Answer:
Yes, Rolle's theorem can be applied
There is only one value of c such that f'(c) = 0, and this is c = 1.5 (or 3/2 in fraction form)
Step-by-step explanation:
Yes, Rolle's theorem can be applied on this function because the function is continuous in the closed interval (it is a polynomial function) and differentiable in the open interval, and f(a) = f(b) given that:
[tex]f(0)=-0^2+3\,(0)=0\\f(3)=-3^2+3\,(3)=-9+9=0[/tex]
Then there must be a c in the open interval for which f'(c) =0
In order to find "c", we derive the function and evaluate it at "c", making the derivative equal zero, to solve for c:
[tex]f(x)=-x^2+3\,x\\f'(x)=-2\,x+3\\f'(c)=-2\,c+3\\0=-2\,c+3\\2\,c=3\\c=\frac{3}{2} =1.5[/tex]
There is a unique answer for c, and that is c = 1.5
Rolle's theorem is applicable if [tex]f(a)=f(b)[/tex] and $f$ is differentiable in $(a,b)$
since it's polynomial function, it's always continuous and differentiable..
and you can easily check that $f(0)=f(-3)=0$
so it is applicable.
now, $f'(x)=-2x+3=0 \implies x=\frac32$
there is only once value (as you can imagine, the graph will be downward parabola)
power sharing helps the ruling party to retain power for a long time. tick or wrong
Fill in the following blanks to prove that n 2^1 n < 2^n n+1 < 2^(n+1) is Box 3 Options: True | False Next, assume that Box 4 Options: 1 < 2^1 k + 1 < 2^(k+1) k < 2^k as we attempt to prove Box 5 Options: k < 2^k k + 1 < 2^(k+1) 2 < 2^1 Therefore, we can conclude that Box 6 Options: k < 2^k k + 1 < 2^(k+1) 2^1 < 2^k k + 2 < 2^(k+2)
Answer:
see below
Step-by-step explanation:
n < 2^n
First let n=1
1 < 2^1
1 <2 This is true
Next, assume that
(k) < 2^(k)
as we attempt to prove that
(k+1) < 2^(k+1)
.
.
.
Therefore we can conclude that
k+1 < 2^(k+1)
Answer:
Step-by-step explanation:
Hello, please consider the following.
First, assume that n equals [tex]\boxed{1}[/tex]. Therefore, [tex]\boxed{1<2^1}[/tex] is [tex]\boxed{\text{True}}[/tex]
Next, assume that [tex]\boxed{k<2^k}[/tex], as we attempt to prove [tex]\boxed{k+1<2^{k+1}}[/tex]
Since .... Therefore, we can conclude that [tex]\boxed{k+1<2^{k+1}}[/tex]
The choice for the last box is confusing. Based on your feedback, we can assume that we are still in the step 2 though.
And the last step which is not included in your question is the conclusion where we can say that we prove that for any integer [tex]n\geq 1[/tex], we have [tex]n<2^n[/tex].
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
How many solutions does the system have? x+2y=2 2x+4y=−8
Answer:
Step-by-step explanation:
x + 2y = 2
2x + 4y = -8
-2x - 4y = -4
2x + 4y = -8
0 not equal to -12
no solution
A local food bank uses volunteers to staff the kitchen. If there are 30 college students working there out of a total of 100 volunteers, what is the probability that in a sample of 10 volunteers, 4 of them are college students? Four decimal places please!
About 10% of 8900 commuters carpool to work. Find the number of commuters who carpool.
How many commuters carpool?
Answer: 890 commuters carpool
Step-by-step explanation:
10% of 8900 = 890
8900/10= 890
Note: 10% to decimal form is 10
Answer:
10% of 8900
10/100×8900
=890
hope this is helpful
17. In figure, BAC -859, CA = CB and BD - CD. Find the measure of ZX, Zy and Zz. Give
reasons to support your answer.
