Answers
9514 1404 393
Answer:
7953.873
Step-by-step explanation:
The first derivative is ...
f'(x) = 4·3x²·e^x +4x³·e^x = e^x(4x³ +12x²)
Then the second derivative is ...
f''(x) = (12x² +24x)e^x +(4x³ +12x²)e^x
f''(x) = e^x(4x³ +24x² +24x)
So, f''(3) = (e^3)(4·27 +24·9 +24·3) = 396e^3 = 7953.87262158
Rounded to thousandths, this is ...
f''(3) = 7953.873
Answer:
f''(x) ≈ 7953.87
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FactoringCalculus
Derivatives
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Product Rule: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule: [tex]\displaystyle \frac{d}{dx} [e^x]=e^x[/tex]
Step-by-step explanation:
Step 1: Define
f(x) = 4x³eˣ
f''(x) is x = 3 for 2nd Derivative
Step 2: Differentiate
[1st Derivative] Product Rule [Basic Power Rule]: f'(x) = 3 · 4x³⁻¹eˣ + 4x³eˣ[1st Derivative] Simplify: f'(x) = 12x²eˣ + 4x³eˣ[1st Derivative] Factor: f'(x) = eˣ(12x² + 4x³)[2nd Derivative] Product Rule [Basic Power Rule]: f''(x) = eˣ(12x² + 4x³) + eˣ(2 · 12x²⁻¹ + 3 · 4x³⁻¹)[2nd Derivative] Simplify: f''(x) = eˣ(12x² + 4x³) + eˣ(24x + 12x²)[2nd Derivative] Distribute eˣ: f''(x) = 12eˣx² + 4eˣx³ + 24eˣx + 12eˣx²[2nd Derivative] Combine like terms: f''(x) = 24eˣx² + 4eˣx³ + 24eˣx[2nd Derivative] Factor: f''(x) = 4xeˣ(x² + 6x + 6)Step 3: Evaluate
Substitute: f''(x) = 4(3)e³(3² + 6(3) + 6)Exponents: f''(x) = 12e³(9 + 6(3) + 6)Multiply: f''(x) = 12e³(9 + 18 + 6)Add: f''(x) = 12e³(27 + 6)Add: f''(x) = 12e³(33)Multiply: f''(x) = 396e³Evaluate: f''(x) ≈ 396(20.0855)Multiply: f''(x) ≈ 7953.87Related Questions
On a windy morning, a hot air balloon starts rising and flying away from the top of a
hill. The altitude, h, in feet, of the balloon x hours after starting its ascent from the
hill, can be modeled by the function: h(x) = -16x2 + 64x + 80.
The balloon will reach its maximum height after how many hours?
Answers
Answer: (2,144)
Step-by-step explanation:
3. 1,199 / 5 =
What is the compatible number to find two estimate the quotient is between
Answers
Answer:
in decimal = 239.8
........
Why does every prism have 2/3 as many vertices as edges?
Answers
Step-by-step explanation:
Because it's impossible to not have a shape without edges
points for you........................................
Answers
Answer:
Thanks man..............
Answer:
thx
Step-by-step explanation:
Are the vectors U1 = and U2 = parallel?
Answers
Answer:
Express the vector →u below as a sum of two vectors →u1 and →u2, where →u1 is parallel to the vector →v given below, and →u2 is perpendicular to →v.
The price of a large pack of toilet paper before the pandemic was about $9. During the crazy
toilet paper rush of 2020, the price rose to around $20. State whether this was an increase or
decrease, and calculate the percent of change. I
Answers
Answer:
it is an increase because it is going up
Step-by-step explanation:
it is a 122.222% increase
The melting/freezing point of mercury is –39ºC. A scientist put liquid mercury into a freezer that is kept at a constant temperature of –35ºC. Will the liquid mercury freeze?
Answers
Answer:
The mercury will not freeze because the freezer is warmer than the freezing point of mercury.
