Question 2, please let me know if you have any questions regarding the materials, I'd be more than happy to help. Thanks!
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Mean Value Theorem
Supposing that f(x) is a continuous function that satisfies the conditions below:
0. f(x) ,is continuous in [a,b]
,1. f(x) ,is differentiable in (a,b)
Then there exists a number c, s.t. a < c < b and
[tex]f\mleft(b\mright)-f\left(a\right)=f‘\left(c\right)b-a[/tex]However, there is a special case called Rolle's theorem which states that any real-valued differentiable function that attains equal values at two distinct points, meaning f(a) = f(b), then there exists at least one c within a < c < b such that f'(c) = 0.
As in our case there is no R(t) that repeats or is equal to other R(t), then there is no time in which R'(t) = 0 between 0 < t < 8 based on the information given.
Answer: No because of the Mean Value Theorem and Rolle's Theorem (that is not met).
Related Questions
Hello I need help with the following question. 8. Use the given graph of the function f to find the domain and range(−6,6)8 The domain of f is(Type a compound inequality.)The range of f is(Type a compound inequality.)
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We are to use the given graph in the question to find the domain and range
From the graph,
The lowest value of x plotted is x = -14
The highest value of x plotted is x = 12
The loowest value of y is y= -4
The highest value of y is y = 6
Hence, the domain is
[tex]-14\leq x\leq12[/tex]While the range is
[tex]-4\leq y\leq6[/tex]I will give brainlist
The Busy Bee store bottles fresh jars of honey at a constant rate. In 2 hours, it bottles 18 jars, and in 6 hours, it bottles 54 jars of honey.
Determine the constant of proportionality.
9
18
0.11
4.5
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The constant of proportionality is A. 9.
What is a constant of proportionality?The constant of proportionality is simply used to show that the numbers given have a constant value.
From the information, the Busy Bee store bottles fresh jars of honey at a constant rate. In 2 hours, it bottles 18 jars. The constant will be:
= Number of jars / Number of hours
= 18/2
= 9
In 6 hours, it bottles 54 jars of honey. The constant will be:
= 54 / 6
= 9
Therefore, the constant is 9.
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What’s the correct answer answer asap for brainlist please
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Reason: medley is a mixture or assortment, not a verb as it’s used in this sentence
Solve T=C(8+AB) for A
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JUIVE Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by A(t) = 800e 0.86t. Find the rate of change of the quantity present at the time when t = 5. 9.3 grams per year 0 -72.7 grams per year -9.3 grams per year 0 72.7 grams per year
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
A(t) = 800e^(-0.86t)
Step 02:
Rate of change
t1 = 0
A(t) = 800e^(-0.86t)
A(t) = 800e^(-0.86*0)
A(0) = 800
t2 = 5
A(t) = 800e^(-0.86t)
A(t) = 800e^(-0.86*5)
A (t) = 800e^(-4.3)
A(5) = 10.85
Step 03:
[tex]\frac{\Delta y}{\Delta x}=\frac{A(5)\text{ - A(0)}}{5-0}[/tex][tex]\frac{\Delta y}{\Delta x}=\frac{10.85-800}{5-0}=\frac{-789.15}{5}=-157.83[/tex]3x+5=8(x-2)+1
Solve the following equation for x
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Answer: x=4
Step-by-step explanation:
1. 3x+5 = 8x-16+1
2. 3x+5 = 8x-15
3. 3x+20 = 8x
4. 20 = 5x
5. x = 4
i need help please,solve and explain it's 4th grade math.. thank you.
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What you can say about 12th, 18th and the 21st child, depends if these numbers are multiples of 4 (every 4th child is wearing spectacles), 3 (every 3rd child is a girl) and 2 (every 2nd child is wearing a white shirt).
If a numer is multiple of another one, then the quotient between them is an integer number.
for 12th:
12/4 = 3
12/3 = 4
12/2 = 6
12 is multiple of 3, 4 and 6.
Then, 12th child is wearing spectacles, a white shirt and is a girl.
for 18th:
18/4 = 4.5
18/3 = 6
18/2 = 9
18 is multiple of 3 and 2.
Then, 18th child is a girl and is weraing a white shirt
for 21th:
21/4 = 5.25
21/3 = 7
21/2 = 11.5
21 is multiple of 3.
THen, 21st child is a girl.
