Answer:
8.75
Step-by-step explanation:
7/4 = 1.75 and ?/5 (5x1.75) = 8.75
Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = xe^−x^2/32, [−2, 8]
The question is missing parts. Here is the complete question.
Find the absolute maximum and absolute minimum values of f on the given interval.
[tex]f(x)=xe^{-\frac{x^{2}}{32} }[/tex] , [ -2,8]
Answer: Absolute maximum: f(4) = 2.42;
Absolute minimum: f(-2) = -1.76;
Step-by-step explanation: Some functions have absolute extrema: maxima and/or minima.
Absolute maximum is a point where the function has its greatest possible value.
Absolute minimum is a point where the function has its least possible value.
The method for finding absolute extrema points is
1) Derivate the function;
2) Find the values of x that makes f'(x) = 0;
3) Using the interval boundary values and the x found above, determine the function value of each of those points;
4) The highest value is maximum, while the lowest value is minimum;
For the function given, absolute maximum and minimum points are:
[tex]f(x)=xe^{-\frac{x^{2}}{32} }[/tex]
Using the product rule, first derivative will be:
[tex]f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )[/tex]
[tex]f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )[/tex] = 0
[tex]1-\frac{x^{2}}{16}=0[/tex]
[tex]\frac{x^{2}}{16}=1[/tex]
[tex]x^{2}=16[/tex]
x = ±4
x can't be -4 because it is not in the interval [-2,8].
[tex]f(-2)=-2e^{-\frac{(-2)^{2}}{32} }=-1.76[/tex]
[tex]f(4)=4e^{-\frac{4^{2}}{32} }=2.42[/tex]
[tex]f(8)=8e^{-\frac{8^{2}}{32} }=1.08[/tex]
Analysing each f(x), we noted when x = -2, f(-2) is minimum and when x = 4, f(4) is maximum.
Therefore, absolute maximum is f(4) = 2.42 and
absolute minimum is f(-2) = -1.76
The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
The function is given as:
[tex]\mathbf{f(x) = xe^{-\frac{x^2}{32}}}[/tex]
Start by differentiating the function
[tex]\mathbf{f'(x) = e^{-\frac{x^2}{32}} - \frac{x^2}{16}e^{-\frac{x^2}{32}}}[/tex]
Set to 0
[tex]\mathbf{ e^{-\frac{x^2}{32}} - \frac{x^2}{16}e^{-\frac{x^2}{32}} = 0}[/tex]
Rewrite as:
[tex]\mathbf{ \frac{x^2}{16}e^{-\frac{x^2}{32}} = e^{-\frac{x^2}{32}}}[/tex]
Cancel out common factors
[tex]\mathbf{ \frac{x^2}{16}=1}[/tex]
Multiply both sides by 16
[tex]\mathbf{ x^2=16}[/tex]
Take square roots of both sides
[tex]\mathbf{ x=\pm 4}[/tex]
The interval is given as: [-2,8]
This means that the value of x = -4, is out of the interval.
So, we have the following critical points:
x = (-2, 4, 8)
Calculate f(x) at the these points
[tex]\mathbf{f(-2) = -2 \times e^{-\frac{(-2)^2}{32}}}[/tex]
[tex]\mathbf{f(-2) = -2 \times e^{-\frac{4}{32}}}[/tex]
[tex]\mathbf{f(-2) = -1.765}[/tex]
[tex]\mathbf{f(4) = 4 \times e^{-\frac{(4)^2}{32}}}[/tex]
[tex]\mathbf{f(4) = 4 \times e^{-\frac{16}{32}}}[/tex]
[tex]\mathbf{f(4) = 2.426}[/tex]
[tex]\mathbf{f(8) = 8 \times e^{-\frac{(8)^2}{32}}}[/tex]
[tex]\mathbf{f(8) = 8 \times e^{-\frac{64}{32}}}[/tex]
[tex]\mathbf{f(8) = 1.083}[/tex]
By comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
Read more about absolute maximum and absolute minimum values at:
https://brainly.com/question/12752779
- 11/5 -2.4 1.6 15/10 - 2.25 in order from least to greatest
Answer (least to greatest):
-2.4-2.25-11/515/101.6I hope this helps!