Step-by-step explanation:
A "freezing point" is a point that allows a liquid to solidify. This is lower than the melting point (of course). However, specific liquids freeze at varying freezing points.
For example, the freezing point of water is 0°C while the freezing point of Mercury is -39°C. This means that water will only freeze once it reaches a temperature of 0°C or lower than this. Same goes for Mercury–it needs to reach the temperature of -39°C or lower in order to freeze.
Simplify the expression, 18 + (-5) -5/7j - 3/7j + 6
Answers
Answer:
[tex]18 + ( - 5) - \frac{5}{7j} - \frac{3}{7j} + 6 \\ = (18 - 5 + 6) - ( \frac{5}{7} + \frac{3}{7} ) \frac{1}{j} \\ = 19 - \frac{8}{7j} [/tex]
Graph: y=3/4x+5 Please let me know guys
Answers
2-b/3=-5/2 what dose b =
Answers
Answer:
I believe that the answer is b= 19/2.
8th Grade Math, Helppppppppp Now Plsssssss! What is the function of the nucleus in plant and animal cells? A. Produces all the power of the cell B. Creates proteins within the cell C. Control all cells activity, contains DNA D. Allows things in an out of the cell
Answers
Answer:
science budo but nucleus controls cell activity and contains dna
Answer:
C. Control all cells activity, contains DNA
Step-by-step explanation:
The nucleolus makes ribosomal subunits from proteins and ribosomal RNA, also known as rRNA. It then sends the subunits out to the rest of the cell where they combine into complete ribosomes.
Also.... that's not math.
Evaluate the equation r-4.012=5.313
Answers
Answer:
r = 9.325
Step-by-step explanation:
Hope this helps!!!
2 divided by 9/10 (in fraction or mixed number form)
Answers
Answer:
decimal: 2.22 mixed number: 2 2/9
Amelia launched her science fair rocket, and then backed away. The path of the rocket is given by the equation below, where y is the the height in feet amd x is the time in seconds the rocket is in the air y=-2×^2+5x+7
1)when does the rocket hit the ground?
2)what is the maximum height of the rocket?
Answers
Answer:
1)The rocket hit the ground at [tex]x = \frac{5}{4}[/tex]
2)The maximum height of the rocket = 12.468 feet
Step-by-step explanation:
Step(i):-
Given equation
y = -2 x² + 5 x + 7 ...(i)
Differentiating equation (i) with respective to 'x' , we get
[tex]\frac{dy}{dx} = -2( 2x) +5(1) = -4x +5[/tex]
Equating zero
[tex]\frac{dy}{dx} = 0[/tex]
⇒ -4 x +5 =0
⇒ -4 x = -5
⇒ [tex]x = \frac{5}{4}[/tex]
The rocket hit the ground at [tex]x = \frac{5}{4}[/tex]
Step(ii):-
[tex]\frac{dy}{dx} = -4x +5[/tex] ...(ii)
Again differentiating equation (ii) with respective to 'x' , we get
[tex]\frac{d^{2} y}{dx^{2} } = - 4(1) <0[/tex]
The maximum height at x = [tex]\frac{-5}{4}[/tex]
y = -2 x² + 5 x + 7
[tex]y = -2 (\frac{5}{4})^{2} + 5 (\frac{5}{4} ) + 7[/tex]
[tex]y = \frac{-2(25)+ 25 (16)+7(64)}{64}[/tex]
[tex]y = \frac{798}{64} = 12.468 feet[/tex]
The maximum height of the rocket = 12.468 feet
some one please help me
Answers
Answer:
b>k c>L ac>JL bc>KL
Step-by-step explanation:
poggers
Answer:
B = K
C = L
AC = JL
BC = KL
hope this helps!
just helping people get points :D
Answers
Answer:
thank you so much for the points
Step-by-step explanation:
:D
Hello! Please answer this question with all of the info it is asked for. Please be sure to include all of your work and share any of your thoughts you had when solving. Please do not answer unless you know the answer. Thanks! Good Luck!