The graph shows the absolute value parent function. 6 Which statement is true? A. (0,1) is the x- and y-intercept of the function. B. (1,1) is the x- and y-intercept of the function. O C. (0,0) is the x- and y-intercept of the function. D. The function has no intercepts.
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From the graph;
(0,0) is the (x, y) intercept of the graph
since the function passes through (0,0)
help I'm practicing
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Remember that the volume of a rectangular pyramid is given by the expression:
[tex]v=\frac{1}{3}abh[/tex]Where:
• a ,and ,b ,are the lenght of the sides of the rcetangle (base)
,• h, is the height of the pyramid
Using this, and the data given, we'll get that:
[tex]\begin{gathered} v=\frac{1}{3}(14)(9.5)(15) \\ \Rightarrow v=665 \end{gathered}[/tex]The volume of the pyramid is 665 cubic feet
What is the vertex and intercept form for the equation y=x²-2x-3? What is the standard form and intercept form for the equation y-5= -2(x+1)?What is the vertex and standard form for the equation y= (x+2)(x-3)?
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Let's find the vertex for the following equation:
y = x² - 2x - 3
As you can see, we found graphically that (1, -4) is the vertex for this equation.
Now, let's find the intercept form, as follows:
x-intercept:
0 = -1² -2 * - 1 - 3
0 = 1 + 2 - 3
Then, (-1, 0)
0 = 3² - 2 * 3 - 3
0 = 9 - 6 - 3
Then (3, 0)
y-intercept:
yy
Give the sample space describing all the outcomes. Then give all of the out comes for the event that the number 3 chosen. Use the format H1 to mean that the coin toss is heads and the number chosen is 1. If there is more than one element in the set separate them with commas
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The sample space is composed of all the possible outcomes i.e. of all the possible combinations between the result of tossing the coin and picking the card. There are two possible outcomes for the coin and four for the cards so there will be 8 different combinations in the saple space. These are:
[tex]H1,H2,H3,H4,T1,T2,T3,T4[/tex]Then we must show all the outcomes where the card with the 3 is picked. This set is composed of all the elements with a 3 in the list above. There are two:
[tex]H3,T3[/tex]AnswersThen the answers are:
Sample space: {H1,H2,H3,H4,T1,T2,T3,T4}
Event that the number chosen is 3: {H3,T3}
Given the median QR and trapezoid MNOP, what is the value of X?M3.8033Rکد 73PA. 6B. 19(C. 2D, 5E 7F. Cannot be determined
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SOLUTION
Consider the diagram below
Applying the rule in the diagram above, we have
[tex]|QR|=\frac{1}{2}(|ON|+|PM|)[/tex]Recall from the questions
[tex]\begin{gathered} |QR|=33 \\ |ON|=3x-8 \\ |PM|=7x+4 \end{gathered}[/tex]Then we substitute the parameters above into the expression above
[tex]\begin{gathered} 33=\frac{1}{2}(3x-8+7x+4) \\ \text{ Multiply both sides by 2} \\ 66=3x-8+7x+4 \\ \text{rerrange the terms and simplify } \\ 66=10x-4 \\ \text{collect like terms } \\ 66+4=10x \end{gathered}[/tex]simplify further
[tex]\begin{gathered} 70=10x \\ \text{divide both sides by 10} \\ x=\frac{70}{10} \\ \text{then} \\ x=7 \end{gathered}[/tex]Therefore the value of x is 7
Therefore the right option is E
18. The table below gives the population of a town (in thousands) from the year 2000 to the year 2008. Year '00 '01 '02 03 04 '05 06 '07 '08 Population 87 84 83 80 77 76 78 81 85 (thousands) What was the average rate of change of population: a. between 2002 and 2004? b. between 2002 and 2006?
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a . Average rate of change between 2002 and 2004 can be calculated below
[tex]\begin{gathered} average\text{ rate of change=}\frac{chang\text{e in y}}{\text{change in x}} \\ average\text{ rate of change = }\frac{77-83}{2004-2002} \\ average\text{ rate of change}=\frac{-6}{2}=-3(thousand) \end{gathered}[/tex]b. Average rate of change between 2002 and 2006 is
[tex]\begin{gathered} \text{average rate of change = }\frac{78-83}{2006-2002} \\ average\text{ rate of change}=\frac{-5}{4}=-\frac{5}{4}(thousand) \end{gathered}[/tex]Ali took 3 1/4 hours to clean the bathroom. Then he took 1/8 hours to clean the kitchen. How much total time did Ali take to clean the two rooms?Write your answer as a mixed number in the simplest form.
