Determine the location and values of the absolute maximum and absolute minimum for given function : f(x)=(‐x+2)4,where 0<×<3
Answer:
Where 0 < x < 3
The location of the local minimum, is (2, 0)
The location of the local maximum is at (0, 16)
Step-by-step explanation:
The given function is f(x) = (x + 2)⁴
The range of the minimum = 0 < x < 3
At a local minimum/maximum values, we have;
[tex]f'(x) = \dfrac{(-x + 2)^4}{dx} = -4 \cdot (-x + 2)^3 = 0[/tex]
∴ (-x + 2)³ = 0
x = 2
[tex]f''(x) = \dfrac{ -4 \cdot (-x + 2)^3}{dx} = -12 \cdot (-x + 2)^2[/tex]
When x = 2, f''(2) = -12×(-2 + 2)² = 0 which gives a local minimum at x = 2
We have, f(2) = (-2 + 2)⁴ = 0
The location of the local minimum, is (2, 0)
Given that the minimum of the function is at x = 2, and the function is (-x + 2)⁴, the absolute local maximum will be at the maximum value of (-x + 2) for 0 < x < 3
When x = 0, -x + 2 = 0 + 2 = 2
Similarly, we have;
-x + 2 = 1, when x = 1
-x + 2 = 0, when x = 2
-x + 2 = -1, when x = 3
Therefore, the maximum value of -x + 2, is at x = 0 and the maximum value of the function where 0 < x < 3, is (0 + 2)⁴ = 16
The location of the local maximum is at (0, 16).
In the matrix below, what is the value of f32?
2
21
9
1
0
5
T-
16
8
4
0
32
7
Answer:
ans: 8
Step-by-step explanation:
t3×2 mean see the term in 3rd row and second column,
The value of the f 32 in the given matrix is 8.
What is matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
For example, is a matrix with two rows and three columns.
Given is a matrix of order 3x4, we need to find the object in f 32,
So, f 32
This means the entry in Row 3 Column 2
From the matrix we can see that f 32 = 8
Hence, the value of the f 32 in the given matrix is 8.
Learn more about matrix, click;
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Kofi paid rent of GH¢ 1,800.00 each year. If the rent is 0.3 of his annual income, find his annual income
Answer:
To find = his annual income
solution = annual income be = x
0.3 of x = 1,800
= 0.3x = 1, 800
= x = 6, 000
Annual income of GH¢ is = 6 , 000
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
Please help!
The table shows the game scores of five players. Andy’s brother, Kevin, also plays and gets a score of 9. Find the mean, median, and mode of the data in the table. Then, find the mean, median, and mode of the data in the table and Kevin’s score.
Answer:
The third one
Step-by-step explanation:
Median - Middle number in terms of value
Mode - outcome that appears the most
Mean - average ( add the numbers together and divide that by the amount of numbers )
Data without Kevins score
13, 21, 28, 9, 31
First let's find the mean
To find the mean we simply add the numbers up and divide that by the total amount of numbers ( there are 5 numbers )
13 + 21 + 28 + 9 + 31 = 102
102/5=20.4
So the mean without Kevins score is 20.4
Next let's find the mode
The mode is the number that appears the most
Looking at the data no number appears more than once so there is no mode
Finally let's find the median.
To make it easier to find let's list the numbers in order from least to greatest
9, 13 , 21 , 28, 31
We then go to the middle number ( which would be 21 )
The mode is 21
So for data without Kevins score the mean would be 20.4, the median would be 21 and the mode would be none
Now let's add in Kevin's score and repeat this process
Data with Kevin's score
13, 21, 28, 9, 31, 9
First let's find the mean
( Note that there is 6 numbers this time )
13 + 21 + 28 + 9 + 31 + 9 = 111
111/6 = 18.5
So mean with Kevin's score = 18.5
Next let's find the mode
The number 9 appears the most so the mode is 9
Finally let's find the mean
Once again let's list the numbers from least to greatest
9, 9, 13 , 21 , 28, 31
Because there is an even amount of numbers we will take the sum of the two middle numbers and divide that by 2
The two middle numbers would be 21 and 13
21 + 13 = 34
34/2=17
So median = 17
In the end we get the following
Without Kevins score
Mean = 20.4
Median = 21
Mode = none
With Kevin's score
Mean = 18.5
Median = 17
Mode = 9
This information corresponds with the third table
It costs £420 for six tickets how much would 5 tickets be
1. Harsha makes a scale drawing of a window. She uses the scale 1cm represents 20cm.
A).on her drawing the window is 6cm wide. How wide is the window in real life?
B).The window in real life is 2.2m high. How high is the window on the scale drawing?
Give your answer in centimeters.
Part (A)
(1 cm)/(20 cm) = (6 cm)/(x cm)
1/20 = 6/x
1*x = 20*6
x = 120
120 cm = 120/100 = 1.2 m
Answer: 1.2 m=========================================================
Part (B)
2.2 m = 2.2*100 = 220 cm
(1 cm)/(20 cm) = (x cm)/(220 cm)
1/20 = x/220
1*220 = 20*x
20x = 220
x = 220/20
x = 11
Answer: 11 cmGiven the system of equations.
{-4x+y = 3
{2x - y = 12
Which of the options represents the resulting equation after an equivalent expression for y ls substituted into the
second equation.
2x - (4 X+3) = 12
-4(4y+)+y=3
2 (4x+3) - y
-4x+4 x-3=3
Answer:
A. 2x - (4x + 3) = 12
Step-by-step explanation:
A. 2x - (4x + 3) = 12
B. -4(4y+)+y=3
C. 2 (4x+3) - y
D. -4x+4 x-3=3
Given equation:
-4x+y = 3. (1)
2x - y = 12. (2)
From (1)
y = 3 + 4x
Substitute y = 3 + 4x into (2)
2x - y = 12 (2)
2x - (3 + 4x) = 12
Or
2x - (4x + 3) = 12
2x - 4x - 3 = 12
- 2x = 12 + 3
- 2x = 15
x = 15/-2
x = -7.5
Substitute x = -7.5 into (1)
-4x+y = 3 (1)
-4(-7.5) + y = 3
30 + y = 3
y = 3 - 30
y = -27
I need help asap!!!! 13 points
If IK is the whole length of the line segment, then IJ + JK = IK.
IJ + JK = IK
(3x - 5) + (2x - 1) = (3x + 2)
3x + 2x - 5 - 1 = 3x + 2
5x - 6 = 3x + 2
2x - 6 = 2
2x = 8
x = 4
Now that we know the value of x, we can plug this value back into the expression for JK and evaluate.
JK = 2x - 1
JK = 2(4) - 1
JK = 8 - 1
JK = 7
Hope this helps!
t has a value of 5/2. p is the sum of t and v, and p has a value of 0. What is the value of v?
Answer:
Step-by-step explanation:
If p = t + v and t is 5/2 and p is 0, then
0 = 5/2 + v and
v = -5/2
the mean age of 8 people is 16 years. when mrs. hernandez's age is included, the mean age increases to 20. how old is mrs. hernandez?
Answer:
52
Step-by-step explanation:
8*16 = 128
8*20 = 180
180-128 =52
I honestly am so confused right now , pleas help
Answer:
never really liked accounting, but...
The Assets seem to total $33000
and the Liabilities also seem to add to $33000
that seems to be what is supposed to happen in an accounting problem
Step-by-step explanation:
The graph shows the function f(x) = 2*.
What is the value of x when f(x) = 8?
a ) 0
b) 3
c) 1
d) 2
Answer:
3
Step-by-step explanation:
you can see this on the graph; just find 8 on the y axis and look for the value of x that corresponds to it
This is for Algebra 2 please someone help T^T
Answer:
-(a)^2 + a - 11
Step-by-step explanation:
N - T = -3(a)^2 + 2a - 5 - (-2(a)^2 + a + 6)
= -3(a)^2 + 2a - 5 +2(a)^2 - a - 6
= -3(a)^2 + 2(a)^2 + 2a - a - 6 -5
= -(a)^2 + a - 11
Evaluate.
3·(7-3)²=?
Please help I’ll give brainliest
For this question, we will need to know that when we divide two numbers with the same base but different exponents, we must subtract the exponents.
[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]
Solving the Question[tex]\dfrac{9^5}{9^3}[/tex]
Subtract the exponents:
[tex]9^2[/tex]
Answer[tex]9^2[/tex]
find the measure of the missing angle (#4 btw)
Answer:
Step-by-step explanation:
1)
∠1 = ∠2 {Angles opposite to equal angles are equal}
∠1 = ∠2 = x
x +x + 55 = 180 {angle sum property of triangle}
2x + 55 = 180
2x = 180 - 55
2x = 125
x = 125/2
x = 62.5
∠1 = 62.5
2) ∠2 = 62.5
3) ∠3 = 55 {Vertically opposite angles are congruent}
4) ∠4 + 105 = 180 {linear pair}
∠4 = 180 - 105
∠4 = 75
5) ∠3 + ∠4 + ∠5 = 180 {Angle sum property of triangle}
55 + 75 +∠5 = 180
130 + ∠5 = 180
∠5 = 180 - 130
∠5 = 50
Nishi invests £4700 at 6% interest per year. Work out how much she will have altogether after: 2 years- £ 5 years- £ 7 years- £ 10 years- £
Answer:
Step-by-step explanation:
To calculate the compound interest we want to multiply the amount of money (£4700) by the interest (6%) which would be the percentage multiplier!
To get the new amount we do:
Original amount × (percentage multiplier)ⁿ
The amount of years would be the indices.
For the first year:
£4700x1.06= £4982.
But we want to find out how much she will have altogether in different years.
So for two years:
£4700x1.03²= £5280.90 (rounded)
As you can see the amount of years will be the indices with the interest as our multiplier.
We do this again for 5 years and 10 years:
£4700x1.06⁵= £6289.70 (rounded)
£4700x1.06¹⁰=£8416.20 (rounded)
Hope this helps!
20 points for this make sure u explain
Answer:
it literally says +10
Step-by-step explanation:
scammer
Answer:
Step-by-step explanation:
6,7,8
4
On Monday, Lucy had
$40.00. She spent $12.00
on lunch on Tuesday. On
Wednesday, Lucy's mother
found $6.90 in change and
gave half of the money to
Lucy. How much money
does Lucy have now?
Answer:
40-12=28
28+3.45=31.45
so now lucy has 31.45
Your Welcome
BIFFY OUT!!!
Pls help with step by step :)
Answer:
Step-by-step explanation:
Hope this helps u !!
A water tank has a dimension 3 m long, 1.8 m wide and 2.2 m
high. It has a capacity of:
Answer:
The answer is 11.8 m
Step-by-step explanation:
Hey Mate,
the volume of a cuboid is = whl....so the volume of it is the capacity of the tank
so 3 x 1.8 x 2.2 = 11.88 m is the answer
Using the equality of surds theorem, solve this question
In the question solve for a and b
Step-by-step explanation:
76.72135955 is the answer I think So if the answer is correct then plz mark me as brainliest
On Monday the temperature was 12°C. On Tuesday it decreased by 12°C. Which expression can be used to represent this situation?
What method would I use? I am confused on how to solve it. [tex]9k^2+3=-20[/tex]
What is the solution to the system of equations?
One-fourth x minus one-half y = 8
One-half x + three-fourths y = negative 5
(–8, –12)
(–8, 12)
(8, 12)
(8, –12)
Answer:
(8 - 12 )
Step-by-step explanation:
Given
[tex]\frac{1}{4}[/tex] x - [tex]\frac{1}{2}[/tex] y = 8
[tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{4}[/tex] y = - 5
Multiply both equations through by 4 to clear the fractions
x - 2y = 32 → (1)
2x + 3y = - 20 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate the x- term
- 2x + 4y = - 64 → (3)
Add (2) and (3) term by term to eliminate x
0 + 7y = - 84
7y = - 84 ( divide both sides by 7 )
y = - 12
Substitute y = - 12 into either of the 2 equations and solve for x
Substituting into (1)
x - 2(- 12) = 32
x + 24 = 32 ( subtract 24 from both sides )
x = 8
solution is (8, - 12 )
Answer:D:(8,-12)
Step-by-step explanation:took a test:D
she does 3 sets of 8 pushups 7 days a week, how many pushups does she do in one week
Answer:
24 push ups3 x 8 = 24ksjsjsowjsnsoajjsodhew
??? What’s the answer
let's calculate the front face area and then multiply by 8cm to get the volume
18cm*24cm / 2 *8cm
= 1728cm³
Kendra bought a gallon of milk and StartFraction 5 over 6 EndFraction of a pound of oranges. If the gallon of milk cost $3.60 and she spent a total of $4.35, which equation can be used to determine x, the cost of a pound of oranges?
3.60 + StartFraction 5 over 6 EndFraction x = 4.35
4.35 + StartFraction 5 over 6 EndFraction x = 3.60
3.60 x + StartFraction 5 over 6 EndFraction = 4.35
4.35 x + StartFraction 5 over 6 EndFraction = 3.60
Answer:
A. 3.60+5/6x=4.35
Step-by-step explanation:
Total cost = milk + price per pound of oranges* number of pounds
We know the total cost = 4.35 and the cost of the milk = 3.60 and the number of pounds of oranges = 5/6
4.35 = 3.6 +5/6 * x
Answer:
a
Step-by-step explanation:
(x+4)+(x-3)+(2x+2)+(x^2+3x+1)
Answer:
X^2+7x+4
Step-by-step explanation:
4x-10+1.5x-4x+11=8.5-6
Answer:
x=1
Step-by-step explanation:
4x-10+1.5x-4x+11=8.5-6
Combine like terms
1.5x+1=2.5
Subtract 1 from each side
1.5x+1-1=2.5-1
1.5x = 1.5
Divide by 1.5
1.5x/1.5 = 1.5/1.5
x=1
Answer:
x=1
Step-by-step explanation:
Given :
4x-10+1.5x-4x+11=8.5-6
4x+1.5x-4x=8.5-6-11+10
1.5x=1.5
x=1
Value of x=1