Answer:
1.6,- 11/5 ,2.25 , -2.4 15/10
Step-by-step explanation:
Alison can swim 75 feert in 12 seconds. What is he rate to the nearest mile per hour?.
Answer:
in an hour she can swim around 22,500 feet which is about 4.26 miles
Step-by-step explanation:
Answer:
22,500 miles per hour
Step-by-step explanation:
60 seconds in a minute times 60 minutes in one hour. 3600
Divide that by 12 then multiply by 75 to get your answer
PLZ MARK BRAINLIEST
which point on the line number line represntes -1/3
Answer:
Point C
Happy Holidays!
Step-by-step explanation:
ay
We need to find the homeownership proportion in Southern California. The homeownership proportion is believed to be around 50%. How many householders would you survey for a 93% CI where the maximum likely sampling error is 1.5%?
Answer:
The value is [tex]n = 3648 [/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\^ p = 0.5[/tex]
The margin of error is [tex]E = 0.015[/tex]
From the question we are told the confidence level is 93% , hence the level of significance is
[tex]\alpha = (100 - 93 ) \%[/tex]
=> [tex]\alpha = 0.07[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.812[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{ 1.812 }{ 0.015} ]^2 *0.5 (1 - 0.5 ) [/tex]
=> [tex]n = 3648 [/tex]
What is the slope of the line that passes through the points A (–4, 3) and B (–2, –5)?
An experienced carpenter can panel a room 3 times faster than an apprentice can. Working together, they can panel the room in 6 hours. How long would it take each one working alone to do the job
Answer:
experienced carpenter would need 1 and 1/2 hours
apprentice would need 4 1/2 hours
Step-by-step explanation:
experienced = e
apprentice = 3e
3e + e = 6
4e = 6
e = 6/4 or 3/2
6 - 3/2 = 9/2
help algebra 1 !! help me with this question
Can someone answer please
Answer:
9
Step-by-step explanation:
thank me later :)
Which best describes a system of equations that has no solution?
-consistent, independent
-inconsistent, dependent
-consistent, dependent
-inconsistent
thank you for your help
Answer: inconsistent
Step-by-step explanation:
The sum of two numbers is -10.5. Can one of these addens be positive and the other negative? Provide an example to prove your answer.
Step-by-step explanation:
In order for the solution of a problem to be negative, you need one negative number and one positive number. Same goes for when having a positive sum, you know that the equation has an even number of negative numbers.
-6 + 3 = -3
You get -3 because you have both a positive and negative number in the equation.
TARGET SELLS 24 BOTTELS OF WATER FOR 3 DOLARS AND 36 DOLARS WHICH IS THE BETTER BUY AND BY HOW MUCH
Answer:
The 36-pack is a better buy by $0.50 per 36 bottles.
Step-by-step explanation:
24 bottles for $3 compared to 36 bottles for $4
Unit rates:
$3/24 = $0.125/bottle
$4/36 = $0.111/bottle
The 36-pack is a better buy since the unit price is lower.
$0.125 - $0.111 = $0.013888...
$0.01388888... * 36 = $0.50
Answer: The 36-pack is a better buy by $0.50 per 36 bottles.
Graph: y = 3/4 x + 5
Click or tap the graph to plot a point.
Answer:
Put the dot on the 5 on the Y-axis
Step-by-step explanation:
Put the initial dot on the 5 on the y-axis (vertical), then it's rise over run if plotting a line. Since it's 3/4 you would go up 3 and over to the right four. You can get the rest of the line by going down 3 from the initial point on five, down left 3.
I need the answer quickly
How many cubic inches are in one-sixth of one cubic yard?
Answer:
7776
Step-by-step explanation:
Which operation is NOT closed for polynomials?
es )
A)
add a trinomial to a trinomial
B)
divide a binomial by a trinomial
multiply a binomial by a binomial
D)
subtract a binomial from a trinomial
Answer:
B) divide a binomial by a trinomial
Step-by-step explanation:
We know that the polynomials are very nearest to the addition, subtraction and the multiplication part but the same cannot happen under the division part since the division of two polynomials could not become a polynomial it is not necessary condition that it could become a polynomial
So if we divide the binomial by a trinomial therefore it would provides a rational expression and have a negative exponent and a negative exponent is not permitted under the polynomial
Therefore the option B is correct
WILL MARK BRAINLIEST PLEASE ANSWER 12/15+5/15 1 NUMBER FOR EACH SLOT
Answer:
17/15
Step-by-step explanation:
or if u reduce it would be 12/15
Try this hard Math Problem if you dare!!