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He took 3 1/4 hours to clean the bathroom and then he took 1/8 hours to clean the kitchen.
First, we can convert the mixed number 3 1/4 into a fraction:
3 1/4 = 3/1 + 1/4 = 13/4
Now, we can sum both times:
13/4 + 1/8 = ((13*8)+(4*1)) / (4*8) = (104 +4)/ 32 = 108/32 = 27/8
Finally, we need to convert the total of hours 27/8 as a mixed number:
If 27/8 = 3.375
We take the whole number and then convert the decimal remaining into a fraction:
3 - whole number
0.375* (1000/1000) = 3/8
Hence, the mixed number for the total time that Ali spent cleaning both rooms is 3 3/8
Which is closest to the circumference of the earth if it's diameter is 7926.41 miles?
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ANSWER
24901.55 miles
EXPLANATION
We have to find the circumference of the earth using the diameter given.
The formula for circumference is:
[tex]C=\pi\cdot D[/tex]where D = diameter
Therefore, the circumference is:
[tex]\begin{gathered} C=\pi\cdot7926.41 \\ C=24901.55\text{ miles} \end{gathered}[/tex]Please help.
A circle has a diameter of 18 inches. A central angle of 75° intercepts an arc of the circle. What is the intercepted arc length to the nearest tenth of an inch?
A.) 2.08 inches
B.) 3.8 inches
C.) 11.8 inches
D.) 23.6 inches
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Answer:
C.) 11.8 inches===========================
GivenA circle with diameter d = 18 in,Central angle θ = 75°.To findThe length of the given arcSolutionUse arc length formula:
s = πdθ/360Substitute the values and calculate:
s = 3.14 * 18 in * 75°/360° = 11.8 in (rounded)The matching answer choice is C.
The domain and ranger of a linear function is always all real numbers true or false ?
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Answer:
Step-by-step explanation:
The domain and range of a linear function is always real numbers (T or F)
It is True. This is because of a couple of reasons.
1.) You cannot divide by 0.
2. A negative number cannot have its square root taken.
The range is determined by the domain in a linear function, and thus it must always consist of real numbers.
1/b + 1/9 + = 1/tSolve for t
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The given expression is
[tex]\frac{1}{b}+\frac{1}{9}=\frac{1}{t}[/tex]First, we multiply the equation by t
[tex]\begin{gathered} (\frac{1}{b}+\frac{1}{9})\cdot t=\frac{1}{t}\cdot t \\ (\frac{1}{b}+\frac{1}{9})\cdot t=1 \end{gathered}[/tex]Now, we divide the equation by 1/b + 1/9
[tex]\begin{gathered} \frac{(\frac{1}{b}+\frac{1}{9})\cdot t}{(\frac{1}{b}+\frac{1}{9})}=\frac{1}{(\frac{1}{b}+\frac{1}{9})} \\ t=\frac{1}{(\frac{1}{b}+\frac{1}{9})} \end{gathered}[/tex]Now, we sum fractions
[tex]t=\frac{1}{\frac{9+b}{9b}}[/tex]Then, we solve this combined fraction
[tex]t=\frac{9b\cdot1}{9+b}=\frac{9b}{9+b}[/tex]Therefore, the final expression is
[tex]t=\frac{9b}{9+b}[/tex]write the slope-interference form of the equation of each line
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The slope interference form of straight line is given by
[tex]y=mx+c[/tex]Here is the slope of the line and c is the y-intercept
Now, from the graph, it is seen that the line passes through the points (0,4) and (3,5)
So,
[tex]\begin{gathered} \frac{y-4}{5-4}=\frac{x-0}{3-0} \\ \frac{y-4}{1}=\frac{x}{3} \\ 3(y-4)=x \\ 3y=x+12 \\ y=\frac{x}{3}+4 \end{gathered}[/tex]So, the required equation is
[tex]y=\frac{x}{3}+4[/tex]
Fill in the blank. In the triangle below, Z = 52° 35
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Solution
Since the diagram given is a Triangle, therefore, the sum of it's interior angles is 180 degrees
However, the Triangle is a right angle Triangle since on of its angles is 90 degrees.
