Answers
Answer:
[tex]\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
Expanding/FactoringCalculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{\sqrt{x}}{e^x}[/tex]
Step 2: Differentiate
Derivative Rule [Quotient Rule]: [tex]\displaystyle f'(x) = \frac{(\sqrt{x})'e^x - \sqrt{x}(e^x)'}{(e^x)^2}[/tex]Basic Power Rule: [tex]\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}(e^x)'}{(e^x)^2}[/tex]Exponential Differentiation: [tex]\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{(e^x)^2}[/tex]Simplify: [tex]\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{e^{2x}}[/tex]Rewrite: [tex]\displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}[/tex]Factor: [tex]\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Related Questions
those are currency exchange rates 1 us dollar = 7.76 hk dollars 1 us dollar =1.47 nk dollars work out the value of 1000 hk dollars in nz dollars
Answers
Answer: 1000 HK dollars has the same value as 188.15 NZ dollars.
Step-by-step explanation:
We know that:
1 US dollar = 7.76 HK dollars
1 US dollar = 1.46 NZ dollars.
We have 1000 HK dollars, and we want to know the value in NZ dollars.
First, let's rewrite the 1000 HK dollars in US dollars.
Here we use the relation:
1 US dollar = 7.76 HK dollars
Then:
1 = (1 US dollar/7.76 HK dollars)
Then we can write:
1000 HK = (1000 HK)*1 = (1000 HK)*( (1 US /7.76 HK ))
1000 HK = (1000 HK/7.76 HK)* 1 US = 128.87 US
1000 HK = 128.87 US
Now we can use the relationship:
1 US = 1.46 NZ
Then:
1 = (1.46 NZ)/(1 US)
So we can rewrite:
128.87 US = (128.87 US)*1 = (128.87 US)*( (1.46 NZ)/(1 US))
128.87 US = (128.87 US/1 US)*1.46 NZ = 188.15 NZ
Then:
1000 HK = 128.87 US = 188.15 NZ
So we can conclude that 1000 HK dollars has the same value as 188.15 NZ dollars.
For f (x) = 2x+1 and g(x) = x2 - 7, find (fºg)(2).
Answers
Answer:
Step-by-step explanation:
Your first step will be to set up the problem:
f(x) - g(x)
Next you will substitute in your values:
(2x + 1) - (x2 - 7)
The easiest way to do the subtraction problems is to distribute your negative into your second set of parenthesis, so your expression would become:
2x + 1 - x2 + 7
Then combine your like terms:
2x - x2 + 8
Lastly put your expression in standard form (highest exponent to lowest)
-x2 + 2x + 8
Hope this helped!
(-18)/(-3) calculate value expression
Answers
Answer:
6
Step-by-step explanation:
In the year 2005, a person bought a new car for $24500. For each consecutive year
after that, the value of the car depreciated by 9%. How much would the car be worth
in the year 2008, to the nearest hundred dollars?
Answers
because, in three years it would have depreciated by 18% (9%*3=18) so you would subtract 18% off of $24500
Answer:
18500
Step-by-step explanation:
Percent decrease:
\text{Multiply by }(1-r)=(1-0.09)=(0.91)
Multiply by (1−r)=(1−0.09)=(0.91)
2005: \color{green}{24500}
2005:24500
2006: \color{green}{24500} (0.91) = \color{blue}{22295}
2006:24500(0.91)=22295
2007: \color{blue}{22295} (0.91) = \color{red}{20288.45}
2007:22295(0.91)=20288.45
2008: \color{red}{20288.45} (0.91) = \color{orange}{18462.49}
2008:20288.45(0.91)=18462.49
\text{Car value in 2008:}
Car value in 2008:
\$18500
$18500
Help me with this plzz pt.2
Answers
Answer:
3 feet by 8 feet= 24 square feet
9 feet by 10 feet= 90 square feet
5 feet by 7 feet= 35 square feet
13 feet by 2 feet= 26 square feet
8 feet by 8 feet= 64 square feet
Step-by-step explanation:
Answer:
Sheesh that sucks um go help urself
Step-by-step explanation:
if x degree + x + 10 degree + x + 15 degree + x + 20 degree + x + 25 degree + x + 30 degree
Answers
Answer:
x° + x° + 10° + x° + 15° + x° + 20° + x° + 25° + x° + 30°
= 6x° + (10 + 15 + 20 + 25 + 30)°
= 6x° + 100
0 = 6x + 100
6x = 100
X = 100/6
X = 16.66
what is rank correlation?
Answers
Step-by-step explanation:
it's any of several statistics that measure an ordinal association. Measures the degree of similarity between two rankings.
PLEASE HELP!!! I WILL GIVE BRAINLIEST
Answers
Answer:x=2y=3
Step-by-step explanation: I did this before
ISF YOU GET IT RIGHT I WILL NAME YOU BRAINLIST.