Answer:
a. [tex](x - 3)^2 + 16[/tex]
b. [tex]8(x -7)^2[/tex]
c. [tex](a^2 - 1)(7x - 6)[/tex] or [tex](a+1)(a-1)(7x-6)[/tex]
d. [tex](x^2-4)(x^2+3)[/tex] or [tex](x-2)(x+2)(x^2+3)[/tex]
e. [tex](a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})[/tex]
Step-by-step explanation:
[tex]a.\ (x + 1)^2 - 8(x - 1) + 16[/tex]
Expand
[tex](x + 1)(x + 1) - 8(x - 1) + 16[/tex]
Open brackets
[tex]x^2 + x + x + 1 - 8x + 8 + 16[/tex]
[tex]x^2 + 2x + 1 - 8x + 24[/tex]
Collect Like Terms
[tex]x^2 + 2x - 8x+ 1 + 24[/tex]
[tex]x^2 - 6x+ 25[/tex]
Express 25 as 9 + 16
[tex]x^2 - 6x+ 9 + 16[/tex]
Factorize:
[tex]x^2 - 3x - 3x + 9 + 16[/tex]
[tex]x(x -3)-3(x - 3) + 16[/tex]
[tex](x - 3)(x - 3) + 16[/tex]
[tex](x - 3)^2 + 16[/tex]
[tex]b.\ 8(x - 3)^2 - 64(x-3) + 128[/tex]
Expand
[tex]8(x - 3)(x - 3) - 64(x-3) + 128[/tex]
[tex]8(x^2 - 6x+ 9) - 64(x-3) + 128[/tex]
Open Brackets
[tex]8x^2 - 48x+ 72 - 64x+192 + 128[/tex]
Collect Like Terms
[tex]8x^2 - 48x - 64x+192 + 128+ 72[/tex]
[tex]8x^2 -112x+392[/tex]
Factorize
[tex]8(x^2 -14x+49)[/tex]
Expand the expression in bracket
[tex]8(x^2 -7x-7x+49)[/tex]
Factorize:
[tex]8(x(x -7)-7(x-7))[/tex]
[tex]8((x -7)(x-7))[/tex]
[tex]8(x -7)^2[/tex]
[tex]c.\ 7a^2x - 6a^2 - 7x + 6[/tex]
Factorize
[tex]a^2(7x - 6) -1( 7x - 6)[/tex]
[tex](a^2 - 1)(7x - 6)[/tex]
The answer can be in this form of further expanded as follows:
[tex](a^2 - 1^2)(7x - 6)[/tex]
Apply difference of two squares
[tex](a+1)(a-1)(7x-6)[/tex]
[tex]d.\ x^4 - x^2 - 12[/tex]
Express [tex]x^4[/tex] as [tex]x^2[/tex]
[tex](x^2)^2 - x^2 - 12[/tex]
Expand
[tex](x^2)^2 +3x^2- 4x^2 - 12[/tex]
[tex]x^2(x^2+3) -4(x^2+3)[/tex]
[tex](x^2-4)(x^2+3)[/tex]
The answer can be in this form of further expanded as follows:
[tex](x^2-2^2)(x^2+3)[/tex]
Apply difference of two squares
[tex](x-2)(x+2)(x^2+3)[/tex]
[tex]e.\ a^{4n} -b^{4n}[/tex]
Represent as squares
[tex](a^{2n})^2 -(b^{2n})^2[/tex]
Apply difference of two squares
[tex](a^{2n} -b^{2n})(a^{2n} +b^{2n})[/tex]
Represent as squares
[tex]((a^{n})^2 -(b^{n})^2)(a^{2n} +b^{2n})[/tex]
Apply difference of two squares
[tex](a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})[/tex]
A large aquarium has 6 more fish than a small aquarium. There are 19 fish in the large aquarium. How many fish are in the small aquarium
Answer: 13
Step-by-step explanation:
What is the are of parallelogram ABDC?