The sum of its Interior angles is given by;
[tex]\begin{gathered} z+52+90=180 \\ \\ \Rightarrow z+142=180 \end{gathered}[/tex]subtracting 142 from both sides,
[tex]\begin{gathered} \Rightarrow z+142-142=180-142=38 \\ \\ \Rightarrow z=38^0 \end{gathered}[/tex]Therefore, z = 38
Mary is x years old. How old will she be in 10 years? How old was she 2 years ago?
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We know that Mary is x years old.
The age in 10 years will be x plus 10, as follows:
[tex]M_{\text{age}+10}=x+10[/tex]And the age she had two years ago was:
[tex]M_{\text{age}-2}=x-2[/tex]An example of this could be: imagine that Mary is 10 years now. In ten years, she will have:
10 + 10 = 20 years ( we add 10 to the original number). Likewise, 2 years ago, she had 10-2 = 8 years.
Therefore, the answers are two equations:
[tex]M_{age+10}=x+10[/tex][tex]M_{\text{age}-2}=x-2[/tex]Given that figure ABCD is a dilation of figure KLMN, find the missing values:(note that values are slightly different because of a round-off error)
Answers
• Given the dimensions of ABCD:
m∠A = 71.68 degrees
m∠C = 47.68 degrees
m∠D = 141.87 degrees
CD = 4
AD = 6
BC = 8
• Dimensions of KLMN:
m∠K = 71.52 degrees
m∠L = 98.87 degrees
m∠M = 47.53 degrees
KL = 10
KN = 15
MN = 10
Let's find the missing values.
Given that figure ABCD is a dilation of KLMN, both figures are similar.
• Similar figures have proportional corresponding sides.
,• Similar figures have equal corresponding angles.
Therefore, we have the corresponding sides:
AB ⇔ KL
BC ⇔ LM
CD ⇔ MN
AD ⇔ KN
The corresponding angles are:
m∠A = m∠K
m∠B = m∠L
m∠C = m∠M
m∠D = m∠N
Thus, to find the missing values, we have:
• X = m∠B = m∠L = 98.87 degrees
X = 98.87 degrees.
• Y = m∠N = m∠D = 141.87 degrees.
Y = 141.87 degrees
• To find the value of ,a,, apply the proportionality equation:
[tex]\frac{AB}{AD}=\frac{KL}{KN}[/tex]Plug in values and solve for a:
[tex]\begin{gathered} \frac{a}{6}=\frac{10}{15} \\ \\ \text{Cross multiply:} \\ 15a=10\times6 \\ \\ 15a=60 \\ \\ a=\frac{60}{15} \\ \\ a=4 \end{gathered}[/tex]• To find the value of ,b,, apply the proportionality equation:
[tex]\begin{gathered} \frac{DC}{BC}=\frac{NM}{LM} \\ \\ \frac{4}{8}=\frac{10}{b} \\ \\ \text{Cross multiply:} \\ 4b=10\times8 \\ \\ 4b=80 \\ \\ b=\frac{80}{4} \\ \\ b=20 \end{gathered}[/tex]ANSWER:
• X = 98.87°
,• Y = 141.87°
,• a = 4
,• b = 20
write in exponential form5x5x5
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5 x 5 x 5 = 5^3
[tex]\begin{gathered} \\ 5x5x5=5^{3\text{ }}\text{ = 125} \end{gathered}[/tex][tex]=16^{5\text{ }}\text{ = 16 x 16 x 16 x 16 x 16 = 1,048,576}[/tex]Finding a polynomial of a given degree with given zeros: Complex zeros
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Given:
• Degree of polynomial = 3
,• Zeros of the polynomial: 2, 3 - 2i
Let's find the polynomial.
Since the polynomail is of degree 3, it's highest exponent will be 3.
Equate the zeros to zero:
x = 2
Subtract 2 from both sides:
x - 2 = 2 - 2
x - 2 = 0
x = (3 - 2i)
Since this root is a complex conjugate, we have the other complex root: (3 + 2i)
Hence, we have:
(x - (3 - 2i)) and (x - (3 + 2i)).