A sequence can be generated using a, = 60(1/2)"-1. What are the first four terms in the sequence? A 60, 120, 240, 480 B 60, 30, 15, 7.5 C С 60, 120, 180, 240 60, 90, 135, 202.5 ОА B. D
Answers
Answer:
C
Step-by-step explanation:
You just plug in the # in the sequence you wanna find,
n=1
60((1)/(2))^(1-1) = 60 (1st term)
--
n=2
60((1)/(2))^(2-1) = 30 (2nd term)
--
n=3
60((1)/(2))^(3-1) = 15 (3rd term)
--
n=4
60((1)/(2))^(4-1) = 7.5 (4th term)
Find the measures of all angles and sides help
Answers
Answer:
Step-by-step explanation:
All the angles in a triangle add up to 180 degrees. Both angles are 36 degrees so that's 72 degrees.
Angle L = Angle J (Opposite angles are equal)
Angle L = 98
Angle K + Angle L = 180 (Adjacent angles are supplementary)
Angle K + 98 = 180
Angle K = 180 - 98
Angle K = 82
Angle M = Angle K (Opposite angles are equal)
Angle M = 82
Plz help! Gonna need to turn it soon
Answers
Answer:
C - 13*
Step-by-step explanation:
I need help plz hurry before the time is over plz plz
Answers
Answer:
JK
Step-by-step explanation:
As it is shown in the diagram JK is the segment bisector of MN. That means JK cuts MN in half.
It takes 3 hours 15 minutes to fly from city A
to city B at a constant speed. Find how long
the journey takes if
a) the speed is 1.5 times that of the original
speed and
b) if the speed is three-quarters of the original
speed.
Answers
Answer:
19.5
4555.555555555555 hz
Step-by-step explanation:
Which equation is an identity?
Answers
HELP WITH 8 & 9 PLEASEEEEEE!?!?!?!?!,
Answers
Answer:
8. D
9. C
10. B. - 50
Step-by-step explanation:
8.y+3 = 1/2 (x+4)
x=-4 y+3=0 y=-3 pass(-4,-3)
9.only C passed the vertical line test
10. a₁ = 4
a₂ = 4-2 = 4 - (2*1) = 2
a₃ = 2-2=0 = 4 - (2*2)
...
a₂₈ = 4 - (2*27) = 4-54 = -50
Graph g(x) = -3(x + 2)2 + 2. Compare the graph to the graph of f(x) = x2. Give me five points that you use to graph g(x). Then describe the transformation from the graph of g to the graph of f.
Answers
What is the short form of 5000+100
Answers
Answer:
5000+100=5100 it is short form
Answer:
5 x 10³ + 10²
hope it helps.....
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. Previously research has shown the variability in the number to be σ = 2. The researchers wish the margin of error to be no larger than 0.5 for a 99% confidence interval. To obtain such a margin of error the researchers need at least:
A. 53 observations.
B. 107 observations.
C. 106 observations.
D. 54 observations.
2.
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or ultrasound. This requires the participation of a radiologist and a surgeon in the study. The researchers decide that they should only enroll horses seen at the best veterinary hospital in the country to ensure correct counts. Such a hospital will typically see the most severe cases. The researchers will enroll the first 100 horses seen beginning on the day the study is funded. The resulting interval is likely biased because:
A. the first 100 horses seen is not an SRS of all horses with enteroliths and therefore never representative.
B. a sample of 100 horses is too small to obtain an unbiased estimate.
C. the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths.
D. All of the above
3.
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or ultrasound. This requires the participation of a radiologist and a surgeon in the study. The researchers decide that they should only enroll horses seen at the best veterinary hospital in the country to ensure correct counts. Such a hospital will typically see the most severe cases. The researchers will enroll the first 20 horses seen beginning on the day the study is funded. The researchers will calculate a 95% confidence interval. The procedure is not valid because the:
A. sample size is too small for the central limit theorem to apply.
B. average number is not an integer and does not reflect any actual observation.
C. None of the above. The procedure is valid.
D. data are counts and, therefore, not Normally distributed.
4.
In a test of hypothesis for a mean, which statement is CORRECT?
A. The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
B. As long as the population distribution consists only of positive values, sample size does not matter.
C. The population distribution can be any distribution because the sample mean is always Normally distributed.
D. The population must be normal because that is the only case when the sample mean is Normally distributed.
5.
A "false negative," in which no effect is detected when in reality one exists, is an example of:
A. a Type I error.
B. the power of the test.
C. a Type II error.
D. None of the above
Answers
Answer:
1.) 107 observations
2.) the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths
3.) A. sample size is too small for the central limit theorem to apply.