A
85°
ب
B
H
V
Answer:
x = 10°, y = 10° and z = 160°
Step-by-step explanation:
Given : m∠BAC = 85°
CA ≅ CB and BD ≅ CD
In the given ΔABC,
Since, CA ≅ CB
Angles opposite to these equal sides will be equal in measure.
m∠BAC ≅ m∠ABC ≅ 85°
Since, sum of interior angles of a triangle = 180°
m∠BAC + m∠ABC + m∠BCA = 180°
85° + 85° + m∠BCA = 180°
m∠BCA = 180° - 170°
m∠BCA = 10°
x = 10°
In ΔBDC,
Since, BD ≅ DC [Given]
Opposite angles to these equal sides will be equal in measure.
Therefore, x° = z° = 10°
Since, x° + y° + z° = 180°
10° + y° + 10° = 180°
y = 180 - 20°
y = 160°
6. Sam is buying tickets to a movie
online. The price of one ticket is $8.50.
An equation showing the total cost is
C = 8.50t +3.50 where t is the
number of tickets and $3.50 is a
convenience fee. What is the total cost
if he buys 4 tickets?
4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced? Answer: A= the cube with side length 6 cm, B= the cube with side length 8 cm, C= the cube with side length 10 cm, D= the cube with side length 12 cm. On one side of the scale : , on the other side of the scale
Answer: The cube with side length of 12cm is alone in one plate, the other 3 cubes are in the other plate.
Step-by-step explanation:
We have 4 cubes with side lengths of:
6cm, 8cm, 10cm and 12cm.
Now, some things you need to know:
If we want a scale to be balanced, then the mass in both plates must be the same.
The volume of a cube of side length L is:
V = L^3
And the mass of an object of density D, and volume V is:
M = D*V.
As all the cubes are of the same material, all of them have the same density, so the fact that we do not know the value of D actually does not matter here.
Then we want to forms two groups of cubes in such a way that the total volume in each plate is the same (or about the same), the volumes of the cubes are:
Cube of 6cm:
V = (6cm)^3 = 216cm^3
Cube of 8cm:
V = (8cm)^3 = 512cm^3
Cube of 10cm:
V = (10cm)^3 = 1000cm^3
cube of 12cm
V = (12cm)^3 = 1728cm^3
First, if we add the volumes of the first two cubes, we have:
V1 = 216cm^3 + 512cm^3 = 728cm^3
Now we can see that we add 1000cm^3 the volume will be equal to the volume of the larger cube, so here we can also add the cube with side length of 10cm
Then the volume of the 3 smaller cubes together is:
V1 = 216cm^3 + 512cm^3 + 1000cm^3 = 1728cm^3.
Then, if we want to have the same volume in each plate, then we need to have the 3 smaller cubes in one plate, and the larger cube in the other plate.
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find area of an older 35-inch television whose screen has an aspect ratio of 4:3
Greetings from Brasil...
The TV format is 4:3.
4 ÷ 3 = 1.33...
Let's assign the smallest side of the TV screen as X. Since the ratio between the sides is 4:3 = 1.33, then the other side (the largest) will be 1.33 times larger than the smaller side X, that is
smaller side = X
bigger side = 1.33X
The diagonal expression of the rectangle is:
D = √(base² + height²)
35" = √[(1.33X)² + X²]
35" = √(1.7689X² + X²) squaring both members
(35")² = 1.7689X² + X²
1225" = 2.7689X²
X² = 1225/2.7689
X² = 442.414
X = √442.414
X ≅ 21"
Tthe bigger side:
1.33X
1.33 · 21 ≅ 28"
Rectangle Area = base × height
Rectangle Area = 28 × 21
Rectangle Area = 588Find the value of x show your work
Answer:
x≈13.08
Step-by-step explanation:
We use the pythagora's theorem
[tex]a^{2} +b^2=c^2\\a=5\\b=x\\c=14\\5^2+x^2=14^2\\x^2=196-25\\x^2=171\\x=3\sqrt{19} =13.08[/tex]
A children's rectangular pool holds 480 cubic feet of water. What is the depth of the pool of its length is 30 feet and it's width is 16 feet
Answer:
1 ft
Step-by-step explanation:
1, 480/30=16
2, 16/16=1
3, 1 ft
opposite rays form a?
line
ray
point
plane
Answer:
ray is the answer for this
opposite rays form a line because they provide the two opposite directions in which the line extends infinitely.