Answer:
9 cm2
Step-by-step explanation:
area=3×3=9cm2
.....
Answer:
9 cm^2
Step-by-step explanation:
inside the parallelogram, two right angled triangles form.
Use the formula, A = [tex]\frac{1}{2}[/tex] x base x height (Area of a triangle) and multiply by 2 as there are two triangles. So,
A = ([tex]\frac{1}{2}[/tex] x base x height) x 2
= ([tex]\frac{1}{2}[/tex] x 3 x 3 ) x 2
= 9 cm^2
why can you use fraction multiplication to check the answer to a fraction division problem? How do you use multiplication to check a division problem
Answer:
Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.i hope this helps:)
simplify solution
[tex]6 \sqrt{4 \sqrt{2} } [/tex]
Answer:
16.97
Step-by-step explanation:
15. At a football match, 10 men bought either a pie or a cup of
coffee. A pie costs 60p and a coffee costs 50p. The total
amount spent on pies and cups of coffee was £5.80. How many
of each must have been bought?
Answer:
8 pies and 2 coffees must have been bought.
Step-by-step explanation:
Given that:
10 men bought either a pie or a cup of coffee.
Cost per pie = 60p
Cost per coffee = 50p
Total amount spent = £5.80 * 100 = 580p
Let,
x be the number of pies
y be the number of coffees
According to given statement;
x+y = 10 Eqn 1
60x+50y=580 Eqn 2
Multiplying Eqn 1 by 50
50(x+y=10)
50x+50y=500 Eqn 3
Subtracting Eqn 2 from Eqn 3
(60x+50y)-(50x+50y) = 580-500
60x+50y-50x-50y=80
10x=80
Dividing both sides by 10
[tex]\frac{10x}{10}=\frac{80}{10}\\x=8[/tex]
Putting x=8 in Eqn 1
8+y=10
y=10-8
y=2
Hence,
8 pies and 2 coffees must have been bought.
(18 POINTS!!!) When Katie installed a fence along the 200-
fixed perimeter of her rectangular backyard,
she left an op an opening for a gate. What is
the value of x, if the equation
2(x+ 60) + 2(300) = 200
Answer:
-260
Step-by-step explanation:
Answer:
x = -260
Step-by-step explanation:
Solve the equation. Then check your solution.
-8p =-3 1/4
a. 4 3/4
b. - 13/32
c. 13/32
d. 26
Answer: C
Step-by-step explanation:
-8p = -3 1/4 The first think you want to do is convert the mixed fraction into an improper fraction.
-8p = -13/4 Now multiply both sides of the equation by 4.
-32p = -13 Divide both sides by -32
p = 13/32
Find the slope using the points (0, -2) and (3, 4)
AC =
Round your answer to the nearest hundredth.
Answer:
70 I think but I'm not sure
Step-by-step explanation:
AC=70
What is the solution to this system of equations?
2x-5y=-3
y=16-4x
Answer:
2x-5y=-3
Slope= 2.000 /0.800
x-intercept=-3/2=-1.50000
y-intercept=3/5=0.60000
y=16-4x
Slope=-8.0000/2.0000=-4.000
x-intercept=16/4=4
y-intercept=6/1=16.00000
Step-by-step explanation:
00:00
What is the number of terms in this expression?
m
5
+4x6
5
Enter your answer in the box.
Answer:
40
Step-by-step explanation:
1. Change the following into 12 hour clock time
a) 1720 hours. b)0235 hours
Answer:
A) 5:20 pm
B) 2:35 am
Step-by-step explanation:
The hours in am are from 00:00 - 12:00, the numbers after 12 for example 17, you subtract 12 and the remaining is the hours and what is left of the number for example 20 is the minutes.
I am horrible at explaining but I hope this helps... :)
Answer:
a) 5:20
b) 2:35
Step-by-step explanation:
a) Subtract 12 from the 17 at the beginning of 1720, leaving you with 5. This is the hour component of standard time, and will be placed on the left side of the colon (5:__). Then, put the last two digits onto the other side of the colon in standard time like so: 5:20.
b) For this one, because the first two digits don't exceed twelve, you simply have to divide the first two digits from the last two digits and put a colon between them: 02:35, or 2:35.