A golf ball is launched straight up into the air from the ground with an initial velocity of 160 ft/s. The function that models the ball's height is: h(t) = -16t^2 + 160t.
a) Find how long it takes for the golf ball to reached its maximum height.
b) Determine how long the golf ball is in the air before it hits the ground.
c) Determine the maximum height that the golf ball reaches.
Answers
Answer:
a) 5 secb) 10 secc) 400 mStep-by-step explanation:
Given is the quadratic function:
h(t) = -16t^2 + 160tThis gets maximum value at vertex, which is achieved at:
x = -b/2a, of y = ax^2 + bx + cIn our case:
t = -160/2(-16) = 5 secondsMaximum height is at vertex:
h(5) = -16*5^2 + 160*5 = 400 mTime the ball hits the ground, h(t) = 0:
-16t^2 + 160t = 0t^2 - 10t = 0t(t - 10) = 0t = 0 seconds is the starting pointt = 10 seconds is when the ball hits the groundSolve for x . 955=5x
Answers
Answer:
191
Step-by-step explanation:
955 = 5x
divide both sides by 5 to get x by itself
x = 191
A smart phone regularly sells for $180.00 but is on sale for 30% off. What is the amount of the discount?
Answers
Answer:
$54
Step-by-step explanation:
The amount of the discount can be found by multiplying 180 by 0.3 which is 54.
If you also need to know the new total it would be $126 because
180 - 54 = 126
I WILL GIVE BRAINLIEST !! PLEASE HURRY IM TIMED
(you can still use desmos btw)
answer choices
A. Haley’s family by 5 miles per hour
B. Alex’s family by 10 miles per hour
C. Haley’s family by 10 miles per hour
D. Alex’s family by 5 miles per hour
Answers
Answer:
alexs family by 10 Mph
Step-by-step explanation:
A point that does not fit the overall
or trend of a
scatter plot is known as an "outlier".
• Who was the "outlier" in the scatter plot above? Explain.
OUTLIERS
Answers
Is 18 and 0.3 equivalent
Answers
Answer:
No
Step-by-step explanation:
Because 0.3 is a decimal and 18 is a whole number.
0.3 = 3/10 which is 30%
 (6,-3) and y = - 6x - 3
Answers
is it if this point is on the line?
cause it's not
-y=mx+b
3=-6(6)-3
-3=-36-3
-3 does not equal -39
hence, point is not on the line
write an expression in terms of n
adds 2 to the number and then multiplies the result by 3
Answers
Answer:
Step-by-step explanation:
Let the number = n
Add 2 to the number : n + 2
Multiply the result by 3 : (n + 2) *3
= n * 3 + 2*3
= 3n + 6
4.
Darnell starts saving the same amount from each weeks paycheck. The table shows the total balance f(n) of
his savings account over time in weeks.
Time (weeks) n
2
3
Savings Account Balance(s) fin) $250 $380
$510 $640
Determine the value of f(9), and explain what it represents in this situation.
Answers
Answer:32
Step-by-step explanation:
The director of the admissions at a large university advises parents of incoming students about the cost of textbooks during a typical semester. He selected a sample of 100 students and recorded their textbook expenses for the semester. He then computed a sample mean cost of $315.40 and a sample standard deviation of $43.20
Required:
Using the 0.10 level of significance, is there evidence that the population mean is above $300?