Opposite rays form a what?Opposite rays are two rays that have the same endpoint but extend in opposite directions. When these opposite rays are extended infinitely in both directions, they form a straight line. A line is a set of points that extends infinitely in both directions, and opposite rays provide the two distinct directions in which the line can be extended.
The concept of opposite rays is derived from the concept of a line. A line can be defined as a straight path that extends infinitely in both directions. Opposite rays are a pair of rays that share a common endpoint and extend infinitely in opposite directions along this line.
For example, consider a line segment AB. If we extend one side of the line segment from point A and the other side from point B, we obtain two opposite rays: one from point A to infinity and the other from point B to infinity. Together, these opposite rays form the line on which the line segment AB lies.
Learn more about lines at:
https://brainly.com/question/24607467
#SPJ6
Use Lagrange multipliers to minimize the function subject to the following two constraints. Assume that x, y, and z are nonnegative. Question 18 options: a) 192 b) 384 c) 576 d) 128 e) 64
Complete Question
The complete question is shown on the first uploaded image
Answer:
Option C is the correct option
Step-by-step explanation:
From the question we are told that
The equation is [tex]f (x, y , z ) = x^2 +y^2 + z^2[/tex]
The constraint is [tex]P(x, y , z) = x + y + z - 24 = 0[/tex]
Now using Lagrange multipliers we have that
[tex]\lambda = \frac{ \delta f }{ \delta x } = 2 x[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta y } = y[/tex]
[tex]\lambda = \frac{ \delta f }{ \delta z } = 2 z[/tex]
=> [tex]x = \frac{ \lambda }{2}[/tex]
[tex]y = \frac{ \lambda }{2}[/tex]
[tex]z = \frac{ \lambda }{2}[/tex]
From the constraint we have
[tex]\frac{\lambda }{2} + \frac{\lambda }{2} + \frac{\lambda }{2} = 24[/tex]
=> [tex]\frac{3 \lambda }{2} = 24[/tex]
=> [tex]\lambda = 16[/tex]
substituting for x, y, z
=> x = 8
=> y = 8
=> z = 8
Hence
[tex]f (8, 8 , 8 ) = 8^2 +8^2 + 8^2[/tex]
[tex]f (8, 8 , 8 ) = 192[/tex]
A sports club was formed in the month of May last year. The function below, M(t), models the number of club members for the first 10 months, where t represents the number of months since the club was formed in May. m(t)=t^2-6t+28 What was the minimum number of members during the first 10 months the club was open? A. 19 B. 28 C. 25 D. 30
Answer:
A: 19
Step-by-step explanation:
For this, we can complete the square. We first look at the first 2 terms,
t^2 and -6t.
We know that [tex](t-3)^2[/tex] will include terms.
[tex](t-3)^2 = t^2 - 6t + 9[/tex]
But [tex](t-3)^2[/tex] will also add 9, so we can subtract 9. Putting this into the equation, we get:
[tex]m(t) = (t-3)^2 - 9 +28[/tex]
[tex]m(t) = (t-3)^2 +19[/tex]
Using the trivial inequality, which states that a square of a real number must be positive, we can say that in order to have the minimum number of members, we need to make (t-3) = 0. Luckily, 3 months is in our domain, which means that the minimum amount of members is 19.
You catch an expected number of 1.51.5 fish per hour. You can catch a fish at any instant of time. Which distribution best characterizes the number of fish you catch in one hour of fishing
Answer:
The distribution is Poisson distribution
Step-by-step explanation:
From the question we are told that
An expected number of fish was caught per hour is 1.5
The distribution that best characterize the number of fish you catch in one hour of fishing is the Poisson distribution
This because generally the Poisson distribution is a distribution that shows the number of times a given event will occur within a defined period of time
Find X using the Angle Sum Theorem
Answer:
Step-by-step explanation:
x + 30 + 25 = 180
x + 55 = 180
x = 125
y + 125 = 180
y = 55
When the scale factor is one what is the ratio of the side length of the side opposite angle a and the length of the hypotenuse
Answer:
me ajuda por favor matemática
PLS HELP! VERY URGENT PICTURE INCLUDED!!
