
Step-by-step explanation:
Vertices of a rectangle are normally listed so that adjacent vertices are connected by edges. Therefore, the edges of rectangle HIJK are HI, IJ, JK and KH.
As the opposite sides of a rectangle are congruent:
HI = JK and IJ = KHTherefore, to find the value of x, set the given expressions for HI and JK equal to each other and solve for x:
[tex]\implies \sf HI=JK[/tex]
[tex]\implies 3x+7=6x-11[/tex]
[tex]\implies 3x+7-7=6x-11-7[/tex]
[tex]\implies 3x=6x-18[/tex]
[tex]\implies 3x-6x=6x-18-6x[/tex]
[tex]\implies -3x=-18[/tex]
[tex]\implies -3x \div -3=-18 \div -3[/tex]
[tex]\implies x=6[/tex]
Write an equation in the form y = a(x-r)(x-s) to represent the parabola shown.
Answer:
c
Step-by-step explanation:
because y = 0 when x = 2 and y = -4 when x =0
Dimensional Analysis help. i don’t even know where to start
R13 fiberglass batt insulation, typically used in walls and floors, is 3 5/8 inches thick, according to Energy.gov.
How can you figure out how much insulation you need?To determine the number of insulation batts required, first determine the area to be insulated in square meters (m2). Calculating the square metre (m2) area of your walls is actually fairly simple; simply multiply the length by the breadth.
To assess the cost of cellulose insulation for your project, first decide how much insulation you would require. To do so, divide the square footage of the space by the depth or the desired R-value. R-25 EcoTouch insulation is designed to fit snugly between outside wall wood studs. After installing cover material on one side of the cavity, friction-fit unfaced insulation between studs.
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construct an argument determine whether each statement is sometimes, always, or never true. justify your argument. the opposite angles of an isosceles trapezoid are supplementary.
The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles
The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles.
Always true. The opposite angles of an isosceles trapezoid are supplementary because the diagonals of an isosceles trapezoid bisect each other. Therefore, the angles formed by the intersection of the diagonals are supplementary, since the sum of two supplementary angles is 180 degrees.
The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles.
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If angle A is congruent to angle D and angle C is congruent to angle F , which additional statement does NOT allow you to conclude that triangle ABC is congruent to triangle DEF?
A). line BC is congruent to line EF
B). angle B is congruent to angle E
C). line AC is congruent to line DF
D). line AB is congruent to line DE
The Side-Angle-Side rule is the foundation for this query. The correct response is therefore option A, since ABC=DEF cannot be inferred from the additional statement that AB=EF.
What is SAS criterion?According to this rule, the corresponding two angles of one triangle are congruent with the two angles of the other triangle. The side-angle-side postulate is the only congruence rule that can be applied as a result.
Here,
A=D and C=F in triangle ABC and triangle DEF.
We must choose a statement that prevents you from deducing that triangle ABC = triangle DEF.
The correct response is therefore option A, since ABC=DEF cannot be inferred from the additional statement that AB=EF.
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which of the following are not corresponding parts of the congruent triangles? line segment cap a cap b is congruent to line segment cap c cap d d. $\angle a\cong\angle c$ d., , $\angle a\cong\angle c$ question 2 two triangles, triangle a b e and triangle cde. segments b d and a c intersect at point e to form one vertex and two sides of each triangle. b e is congruent to d e. a e is congruent to c e.
Line segment AB is congruent to line segment CD, ∠A ≡ ∠C, BE is congruent to DE and AE is congruent to CE in triangle ABE and triangle CDE. So all the first four options are corresponding parts of the two congruent triangles.
Therefore, the answer is e. None of the above.
Corresponding parts of congruent triangles are any pair of matching or identical elements in two congruent triangles. These can include:
Sides, such as line segment AB being congruent to line segment CD
Angles, such as ∠A being congruent to ∠C
Vertices, such as point E being the intersection of segments BD and AC in both triangles
Any other element that is identical in both triangles, like height, medians, circumcenters, etc.
