Answer:
There is a value of [tex]c[/tex] in (-1, 1), [tex]c = 0.577[/tex].
Step-by-step explanation:
Let [tex]f(x) = x^{3}+2\cdot x[/tex] for [tex]x \in[-1,1][/tex], we need to prove that [tex]f(x)[/tex] is continuous and differentiable to apply the Mean Value Theorem. Given that [tex]f(x)[/tex] is a polynomical function, its domain comprises all real numbers and therefore, function is continuous.
If [tex]f(x)[/tex] is differentiable, then [tex]f'(x)[/tex] exists for all value of [tex]x[/tex]. By definition of derivative, we obtain the following expression:
[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{(x+h)^{3}+2\cdot (x+h)-x^{3}-2\cdot x}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{x^{3}+3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot x+2\cdot h-x^{3}-2\cdot x}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} \frac{3\cdot x^{2}\cdot h+3\cdot x\cdot h^{2}+h^{3}+2\cdot h}{h}[/tex]
[tex]f'(x) = \lim_{h \to 0} 3\cdot x^{2}+ \lim_{h \to 0} 3\cdot x \cdot h+ \lim_{h \to 0} h^{2}+ \lim_{h \to 0} 2[/tex]
[tex]f'(x) = 3\cdot x^{2}+2[/tex] (Eq. 2)
The derivative of a cubic function is quadratic function, which is also a polynomic function. Hence, the function is differentiable at the given interval.
According to the Mean Value Theorem, the following relationship is fulfilled:
[tex]f'(c) = \frac{f(1)-f(-1)}{1-(-1)}[/tex] (Eq. 3)
If we know that [tex]f(-1) = -3[/tex], [tex]f(1) = 3[/tex] and [tex]f'(c) = 3\cdot c^{2}+2[/tex], then we expand the definition as follows:
[tex]3\cdot c^{2}+2 = 3[/tex]
[tex]3\cdot c^{2} = 1[/tex]
[tex]c = \sqrt{\frac{1}{3} }[/tex]
[tex]c \approx 0.577[/tex]
There is a value of [tex]c[/tex] in the interval (-1, 1), [tex]c = 0.577[/tex].
A large group of 77 people, consisting of students and adults, are going to a museum. An adult ticket costs $6.00 and a student ticket costs $4.00. The group's total ticket cost is $338.00. How many adults went on the trip to the museum? PLS HELP!!!! + extra points if answered
There are 155 adults went on the trip to the museum.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A large group of 77 people, consisting of students and adults, are going to a museum.
And, An adult ticket costs $6.00 and a student ticket costs $4.00. The group's total ticket cost is $338.00.
Now,
Let number of adults went on the trip to the museum = x
And, Number of students went on the trip to the museum = y
Here, A large group of 77 people, consisting of students and adults, are going to a museum.
Hence, We get;
⇒ x + y = 7
⇒ y = 7 - x .. (i)
And, An adult ticket costs $6.00 and a student ticket costs $4.00. The group's total ticket cost is $338.00.
Hence, We get;
⇒ 6x + 4y = 338 .. (ii)
From (i), we can put the value of y in (ii), we get;
⇒ 6x + 4y = 338
⇒ 6x + 4(7 - x) = 338
⇒ 6x + 28 - 4x = 338
⇒ 2x + 28 = 338
⇒ 2x = 338 - 28
⇒ 2x = 310
⇒ x = 310/2
⇒ x = 155
Thus, Number of adults went on the trip to the museum = 155
Learn more about the mathematical expression visit:
brainly.com/question/1859113
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HELP I WILL MARK BRAINLIEST
A property map is drawn at a scale of 1:1000. Calculate the corresponding actual distance if the distance between two points on the map is 1 cm
What is the equation of this graphed line? Enter your answer in slope-intercept form in the box. please i really need help
Answer:
y = -9/8x+7
Step-by-step explanation:
First Find The Slope: 7--2/0-8=-9/8
Find Y Intercept=7
Than Write Equation: y=-9/8x+7
Please help 25 points plus brainlyist
Match the mathematical phrases to the correct equations.
The product of a number and thirty-
point-six is the same as five-point-two.
k(30.6) = 5.2
Five-sixths more than a number
is twenty
x + 5/6 = 20
One-fourth of a number is forty.
1/4n = 40
Four-tenths minus two times a number
is eleven and two-tenths.
0.4-2m = 11.2
Answer:A to C, B to D,C to B, D to A
Step-by-step explanation:
right on edge,if confusing I could try to take a pic
Help me pleaseeeeeeeeee
Alexis paid $30 to activate her cellular phone plus $50 per month.Write and equation in y=mx+b.HELP PLS FAST
Answer:
y = 50x +30
Step-by-step explanation:
Answer:
y = 50x + 30
Step-by-step explanation:
When it says "per" it means you have to multiply x by that number (mx), when it says plus or something that doesn't include the word "per" it means that you just add it with the mx... or in other words, the addition part is (b).