Answer:
y = 6x ^2 - 6x + 9
Step-by-step explanation:
hopefully it's visible
:)
The highest mountain in earth is 29,028 ft. The lowest under sea trench is -35,840ft. Which has the highest absolute value
Answer:
undersea trench
Step-by-step explanation:
Absolute value is the distance from zero
The highest mountain trench is |29028| or 29028 ft from zero
The lowest under sea trench is | -35840| of 35840 ft from zero
The highest absolute value is the undersea trench
Height always be positive .
Highest mountain in earth=29028ftAbsolute value:-
[tex]\\ \sf\longmapsto |29028|=29028ft[/tex]
Lowest undersea trench=-35840ftAbsolute value:-
[tex]\\ \sf\longmapsto |-35840|=35840ft[/tex]
please solve it fastand give the correct answer pleaseeeeee
Answer:
a. False b. True c. True d. False e. False
Step-by-step explanation:
32 to 34 Directions: Given the following set of
numbers find the mean, median, and mode.
12, 13, 15, 15, 16, 19, 19, 19, 20, 21, 25
39.
32. Mean =
a. 17.64
b. 19
c. 15
40. 1
33. Median
a. 17.64
b. 19
c. 15
Answer:
32. A
33. B
Step-by-step explanation:
32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is
33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end
A recipe says to use 2/3 cup milk to make 4/5 serving of pudding. How many cups of milk are in one serving?
Answer:
[tex]\frac56[/tex] cups
Step-by-step explanation:
The serving size is proportional to the amount of milk used, so we have
[tex]\frac{2/3}{4/5}=\frac x1[/tex]
where [tex]x[/tex] is the amount of milk needed for 1 serving. The right side is simply [tex]x[/tex]. We now simplify
[tex]x=\frac23\cdot\frac54=\frac{10}{12}=\frac56[/tex]
Therefore [tex]\frac56[/tex] cups of milk are needed for 1 serving.
Select the graph of the solution. Click until the correct graph appears.
Answer:
convert the 27 degree into grades
Determine the coordinates of the ordered pairs on the coordinate grid.
Answer:
A = (5,7)
B = (0, -1)
C = (-8, -3)
D = (5, -8)
Step-by-step explanation:
Answer:
A = (5, 7)
B = (0, -1)
C = (-8, -3)
D = (5, -8)
To do these problems, trace along in a straight line from the coordinate to the x- axis line and then to the y-axis line. Whatever number you reach will be part of the coordinate.
Hope this helped.
The equation| x + 4| = x has solution a. X = -2 b. X = 2 c. X = -4 d. X = 4
Answer:
B) 2
/////////////////
What is the measure of m?
Answer:
√245
Step-by-step explanation:
altitude on hypotenuse theorem:
m^2=7*35
m^2=245
m=√245
Tickets to a local movie were sold at $6.00 for adults and $4.50 for students. If 390 tickets were sold for a total of $2190.00, how many student tickets were sold
Answer: Therefore 100 student tickets were sold
Step-by-step explanation:
Let the number of student tickets be x
So adult tickets = 390 - x
ATQ
4.5(x) + 6(390-x) = 2190
4.5x + 2340 - 6x = 2190
-1.5x + 2340 = 2190
-1.5x = 2190-2340
-1.5x = -150
x = -150/-1.5
x = 100
Therefore 100 student tickets were sold
please click thanks and mark brainliest if you like :)
Which term best describes a figure formed by three segments connecting three non Collin ear points
Answer:
Triangle
Step-by-step explanation:
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
Find:P(large or blue)
Answer:
7/10
Step-by-step explanation:
Total number = 17+3+8+12 = 40
The ones that are large are 17 and 8
The ones that are blue are 17 and 3
Do not count the 17 twice
P(large or blue) = (17+3+8)/40
= 28/40
=7/10