4.) The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
5.) a Type I error
Step-by-step explanation:
n = [(Zcritical * σ) ÷ E]²
n = sample size
Zcritical at 99% = 2.58
E = error margin = 0.5
Standard deviation, σ = 2
n = [(2.58 * 2) ÷ 0.5]²
n = [5.16 ÷ 0.5]²
n = (10.32)²
n = 106.5024
n = 107 observations
B.) The thought or decision that the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths will introduce a bias in the study.
C.) For central limit theorem ; sample size must be considerably large ; at least sample size, n ≥ 30
D.) Distribution must be normal it approximately normal, obeying the central limit theorem ; sample size must be considerably large ; at least sample size, n ≥ 30
4b + 2b + 1/4 = what
Answers
Answer:
6b+1/4
Step-by-step explanation:
4b+2b+1/4
6b+1/4
cant do anything else because only the b can be added.
ANSWER QUICKLY AND GET 40 POINTS!!
Answers
Answer:
I belibve it's c
Step-by-step explanation:
Answer:
21 savage
Step-by-step explanation:
Add this expression to make it the shortest way of rewriting it as possible!
(2x + 5y + 8f) + (4x + 6f - 2y)
Answers
Find the distance between (−9, 7) and (−6, 7).
Answers
Answer:
(6,7),(9,6)
Step-by-step explanation:
HOPE THIS HELPS!!!!
4/4 pts
***
---the system of simoultanious equation
X+2y+z=6
2x+y+2z=6
X+y+z=5
Answers
Answer:
The system of equations has no solution.
Step-by-step explanation:
Let the following system of linear equations:
[tex]x +2\cdot y + z = 6[/tex] (1)
[tex]2\cdot x + y + 2\cdot z = 6[/tex] (2)
[tex]x + y + z = 5[/tex] (3)
Since the quantity of equations and variables are the same, there is only one solution to this system. First, we clear [tex]x[/tex] in (3):
[tex]x = 5 - y - z[/tex]
And make substitution both in (1) and (2):
[tex](5-y-z) +2\cdot y + z = 6[/tex]
[tex]2\cdot (5-y-z)+y+2\cdot z = 6[/tex]
[tex]y = 1[/tex] (4)
[tex]y = 4[/tex] (5)
Which lead to a contradiction, since [tex]4\ne 5[/tex]. Therefore, the system of linear equations has no solution.
3 1/6-2 7/8 what is the snswer
Answers
Answer:
7/24
Step-by-step explanation:
Hope this helps.
what is the density of the oak board? it is 5.5 inches wide, 1.5 inches thick and 3 feet long
Answers
multiply 5.5 the width with 1.5 by 3 which gives you 24.75 inches feet long.
5.5 x 1.5 x 3=24.75 that's your answer.
Answer:297 cubic inches, other person is incorrect.
Step-by-step explanation:5.5 inches* 1.5inches * 3 feet
Convert 3 feet to inches and you have 36 inches. So now it becomes 5.5inches*1.5inches*36inches = 297 cubic inches
A 30-foot tree casts a 12-foot shadow as shown in the picture.
30 ft
12
Find the angle of elevation to the nearest tenth.
Answers
Answer:
21.8degrees
Step-by-step explanation:
Given the following
Length of shadow =opposite = 12ft
Height of tree = adjacent = 30ft
Required
angle of elevation
tan theta = opposite/adjacent
tan theta = 12/30
tan theta = 0.4
theta = 21.8degrees
angle of elevation is 21.8degrees
Chicago, Illinois has an elevation of 600 feet. Seely, California is -200 feet. What does 0 represent in the context of this situation?
Answers
Answer:
Sea level
Step-by-step explanation:
In geography, 'Elevation' is measured in relation to sea level, so sea level would be zero.
Thus, Chicago is 600 feet above sea level and Seely, California is 200 feet below sea level.
If there were nothing but flat land all the way from Seely to the ocean, sea water would come in and cover Seely. Fortunately for the people in Seely. California's coastal mountain range is between the town and the ocean, so that does not happen.
Answer:
It represents the "SEA LEVEL"
Answer pls is mathematically is due today in 1 m
Answers
Answer:
200.96 units^2 or 64π units^2
Step-by-step explanation:
8^2(3.14) = 200.96 units^2 or 64π units^2
(multiplied by 2 to change the radius to diameter)
what is -4m+5=5-4m show all solutions
Answers
Answer:
m=0
Step-by-step explanation:
How to solve your question 4 +5=5−4
Step 1: Rearrange Terms 4+5=5−4 4+5=−4+5
Step 2 : Subtract 5 from both sides 4+5=−4+5
-5 -5
Step 3 : Simplify 4m= -4m
Step 4: Add 4m to both sides of the equation 4m= -4m
+4 +4
Step 5: Simplify 8m=0
m=0
amber has 200 tickets to sell for her schools play. she sells 40% of the tickets on thursday. how many tickets does amber sell on thursday
Answers
Answer:20
Step-by-step explanation:
just go on omni