In triangle ABE ≡ triangle CDE, congruent sides are
AB ≡ CD
BE ≡ DE
AE ≡ CE
Congruent angles are
∠A and ∠C
∠B and ∠D
∠BEA and ∠DEC
--The question is not readable, answering to the question below--
"Which of the following are not corresponding parts of the congruent triangles, triangle ABE and triangle CDE? Segments BD and AC intersect at point E to form one vertex and two sides of each triangle.
a. line segment AB is congruent to line segment CD
b. ∠A ≡ ∠C
c. BE is congruent to DE
d. AE is congruent to CE
e. None of the above"
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Amelia and Jamal share pizza in the ratio 3:5. Jamal eats 4 more slices than Amelia. How many slices does Jamal eat
The number of slices that Jamal eats will be 10 slices.
How to calculate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Let Amelia's share be x.
Jamal's share will be x + 4.
Therefore, the equation will be Illustrated as:
3/5 = x/(x + 4)
Cross multiply
5x = 3x + 12
5x - 3x = 12
2x = 12
Divide
x = 12 / 2
x = 6
Jamal's share will be
= 6 + 4.
= 10
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Rewrite (2+3) + 4 using the Associative Law of Addition
Answer:
9
Step-by-step explanation:
Which of the following is the correct conversion factor (as written) required to convert a distance of 12 mi to feet, if 1 mi= 5280 ft ?A. 1 mi x 5280 ftB. 5280 ft / 1 miC. 1 mi / 5280 ft
The correct conversion factor is B: 5280 ft / 1 mi.
Option (B) is correct.
What is unit conversion?
Unit conversion is the process of changing a measurement from one unit to another. For example, converting meters to feet, or kilometers to miles. In order to convert from one unit to another, you need to know the conversion factor between the units, which is the ratio of equivalent values in the two units.
When converting a distance in miles to feet, you need to multiply the distance in miles by the number of feet in a mile. The conversion factor that is commonly used to convert miles to feet is 1 mi = 5280 ft.
The correct conversion factor to convert a distance of 12 mi to feet is therefore:
12 mi x (5280 ft / 1 mi) = 12 x 5280 ft
Hence, the correct conversion factor is B: 5280 ft / 1 mi.
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HELP!!
In the figure below, TW and TU are tangent to the circle centered at O. The segment WU passes through the center of the circle. Given that TW=17.4 and WU=12, find WV.
Answer:
WU=4.8
Step-by-step explanation:
put it in the box WU =4.8
Please please look at the picture and answer the question thank you for your help
Answer:
20 for both
Step-by-step explanation:
hope this helps
84.7/14 I don't know ow how to do 84.7/14 without any reminders so please help
The value of the expression 84.7 divided by 14 will be 6.05.
How to calculate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value of the expression 84.7 divided by 14 will be:
= 84.7 / 14
= 6.05
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What does a high graduation rate suggest about a university or college?
A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following is best describes this setting?
a. Y has a binomial distribution with n= 40 observations and probability of success p= 0.5.
b. Y has a binomial distribution with n=40 observations and probability of success p=0.5, provided the deck is shuffled well.
c. Y has a binomial distribution with n=40 observations and probability of success p=0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.
d. None of these.
Answer:
c. Y has a binomial distribution with n=40 observations and probability of success p=0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.
Step-by-step explanation:
if wrong pls tell
(a) Express the general solution of the given system of equations in terms of real-valued functions. (b) Also draw a direction field, sketch a few of the trajectories, and describe the behavior of the solutions as - 8?
the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.
Lx + My = N ---------(1)
Ax + By = C ---------(2)
System 2 :
(L - A)x + (M - B)y = N - C -------(3)
Lx + My = N ---------(4)
If we subtract equation (2) from equation (1),
(Lx + My) - (Ax + By) = N - C
Lx - Ax + My - By = N - C
(L - A)x + (M - B)y = N - C
Which is similar to equation (3) of the system 2.