Therefore, to write the function, we have:
[tex]f(x)=(x-2)(x-(3-2i))(x-(3+2i))[/tex]Now, simplify the expression:
[tex]\begin{gathered} f(x)=(x-2)(x-3+2i)(x-3-2i) \\ \\ f(x)=x(x-3+2i)-2(x-3+2i)(x-3-2i) \\ \\ f(x)=x^2-3x+2ix-2x+6-4i(x-3-2i) \\ \\ f(x)=x^2-5x+2ix-4i+6(x-3-2i) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} f(x)=x(x^2-5x+2ix-4i+6)-3(x^2-5x+2ix-4i+6)-2i(x^2-5x+2ix-4i+6) \\ \\ f(x)=x^3-5x^2+2ix^2-4ix+6x-3x^2+15x-6ix+12i-18-2ix^2+10ix-4i^2x-8-12i^{} \end{gathered}[/tex]Combine like terms:
[tex]\begin{gathered} f(x)=x^3-5x^2-3x^2-4ix-6ix+10ix+2ix^2-2ix^2+6x+15x+12i-12i-8-16 \\ \\ f(x)=x^3-8x^2+25x-26 \end{gathered}[/tex]ANSWER:
[tex]f(x)=x^3-8x^2+25x-26[/tex]An arts academy requires there to be 6 teachers for every 96 students and 3 tutors for every 30 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 100 students?
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If the school requieres 6 teachers for every 96 students then
1 teacher will be required for every
= 96/6
= 16 students
If 3 tutors for every 30 students then 1 tutor is required for
= 30/3
= 10 students
If the academy has 100 students, the number of tutors required would be
= 100/10
= 10 tutors
Hence
The academy requires;
Question 8 of 10If f(x) = - VX-3, complete the following statement (round your answerto the nearest hundredth):3x + 2f(7) = —Answer hereSUBMITplease help
Answers
To find f(7) substitute x by 7 in the function
Tanvir applies the distributive property to the left-hand side of the equation 1/3(3q+15)=101 Which equation shows the correct application of the distributive property?
1: q+15=101
2:3q+5=101
3:3q+15=101
4:q+5=101
Answers
When Tanvir applies the distributive property to the left-hand side of the equation, 1/3(3q+15)=101, the equation that shows the correct application is equation 4: q+5=101.
What is distributive property?The distributive property applies basic mathematical operations, especially in equations.
This property is that when a value is multiplied or divided by a number to a set that will be added or subtracted, the result is the same, notwithstanding if the operation is done before the addition or subtraction.
1/3(3q+15) = 101
(3q/3+15/3) = 101
= q + 5 = 101
q = 96
Check of Distributive Property:
1/3(3q+15) = 101
1/3(3 x 96+15) = 101
= 1 x 96 + 5 = 101
= 96 + 5 = 101
= 101 = 101
Or: 1/3(3q+15) = 101
1/3(3 x 96+15) = 101
= 1/3(288 + 15) = 101
= 1/3(303) = 101
= 101 = 101
Thus, the equation that correctly applies the distributive property is equation 4: q+5=101.
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If the carrier transmits 12 kW, what is the modulated power if modulation index is (1/√2) ?
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The modulated power is 15 kW.
The modulated power is given by the formula P_T= P_C (1+ (m_a^2)/2) and is connected to the total power of the carrier signal and the modulation index.
To obtain the modulated power, substitute the values in the given equation and simplify.
Given,
Power of carrier signal (P_C) = 12 kW
= 12000 W
Modulation index ( m_a) = 1/√2
Consequently, when we change the variables in the equation, we get
P_T= P_C (1+ (m_a^2)/2)
=12000 (1+ (1/√2)^2/2)
= 12000 (1+ 1/4)
= 12000 * 5/4
= 3000*5
= 15000 W
= 15 kW
Hence, modulated power is 15 kW.
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f(x) = x^2 g(x) = x^2 - 8 g(x)= x^2 - 8 We can think of g as a translated (shifted) version of f. Complete the description of the transformation. Use nonnegative numbers. To get the function g, shift f [up/down/left/right] by [ ] units.
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We have that the parent function (the original function is x^2). If we add a number after it as:
[tex]f(x)=x^2_{}+b[/tex]We affect the function in the y-axis, that is, we move the original function upward or downward.
Therefore, to get the function g, we need to shift the f function down by 8 units, that is
[tex]g(x)=f(x)-8=x^2-8[/tex]What’s the correct answer answer asap for brainlist
Answers
Answer:
Progressive Era
Step-by-step explanation: