The local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.
For given question,
We have been given a function f(x) = 6 + 9x² - 6x³
We need to find the local maximum and local minimum of the function f(x)
First we find the first derivative of the function.
⇒ f'(x) = 0 + 18x - 18x²
⇒ f'(x) = - 18x² + 18x
Putting the first derivative of the function equal to zero, we get
⇒ f'(x) = 0
⇒ - 18x² + 18x = 0
⇒ 18(-x² + x) = 0
⇒ x (-x + 1) = 0
⇒ x = 0 or -x + 1 = 0
⇒ x = 0 or x = 1
Now we find the second derivative of the function.
⇒ f"(x) = - 36x + 18
At x = 0 the value of second derivative of function f(x),
⇒ f"(0) = - 36(0) + 18
⇒ f"(0) = 0 + 18
⇒ f"(0) = 18
Here, at x=0, f"(x) > 0
This means, the function f(x) has the local minimum value at x = 0, which is given by
⇒ f(0) = 6 + 9(0)² - 6(0)³
⇒ f(0) = 6 + 0 - 0
⇒ f(0) = 6
At x = 1 the value of second derivative of function f(x),
⇒ f"(1) = - 36(1) + 18
⇒ f"(1) = - 18
Here, at x = 1, f"(x) < 0
This means, the function f(x) has the local maximum value at x = 1, which is given by
⇒ f(1) = 6 + 9(1)² - 6(1)³
⇒ f(1) = 6 + 9 - 6
⇒ f(1) = 9
So, the function f(x) = 6 + 9x² - 6x³ has local minimum at x = 0 and local maximum at x = 1.
Therefore, the local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.
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an irrational number is one that simply can not be worked into any equation.
true or false
Answer:
it can be use in equation
An irrational number is a number that cannot be expressed as a fraction for any integers and. . Irrational numbers have decimal expansions that neither terminate nor become periodic.
Why is APR an important tool for consumers?
a. It allows consumers to borrow from more than one lender at the same time.
b. It allows consumers to compare the full cost of loans from different lenders.
c. It allows consumers to choose their level of down payment.
d. It provides an opportunity for consumers to become familiar with various interest calculators.
e. It provides consumers with negotiating skills to get lenders to reduce rates.
The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.
According to the statement
we have to explain all about the APR and tel that why it is important for the consumers.
So, For this purpose,
We know that the
The term annual percentage rate of charge, corresponding sometimes to a nominal APR and sometimes to an effective APR.
It is the interest rate for a whole year, applied on the loan etc. It is a finance charge expressed as an annual rate
APR is the important tool for the consumers because of some reasons which are written below:
APR is important because it can give you a good idea of how much you'll pay to take out a loan.
APR helps a customer determine the true cost of the loan, allowing them to compare many loans and choose the most advantageous one.
So, The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.
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The SkyWheel has a diameter of 183 feet. What is the radius? (don't round and just write the numerical answer, no units)
Answer:
The answer is
→ 91.5 feet
Step-by-step explanation:
Given:
183 feet
What were supposed to find:
The radius of the SkyWheel
Solve:183 / 2 = 91.5
How to find the radius:
To find the radius, you must divide 183 with 2, giving 91.5
Hence, the answer you are looking for is 91.5
- ✨7272033Alt✨When one organism gains a benefit at the expense of a second organism and causes them harm is called:
A. patasitism
B. Mutualism
C. Commensalism
D. Predation
When one organism gains a benefit at the expense of a second organism and causes them harm is called:
A. Parasitism
B. Mutualism
C. Commensalism
D. Predation
Answer:
Step-by-step explanation:
a
What bearing and airspeed are required for a plane to fly 500 miles due north in 2. 5 hours if the wind is blowing from a direction of 344° at 10 mph?
Answer:
The airspeed is 201.17 mph and bearing is and this can be determined by using the vector form of velocity
Plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 mph
Please help me with algebra 2 questions!
Answer:
5B; 7B; 1,024; see answer
Step-by-step explanation:
5.
We can see from the table that
a1 = 5
a2= 5·2 = 10
a3= 5·2·2 = 5·2² = 20
a4 = 5·2·2·2 = 5·2³ = 40
...
[tex]a_{n} = 5*2^{n-1}[/tex]
7.
Is given that the filter removes 90% of contaminated air
after run 1 :
100% air
90% contamination removed for 100% air
100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%
10% is still contaminated air
after run 2:
10% air
90% contamination removed for 10% air
10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%
1% is still contaminated air
after run 3:
1% air
90% contamination removed for 1% air
1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%
.1% is still contaminated air
11.
Figure 1 = 1 piece
Figure 2 = 4 pieces
Figure 3 = 4² = 16
...
[tex]Figure 6 = 4^{(6-1)} = 4^{5} = 1024[/tex]
12.
[tex](c+d)^{6} \\[/tex]
-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1
-we start with c to the lowest power 0 and d to the highest power 6 and end with d to the lowest power 0 and c to the highest power 6
[tex](c+d)^{6} = 1*c^{0} d^{6} +6*c^{1} d^{5} +15*c^{2} d^{4} +20*c^{3} d^{3} +15*c^{4} d^{2} +6*c^{5} d^{1} +1*c^{6} d^{0}[/tex]
-we simplify to have the final answer:
[tex](c+d)^{6 } = d^{6} +6cd^{5} +15c^{2} d^{4} +20c^{3} d^{3} +15c^{4} d^{2} +6c^{5} d+c^{6}[/tex]
Please help with this question!
Answer:
NONE of these statements are true
[tex] \frac{d}{dx} (f(x).g(x)) = f'(x).g(x) + g'(x).f(x)[/tex]
b) False[tex] \frac{d}{dx} ( \sqrt{x {}^{2} + x} ) {}^{2} = \frac{2x + 1}{2 (\sqrt{x {}^{2} + x}) {}^{2} } = \frac{2(2x + 1)(x {}^{2} + x) }{2|x²+x|} = \frac{(2x + 1)(x { }^{2} +x)}{|x²+x|} [/tex]
Im assuming this is an absolute valuec) True[tex] \frac{d}{dx} ( \sqrt{f(x)} ) = \frac{f'(x)}{2 \sqrt{f(x)} } [/tex]
Option CFind the midpoint of PM=
Help me please thanks :)
Answer:
Midpoints are (-1/2 , - 3)
Step-by-step explanation:
Given P (-4, - 2) and Q (3, - 4)
[tex]x1 = - 4 \\ x2 = 3 \\ y1 = - 2 \\ y2 = - 4[/tex]
[tex]midpoints = (\frac{x1 + x2}{2})( \frac{y1 + y2}{2}) \\ = ( \frac{ - 4 + 3}{2})( \frac{ - 2 + ( - 4)}{2}) \\ = ( \frac{ - 1}{2})( \frac{ - 2 - 4}{2}) \\ = ( \frac{ - 1}{2})( \frac{ - 6}{2}) \\ = ( \frac{ - 1}{2})( - 3)[/tex]
Which table represents a linear function?
The table shows the number of grapes eaten over several minutes.
What is the rate of change for the function on the table?
15 grapes eaten per minute
15 minutes to eat each grape
60 grapes eaten per minute
60 minutes to eat each grape
The rate of change for the function on the table is; 15 grapes eaten per minute.
What is the rate of change of the function described by the table?It follows from the complete question that the table given indicates that;
after 1min, 15 grapes had been eaten, after the next minute, 30 grapes had eaten, after the 3rd minute, 45 grapes had already been eaten.On this note, it is conclusive that the rate of change of the function represented by the table is; 15 grapes eaten per minute.
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help help help help me please
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]-4\leq x[/tex] is what it looks like simplifed. In word form this means x is greater than all values equal to or greater than four. This means that the FOURTH graph is correct.
Step-by-step explanation:
[tex]13-2x\leq 37+4x = -24\leq 6x.[/tex]
Simplify this into [tex]-4\leq x[/tex] or [tex]x\geq -4[/tex]
This in words translates into x is greater than or equal to the value of four. Meaning all values larger than 4 and 4 are equal to x
Meaning the 4th graph is correct because it shows exactly what the word form says.
-------------------------
Have a great day,
Nish
12 in.
14 in.
14 in.
Find the area of the figure above.
[?] square inches please explain how you got the answer for future questions
Answer:
168 square inches
Step-by-step explanation:
A = BH
or
Area = Base x Height
In other words multiply 12 and 14.
jean loads a ream of paper 500 sheets into the tray of her photocopier she has 23 sheets and need 20 copies each sheet how many sheets of paper remain unused
The answer is 40
you just times 23 by the number of photocopies you need with is 20
so 23x20 which is 460
500-460 is 40
The number of sheets of papers remain unused are 40.
Given that, Jean loads a ream of paper 500 sheets into the tray of her photocopier she has 23 sheets and need 20 copies each sheet.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Number of sheets used = 23×20
= 460
Remaining sheets = 500-460
= 40
Therefore, the number of sheets of papers remain unused are 40.
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20 points !!!
help me please !!
Minimum: 59
Lower Quartile: 67
Median: 76
Upper Quartile: 86
Maximum: 92
Interquartile Range: 19
-2x + 7x +34 = -2(1-7x)
[tex]\boldsymbol{\sf{-2x + 7x +34 = -2(1-7x) \ \ \longmapsto \ \ [Add \ -2x+7x]}}[/tex]
[tex]\boldsymbol{\sf{5x+34=-2(1-7x)}}[/tex]
Use the distributive property to multiply −2 by 1−7x.
[tex]\boldsymbol{\sf{5x+34=-2+14x}}[/tex]
Subtract 14x on both sides.
[tex]\boldsymbol{\sf{5x+34-14x=-2}}[/tex]
Combine 5x and −14x to get −9x.
[tex]\boldsymbol{\sf{-9x+34=-2 }}[/tex]
Subtract 34 from both sides.
[tex]\boldsymbol{\sf{-9x=-2-34 \ \ \longmapsto \ \ \ [Subtract] }}[/tex]
[tex]\boldsymbol{\sf{-9x=-36}}[/tex]
Divide both sides by −9.
[tex]\boldsymbol{\sf{x=\dfrac{-36}{-9} \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ x=4 }}}}}[/tex]
[tex] \quad\quad\quad \huge \underline{ \tt{ANSWER}}[/tex]
[tex]\quad\quad\quad\quad\quad\quad[/tex]
[tex]\tt{- 2x + 7x + 34 = - 2(1 - 7x)}[/tex]
[tex]\tt{5x + 34 = - 2(- 7x + 1)}[/tex]
[tex]\tt{5x + 34 = - (- 2 * 7x + 2)}[/tex]
[tex]\tt{5x + 34 = - (- 14x + 2)}[/tex]
[tex]\tt{(5x + 34) + (- 34 - 14x) = (14x - 2) + (- 34 - 14x)}[/tex]
[tex]\tt{5x + 34 - 34 - 14x = 14x - 2 - 34 - 14x}[/tex]
[tex]\tt{5x - 14x + 34 - 34 =14x-14x-2 - 34}[/tex]
[tex]\tt{- 9x = - 36}[/tex]
[tex]\tt{\frac{9x}{9} = \frac{36}{9}}[/tex]
[tex]\tt{x = 4}[/tex]
Find the sum of the convergent series. (round your answer to four decimal places. ) [infinity] (sin(9))n n = 1
The sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31
For given question,
We have been given a series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]
[tex]\sum_{n=1}^{\infty}~(sin(1))^n=sin(1)+(sin(1))^2+...+(sin(1))^n[/tex]
We need to find the sum of given convergent series.
Given series is a geometric series with ratio r = sin(1)
The first term of the given geometric series is [tex]a_1=sin(1)[/tex]
So, the sum is,
= [tex]\frac{a_1}{1-r}[/tex]
= sin(1) / [1 - sin(1)]
This means, the series converges to sin(1) / [1 - sin(1)]
[tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex]
= [tex]\frac{sin(1)}{1-sin(1)}[/tex]
= [tex]\frac{0.8415}{1-0.8415}[/tex]
= [tex]\frac{0.8415}{0.1585}[/tex]
= 5.31
Therefore, the sum of the convergent series [tex]\sum_{n=1}^{\infty}~(sin(1))^n[/tex] is 5.31
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i just need explanations on how to solve this. i have an upcoming test. please help.
[tex]\frac{3x}{6y} x\frac{7}{12y}[/tex]
The product of the given expression is 7x/24y²
Product of fractionsGiven the product of the fractions below
3x/6y * 7/12y
Simplify
x/2y * 7/12y
Multiply the numerator and denominator to have:
7x/24y²
Hence the product of the given expression is 7x/24y²
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Name a pair of vertical angles
Name a pit of adjacent angles
If m
Can someone help I’m confused I never learned this
Answer: Vertical: angles ABF and DBE. Adjacent: angles ABC and CBD
Step-by-step explanation:
vertical angles are angles that share a common point. they are right across from each other, and in this case, share point B. adjacent angles are angles that are directly next to each other, and share a line or segment. in this case, the two angles share the segment BC. hope this helps.
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 241(1.03) t. the variable t represents the number of years since 2000. what is the projected annual percent of growth, and what should the company be worth in 2012?
Answer:
343.608 million to nearest thousand.
Step-by-step explanation:
Projected annual percent of growth = 3% ( from the values 1.03 in the equation)
Worth is 2012 ( 12 years after 2000) is:
241(1.03)^12
= 343.608 million
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 20, 16, 21, 16, 22, 16, 15
Answer:
2.57
Step-by-step explanation:
The mean absolute deviation(MAD) of a data set is given by the formula
[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]
n = number of data set values. Here n=7
[tex]\bar{x}=[/tex]mean of the data set values = [tex](20+16+21+16+22+16+ 15)/7 = 126/7 = 18[/tex]
[tex]x_{i}[/tex] are the n individual values
Substituting in the summation we get
MAD = [tex]\frac{1}{7} |20-18| + |16-18| + |21-18| + |16-18| + |22-18| + |16-18| + |15-18|\\= (2 + 2 + 3 + 2 + 4+ 2 + 3)/7\\= 18/7 = 2.571428 \\[/tex]
Rounded to the nearest hundredth, the answer is 2.57
How to do 8+(-3)+(-2) three diffrent ways on a number line?
3 ways of computing the sum on the number line are:
Start at 8, then move 2 units to the left, then move 3 units to the left.Start at -3, then move 8 units to the right, then move 2 units to the left.Start at -2, then move 3 units to the left, then move 8 units to the right.How to do the sum in three different ways on a number line?
Here we have the sum:
8 + (-3) + (-2)
The first way of doing the sum in a number line is starting on the first number, which is 8.
Then, we move 3 units to the left, to the 5.Then, we move other 2 units to the left, to the 3.Now, we also can think the sum as:
(-3) + 8 + (-2)
So now we can start at the value -3, then move 8 units to the right, and then 2 units to the left.
Or think the sum as:
(-2) + (-3) + 8
So we start at -2, then we move 3 units to the left, and finally 8 units to the right.
So the different ways of computing the sum on a number line depends on where we start.
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1/2 to the 2nd power in fraction form
Answer: [tex]\frac{1}{4}[/tex]
Work Shown:
[tex]\left(\frac{1}{2}\right)^2 = \left(\frac{1}{2}\right)*\left(\frac{1}{2}\right) = \frac{1*1}{2*2} = \frac{1}{4}[/tex]
The mean of continuous data having term 100 is 20.find the sum of terms
Answer:
2000
Step-by-step explanation:
let the sum of the two terms be,x
Then,
x/100=20
where
100=no. of terms
20=mean
Then,
x/100=20
x=20×100
x=2000
So,
Sum of terms=2000
help ASAP!!!!!!!!!!!!!!!
Answer: 4.0 * 10^0 kg = 4.0 kg essentially
Step-by-step explanation:
No need to convert these to numbers...
Weight of 1 bee: 1 * 10^-4 = (0.0001 kg)
Number of bees: 4 * 10^4 = (40000 bees)
(1 * 10^-4) * (4 * 10^4) =
(1 * 4) * (10^-4 * 10^4) =
(10^0 because when multiply exponential numbers, you add the exponents)
4 * 10^0 =
4 * 1 = 4 kg
find unknown angles, value of 'x' and unknown sides:
What is the area of this figure?
14 km
8 km
9 km
8 km
5 km
4 km
4 km
4 km
The Area of the composite figure as shown in the image below is: 105.57 km².
What is the Area of a Composite Figure?Referring to the diagram given below, the shape can be decomposed into one rectangle, one square, and one quarter circle.
The area of the composite figure = area of rectangle + area of square + area of quarter circle.
Area of the Rectangle = length × width
Length = 12 km
Width = 7 km
Area of the Rectangle = 12 × 7
Area of the Rectangle = 84 km²
Area of the square = (s)²
s = 3 km
Area of the square = 3²
Area of the Rectangle = 9 km²
Area of the quarter circle = 1/4(πr²)
r = 4 km
Area of the quarter circle = 1/4(π × 4²)
Area of the quarter circle = 12.57 km²
Area of the composite figure = 84 + 9 + 12.57
Area of the composite figure = 105.57 km².
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Which property is shown in the following statement?
(46 + 17) + 3 = 46 + (17 + 3)
associative property of addition
commutative property of addition
identity property of addition
Answer:
Associative property of addition.
Step-by-step explanation:
The location of the parentheses makes no difference to the sum of these numbers.
The property shown in the statement "(46 + 17) + 3 = 46 + (17 + 3)" is the associative property of addition.
The associative property of addition states that when adding three or more numbers, the grouping of the numbers does not affect the sum
In the given statement, we have three numbers being added: 46, 17, and 3. The statement shows that the addition is grouped differently on each side of the equation, but the result is the same.
On the left side, we have (46 + 17) + 3.
This means we first add 46 and 17, which equals 63. Then we add 3 to the sum, resulting in 66.
On the right side, we have 46 + (17 + 3). Here, we first add 17 and 3, which equals 20. Then we add 46 to the sum, also resulting in 66.
As we can see, no matter how we group the numbers being added, the final sum is the same. This demonstrates the associative property of addition.
Therefore, the property shown in the given statement is the associative property of addition.
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At a school 45% of the students are boys; 30% of the boys and 40% of the girls play soccer. What percentage of the whole school plays soccer?
The percentage of the whole school that plays soccer is 35.5%
How to determine the percentage of the whole school plays soccer?The percentage of the boys is given as
Percentage boys = 45%
This means that the percentage of the girls is given as
Percentage girls = 55%
Also, from the question, we have:
30% of the boys and 40% of the girls play soccer
So, the percentage of the whole school that plays soccer is
P = Boys * Percentage Boys + Girls * Percentage Girls
This gives
P = 45% * 30% + 55% * 40%
Evaluate the product
P = 13.5% + 22%
Evaluate the sum
P = 35.5%
Hence, the percentage of the whole school that plays soccer is 35.5%
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10) James earned $3,000 interest
on an investment that he put in
the bank for 6 years with a 5%
interest rate. How much was his
initial deposit?
Answer:
Step-by-step explanation:
assuming that he has an annual interest of 5% then his initial deposit would be rounded to $2,238.65
Given these facts, determine how many cans of paint you would need to buy to paint 2 walls.
1st wall: 20 ft. x 8ft.
2nd wall: 40ft. x 8ft.
1 can will cover 200 square feet of wall.
You will need 3 cans of paint to cover the two walls
How many cans of paint will you need?
We know that 1 can will cover 200 square feet of wall.
And here we have 2 walls, let's find the total area of these walls.
wall 1 is 20ft by 8ft, then its area is:
A = 20ft*8ft = 160ft^2
wall 2 is 40t by 8 ft, then its area is:
A' = 40ft*8ft = 320ft^2
The total area is:
160ft^2 + 320ft^2 = 480ft^2
The number of cans of paint needed is given by the quotient between the total area and the area that each can cover.
N = 480ft^2/200ft^2 = 2.4
But we can't have a 0.4 of a can, so we should round to the next whole number, which is 3.
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