And equation (1) of the system (1) is similar to the equation (4) of the system (2)
Therefore, equation (3) of the system 2 is the difference of of equations in the system 1. Equation (1) for system 1 is similar to the equation (4) of the system 2.
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Need help on this asap
The Total surface area of a pyramid formula = ½ pl + B, Where 'p' is the perimeter of the base and 'l' is the slant height of the pyramid and B is the area of the base.
What is the formula for volume of pyramids?A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=13Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.
A triangular pyramid, for instance, has a base area of 20 cm2 and a height of 9 cm. The formula V = (1/3) Bh, where "B" stands for the base area and "h" for the height of the pyramid, is used to calculate the volume of a pyramid.
We can use the formulas for the area of polygons to calculate "B" because we know that the base of a pyramid can be any polygon. A pyramid with a triangle base is referred to as a triangular pyramid.
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The value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].
What is the formula for volume of pyramids?A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=1/3Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.
We know that pyramid's volume is
[tex]\mathrm{{\textstyle V={\tfrac {1}{3}}Bh}}[/tex]
B = base area = [tex]25^{1/4} \times25^{1/4}[/tex]
= [tex]\sqrt[4]{25} \times \sqrt[4]{25}[/tex]
= [tex]\sqrt[4]{25}^2[/tex]
= [tex]\sqrt[2]{25}[/tex]
= 5 cm²
and
h = 75 cm
[tex]$\mathrm{{\textstyle V={\dfrac {1}{3}} \times5 \times 75}}[/tex]
V = 125 cm³
Now it is given that [tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]
So,
[tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]
[tex]\mathrm{5^{\tfrac{x}{6}} = \sqrt[3]{5} }[/tex]
[tex]\mathrm{5^{\tfrac{x}{6}} = 5^{\tfrac{1}{3}} }[/tex]
[tex]\dfrac{x}{6} = \dfrac{1}{3}[/tex]
3x = 6
x = 6/3
x = 2
Thus, the value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].
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Housing prices in a particular county have increased by 29.5% over the price of houses five years ago.(a)If $260,000 was the average price of a house five years ago, what is the average price (in $) of a house today?(b)Economists predict that next year housing prices will drop by 5% in this area. Based on your answer from part (a), what will the average price (in $) of a house be next year?
a) The average price of a house today is $341,700.
b) The average price of a house next year is $325,865.
What is the average price?
The average price is a measure of the central tendency of a set of data points. It is defined as the sum of all the data points divided by the number of data points.
(a) To find the average price of a house today, we can use the formula:
New price = Original price x (1 + percentage increase)
New price = 260000 x (1 + 0.295) = 3417000
So, the average price of a house today is $341,700
(b) To find the average price of a house next year, we can use the formula:
New price = Original price x (1 - percentage decrease)
New price = 341700 x (1 - 0.05) = $325,865
So, the average price of a house next year is $325,865
Hence,
a) The average price of a house today is $341,700.
b) The average price of a house next year is $325,865.
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The gate code at your apartment complex is three numerical digits followed by the "#"sign. If each code
contains non-repeating digits, how many possible gate codes does your apartment complex have?
In given word problem the possibility for 3 non repeating digits followed by # sign is 720 ways.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here the gate code at your apartment complex is three numerical digits followed by the "#"sign.
There are 10 digits (0 to 9)
Compute the number of possible gate codes if each code contains non repeating digits as follows,
The first 3 place in the code must be filled by three non-repeating digits.
So, there are 10 possibility for first digit and 9 possibility for second digit and 8 possibility for third digit.
Hence the 3 non repeating digits can occur un 10×9×8 ways.
The three non repeating digit followed by #. Then sign # can occur in only way, then,
Total possibility = 10×9×8×1 = 720 ways.
Hence the possibility for 3 non repeating digits followed by # sign is 720 ways.
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the supplement of an angle is one third of the measure of the angle. find the angle and its supplement
As a result, the angle's measure is 135° and its supplement is 45°.
What is the supplement angle?Two angles are referred to as supplementary angles when the sum of their measures is 180 degrees.
For instance, 70 degrees and 110 degrees complement one another.