Answers
Answer:
The calculated value t = 3.5648> 1.9842 at 0.1 level of significance
The null hypothesis is rejected
The mean of the sample does not come from the Population
Step-by-step explanation:
Step(i):-
Given that sample size 'n' = 100
Mean of the sample x⁻ = 315.40
The standard deviation of the sample (s) = 43.20
Level of significance = 0.1
Mean of the Population = 300
Null hypothesis: H₀: x₀ = μ
Alternative Hypothesis: H₁: x₀ ≠ μ
Step(ii):-
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{315.40-300 }{\frac{43.20}{\sqrt{100} } }[/tex]
t = 3.5648
Degrees of freedom = n-1 = 100-1 =99
[tex]t_{\frac{0.1}{2} , 99} = t_{0.05,99} = 1.9842[/tex]
The calculated value t = 3.5648> 1.9842 at 0.1 level of significance
The null hypothesis is rejected
The mean of the sample does not come from the Population
Drag the missing word into place
0.5 is the ___ that is equal to one half
Fraction
Hundredth
Decimal
Answers
Answer:
Decimal
Step-by-step explanation:
its a Decimal because 0.5 is an fact a decimal and its is equal to half and you can put 2 and 2 together and say it is a decimal just by how it looks
:) i hope you get the question righttt trust me its right i got it right on flocabulary.
The missing word into place is Decimal. Hence option 3 is true.
Used the concept of decimal number that states,
In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.
Given that the number is,
0.5
Now the number is written as,
0.5
5/10
1/2
And, the number 0.5 is in the form of a Decimal.
Hence, The missing word place is Decimal.
Therefore, option 3 is true.
To learn more about decimal numbers:
brainly.com/question/1285738
#SPJ6
4j = 0.7 Solve for j
Answers
Answer:
0.175
Step-by-step explanation:
[tex]\frac{4j}{4} =\frac{0.7}{4}[/tex]
j=0.175
You should get 0.175
DEFG is a parallelogram. Segment DH = 2y + 6, segment HF = 4x + 1, segment HE = 3x + 2 and segment GH = 20. Find the value of GE and DF.
Answers
Answer:
[tex]DF = 38[/tex]
[tex]GE = 40[/tex]
Step-by-step explanation:
Given
[tex]DH = 2y + 6,[/tex]
[tex]HF = 4x + 1,[/tex]
[tex]HE = 3x + 2[/tex]
[tex]GH = 20.[/tex]
See attachment for parallelogram.
Required
Find GE and DF
From the attachment:
[tex]GH= HE[/tex]
Substitute values for GH and HE
[tex]20 = 3x + 2[/tex]
Subtract 2 from both sides
[tex]20-2 = 3x + 2-2[/tex]
[tex]20-2 = 3x[/tex]
[tex]18= 3x[/tex]
[tex]3x = 18[/tex]
Divide both sides by 3
[tex]x = \frac{18}{3}[/tex]
[tex]x=6[/tex]
[tex]GE = GH + HE[/tex]
[tex]GH= HE[/tex]
So:
[tex]GE = GH + GH[/tex]
[tex]GE = 20 + 20[/tex]
[tex]GE = 40[/tex]
To find DF, we find y first:
[tex]DH = HF[/tex]
[tex]2y + 6 = 4x + 1[/tex]
Subtract 6 from both sides
[tex]2y +6- 6 = 4x + 1-6[/tex]
[tex]2y = 4x + 1-6[/tex]
Substitute 6 for x
[tex]2y = 4*6 + 1-6[/tex]
[tex]2y = 19[/tex]
Divide both sides by 2
[tex]y = \frac{19}{2}[/tex]
[tex]y = 9.5[/tex]
DF is then calculated as"
[tex]DF = DH + HF[/tex]
[tex]DF = 2y+6 + 4x+1[/tex]
Substitute values for x and y
[tex]DF = 2*9.5+6 + 4*3+1[/tex]
[tex]DF = 38[/tex]
if x is the first of two consecutive integers, express the sum of the two integers in terms of x
Answers
Answer:
2x+1
Step-by-step explanation:
x = 1st integer
x+1 = next consecutive integer
The sum is
x+ (x+1)
Combine like terms
2x+1
let the first integer be x and the second be x + 2
then the sum is x +x+2 = 2x +2