A fast-food restaurant sold 54 burgers with cheese. If the ratio of burgers sold with cheese compared to without cheese was 9: 5, how many burgers did they sell total?
Answer:
Step-by-step explanation:
We can write an relationship for this as:
3
:
2
→
24
:
b
Where
b
is the number of burgers sold without cheese.
We can rewrite the relationship as an equation and solve for
b
:
3
2
=
24
b
2
3
=
b
24
24
×
2
3
=
24
×
b
24
48
3
=
24
×
b
24
16
=
b
b
=
16
The restaurant would of sold
16
burgers without cheese with the information provided in the problem.
Help please answer!this is on Zearn.org
Answer:
3/14 this is correct answer
Step by step explanation
3 over 14
The expression 7+3x+4 represents the perimeter of the triangle. Simplify the expression.
Answer:
The answer is 3x+11
Step-by-step explanation:
Just add 7 and 4.
You move left 3 units and down 2 units. You end at (0, -1). Where did you start?
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Suppose i started from ( x , y ) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
So ;
3 units left :
[tex]x - 3 = 0[/tex]
Add sides 3
[tex]x = 3[/tex]
_________________________________
2 units down :
[tex]y - 2 = - 1[/tex]
Add sides 2
[tex]y = 1[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Thus i started from ( 3 , 1 ) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
If you get it right I will give a brainlist
Answer:
Flour 5, 10, 15, 20
Sugar 4, 8, 12, 16
Step-by-step explanation:
Answer:
Flour (cups): 5 10 15 20
Sugar (cups): 4 8 12 16
You need 16 cups of sugar
22222222222222200000000
For those unaware of what this means
This is part of the thousands of reviews for a seafood place in China. Don't believe me? Look it up!
Write the equation of the line perpendicular to y = x+ 5 that passes through the point ( -7,3).
Type an equation using slope-intercept form or using the given point in point-slope form.
Answer:
y = - x - 4
Step-by-step explanation:
A line perpendicular to the line: y = x + 5
must have a slope that is the "opposite of the reciprocal" of the slope of the given line. Then the slope of the perpendicular line must be "-1".
Now that we know the slope of the perpendicular line, we use the point (-7, 3) to complete the equation of the line:
y = -1 x + b
3 = -1 (-7) + b
then we solve for "b":
3 = 7 + b
3 - 7 = b
b = -4
Now we can write the total equation of the perpendicular line in slope-intercept form as:
y = - x - 4
make x the subject
thank you
Answer:
[tex]x =\sqrt{\frac{a^6m}{b^2}+n}[/tex]
General Formulas and Concepts:
Order of Operations: BPEMDASEquality PropertiesExponent Power Rule: [tex](b^m)^n=b^{mn}[/tex]Step-by-step explanation:
Step 1: Define equation
[tex]a\sqrt{\frac{x^2-n}{m} } =\frac{a^2}{b}[/tex]
Step 2: Solve for x
Multiply a on both sides: [tex]\sqrt{\frac{x^2-n}{m} } =\frac{a^3}{b}[/tex]Square both sides: [tex]\frac{x^2-n}{m} =(\frac{a^3}{b})^2[/tex]Simplify: [tex]\frac{x^2-n}{m} =\frac{a^6}{b^2}[/tex]Multiply m on both sides: [tex]x^2-n =\frac{a^6}{b^2}m[/tex]Add n to both sides: [tex]x^2 =\frac{a^6}{b^2}m+n[/tex]Simplify: [tex]x^2 =\frac{a^6m}{b^2}+n[/tex]Square root both sides: [tex]x =\sqrt{\frac{a^6m}{b^2}+n}[/tex]Hilah's soccer team is trying to raise $2414 to travel to a tournament in Florida, so they decided to host a pancake breakfast. Each person must pay $34 for the breakfast. How many people need to attend their breakfast in order to raise $2414?
Answer:
Therefore we understand that exactly 71 people will have to attend breakfast in order to raise 2414 dollars.
Step-by-step explanation
We understand that we have to calculate the amount of people paying for breakfast so if 71 people each pay $34 we would get 2414
= 2414 ÷ 34 (This would give us 71 we get this straight away when we read the problem)
We can also fact check this by doing
= 34 x 71 (This gives us 2414)
Determine if The square root of 9 is rational or irrational and give a reason for your answer.
Answer:
As square root of 9 can be written in the required form for being a rational number, so it is a rational number
Step-by-step explanation:
First of all we'll define rational numbers.
A number that can be written in the form p/q where p and q are integers and q≠0 is called a rational number.
Now we have to check if [tex]\sqrt{9}[/tex] is rational or not, we will check if it can be written in the form p/q
[tex]\sqrt{9} => \frac{\sqrt{9}}{1} => \frac{3}{1}[/tex]
As square root of 9 can be written in the required form for being a rational number, so it is a rational number
If you answer I’ll give brainliest and points
(Question in photo!)
Answer:
c
Step-by-step explanation:
Answer:
KKKK
Step-by-step explanation:
Identify proportional realationships from graphs
Answer:
its yes
Step-by-step explanation:
Find the slope of the equation of the line that passes through the given points. through: (0, -3) and (3, 4)
Answer:
7/3
Step-by-step explanation:
The slope is found by dividing the difference in the y-coordinates by the difference in the x-coordinates.
Here, the difference in the y-coordinates is: 4 - (-3) = 4 + 3 = 7. The difference in the x-coordinates is: 3 - 0 = 3.
Dividing 7 by 3, we get a slope of 7/3.
The slope you are looking for is 7.
Enter the decimal equivalent of 9/12
Answer:
Hey! so its simple to find the decimal you need to divide so 12/9 is 1.33
Step-by-step explanation:
Hoped I helped please put me on brainliest oh and have a great day! ^-^
Mr. Grove cut down in tree in his yard. He gave 1/3 of the tree to his neighbor and 1/6 of the tree to his brother. Mr. Grove kept the remaining portion. How much tree did he keep?
A. 1/3
B. 2/3
C. 1/2
D. 5/6
Answer:
1/2 or C
Step-by-step explanation:
1/3 = 2/6. 2/6 + 1/6 = 3/6. that leaves 1/2 left over
What would the set notation for the domain and range of the function, (-3, 6), (-2, -3), and (-1, 6)
Answer:
Domain: {-3, -2, -1}
Range: {-3, 6}
General Formulas and Concepts:
Domain is the set of x-values that can be inputted into function f(x). Range is the set of y-values that are outputted by function f(x).Step-by-step explanation:
Step 1: Define
(-3, 6)
(-2, -3)
(-1, 6)
Step 2: Identify x-values
x = -3, -2, -1
Step 3: Identify y-values
y = -3, 6, 6
Hey, we are doing a review on fractions but I don't remember how to convert fractions do decimals.
Answer:
It's quite simple, for example, 1/2 would be the same as 50%, 1/3rd would be the same as 33.333333333%, and 1/4th would be the same as 25%
dived the numerator by the denominator.
3. $590 is deposited into a
savings account that earns
4.3 % simple interest for 3
years.
Answer:
615.37
Step-by-step explanation:
590 x 1.043
Hope I helped!
Help me please I don’t . Get so please give me the answer
Answer:
1953125
Step-by-step explanation:
Answer:
5⁹ =5⁴
5⁵
Step-by-step explanation:
this is my answer
The volume of a cylinder is 72 if the radius is 3 what is the height
Does ANYONE know how to solve this?
Answer:
yes make the triangle 2/3 the size it is right now most likely by dragging it inwards
Step-by-step explanation:
In Terrance county, 85% of eligible voters are registered to vote, and government records from a recent gubernatorial election indicate that 60% of registered voters actually voted in the election. If there are 21,800 eligible voters in Terrance County, how many people voted in the recent gubernatorial election?
Answer:
The Texas secretary of state’s office reported a tally of 9,669,246 votes for early voting Saturday morning, as some county data continued to trickle in. This year’s turnout for early voting alone exceeded the state’s entire turnout of 8,969,226 in 2016, when the state voted for Donald Trump with a margin of 9 percentage points.
In 2016, turnout for registered voters in Texas was 59.4%, lending credence to its reputation for low turnout. With current early voting totals, the state has already hit 57% turnout, and more than half of registered voters have voted in 128 of the state’s 254 counties. In 29 Texas counties, there was a 60% turnout or better.
Step-by-step explanation:
100 POINTS!!!!
⦁ Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by drawing line segments and . Then construct the perpendicular bisectors of and , and name the point of intersection of the perpendicular bisectors O. How do you know that point O is the center of the circle that passes through the three points? (10 points)
Answer:
O is the center of the circle with radius IE(=ID=EF)
Step-by-step explanation:
Join all 3 points D, E, F, forming the triangle DEF.
Let the midpoint of EF be M and the midpoint of ED be N. (first picture)
Join point I to E, D and F.
Since IN is both an altitude and median to triangle EID, then triangle EID is an isosceles triangle, and IE=ID
similarly, we see that IE=IF.
conclusion: IE=ID=EF.
Answer:
You know its the center of the circle because it is the intersecting point of the perpendicular bisectors of segment DE and EF.
Step-by-step explanation:
i just did it. im not sure if i am correct yet
Answer the question in the picture please!!
Answer:
Step-by-step explanation:
take the 142 degree angle and subtract it from 180 to find value of angle n, you will get 38. then you add 38 and 90 together to get 128. Since all angles of a triangle add up to 180. You subtract 128 from 180 to get 52.
Angle M = 52
Angle L = 90
Angle N = 38
Angle LNM = 180