Two angles are said to be supplementary if their sums total 180 degrees.
A linear pair's two angles, are always supplementary.
Let x be the angle's measurement. If so, (180x) is the size of its supplementary angle.
Now, calculate:
180 - x = 1/3x
3(180 - x) = x
4x = 540
x = 135
Supplementary angle = 180 - 135 = 45°
Therefore, as a result, the angle's measure is 135° and its supplement is 45°.
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el) CC.11 Solve a system of equations using elimination: word problems 297
Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
The box office at a theater is selling tickets for a series of rock concerts. So far, they have
sold 79 balcony tickets and 27 general admission floor tickets for Friday's show, for a total of
$5,550 in receipts. For Saturday's show, 79 balcony tickets and 36 general admission floor
tickets have been sold, equaling $5,820 in receipts. How much does each ticket cost?
A balcony seat ticket costs $
, and a general admission floor ticket costs $
Submit
Work it out
Video
Answer:
balcony: $60general admission: $30Step-by-step explanation:
Given that 79 balcony and 27 general admission tickets sell for $5550, and 79 balcony and 36 general admission tickets sell for $5820, you want the cost of each kind of ticket.
EquationsThe equations representing the sales are ...
79b +27g = 5550
79b +36g = 5820
SolutionSubtracting the first equation from the second, we have ...
(79b +36g) -(79b +27g) = (5820) -(5550)
9g = 270 . . . . . . . . . simplify
g = 30 . . . . . . . divide by 9
79b +27(30) = 5550 . . . . . . substitute into the first equation
79b = 4740 . . . . . . . . . . subtract 810 & simplify
b = 60 . . . . . . . divide by 79
A balcony seat ticket costs $60; a general admission floor ticket costs $30.
Question 10
Here is a figure made of a circle inscribed in a square.
36 m
(a circle within
a square)
What is the area of the shaded region?
(You may round answer to a whole number)
The area of shaded region from the given figure is 278.64 when the diameter of the circle is 36m.
What is area of circle ?
area of circle can be defined as the product of pi and square of radius
and here the value of pi is 22/7 or 3.14
Given in the figure,
a circle is within square with diameter 36m .
So, we have to find the
area of a shaded region = area of square - area of circle .
radius = d/2
radius = 36/2
radius = 18 .
= 36*36 - 3.14 * 18*18
= 1296 - 1017.36
= 278.64
Hence, The area of shaded region from the given figure is 278.64 when the diameter of the circle is 36m.
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1) A philanthropist pledges to donate 20% of a fund each year. If the fund initially has $597,000.00, how much will the fund have after 6 years?
Answer:
$195,345.60
Step-by-step explanation:
We can calculate the amount of money remaining in the fund after 6 years by multiplying the initial amount by (1 - 0.2)^6. In this case,
(1 - 0.2)^6 = 0.32768
So the fund will have $597,000 * 0.32768 = $195,345.60 after 6 years.
A sheet of paper is cut into 3 same-size parts. Each of the parts is then cut into 3 same size parts and so on.
Answer:
wouldnt it just be 1/9
Step-by-step explanation:
We have one whole, ok. Then that is divided into 1/3 pieces. Then, each of those 1/3 pieces is split into thirds. Once here, think about each of the original 1/3 pieces as their own separate wholes.water is flowing into a tank at a rate of r(t) where t is measured in seconds. is there ever a time where the r'(t)
Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)
What is mean value theorem ?
The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].
The property of derivative : r'(t) is the rate of change of water flow.
Justification :
r(s) - r(4) = r'(3) (5-4)
- 5 = r(3)
In (4,5) , r(t) decreasing , so there are value of 3 and r'(3) > 0 , r'(3) = -5.
r(6) - r(5) = r'(3) (6-5)
4 = r'(3)
In (5,6), r(t) increasing , so there are values of 3 and r'(3) > 0, r'(3) = 4.
∴ Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)
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The complete question is :
Water is flowing into a tank at a rate of r(t) where t is measured in seconds. Is there ever a time where the r'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem.
