Answer:
The four first terms are:
[tex]7x,7x^{2},\frac{21x^{3}}{6},\frac{7x^{4}}{6}[/tex]
Step-by-step explanation:
The function is:
[tex]f(x)=7xe^{x}[/tex]
The Taylor series around a is given by:
[tex]F(x)=\sum^{\infty}_{n=0} \frac{f^{n}(a)(x-a)^{n}}{n!}[/tex]
The first 4 terms will be:
[tex]F(x)=f(0)+\frac{f^{'}(0)(x)}{1}+\frac{f^{''}(0)(x)^{2}}{2}+\frac{f^{'''}(0)(x)^{3}}{6}[/tex]
Let's find first the derivatives:
[tex]f'(x)=7(xe^{x}+e^{x})[/tex]
[tex]f'(0)=7(0e^{0}+e^{0})=7[/tex]
[tex]f''(x)=7xe^{x}+7e^{x}+7e^{x}=7xe^{x}+14e^{x}[/tex]
[tex]f''(0)=14[/tex]
[tex]f'''(0)=21[/tex]
[tex]f''''(0)=28[/tex]
[tex]F(x)=0+\frac{7(x)}{1}+\frac{14(x)^{2}}{2}+\frac{21(x)^{3}}{6}+\frac{28(x)^{4}}{24}[/tex]
Therefore, the four first terms are:
[tex]7x,7x^{2},\frac{21x^{3}}{6},\frac{7x^{4}}{6}[/tex]
I hope it helps you!
So the Taylor series for the function informed will be:
[tex]7x; 7x^2; \frac{21x^3}{6} ; \frac{7x^4}{6}[/tex]
The function is:
[tex]f(x)= 7e^xx[/tex]
The Taylor series around a is given by:
[tex]f(x)= \sum \frac{f^n (a) (x-a)^n }{n!}[/tex]
The first four terms will be:
[tex]F(x)=f(0)+\frac{f'(0)(x)}{1}+\frac{f''(0)(x)^2}{2} + \frac{f'''(0)(x)^3}{6}[/tex]
Let's find first the derivaties:
[tex]f'(x)= 7(e^xx+e^x)\\f'(0)= 7\\f''(x)= 7e^xx+14e^xx\\f''(0)=14\\f'''(0)= 21\\f''''(0)= 28[/tex]
[tex]F(x)= 0+\frac{7x}{1}+\frac{14x^2}{2}+\frac{21x^3}{6}+\frac{28x^4}{24}[/tex]
Therefore, the four first terms are:
[tex]7x; 7x^2; \frac{21x^3}{6} ; \frac{7x^4}{6}[/tex]
See more about Taylor series at : brainly.com/question/6953942
These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
2 cm
3 cm
Surface Area = [ ? ) cm2 Surface Area = 75 cm2
Helppppp plssss
Answer:
33.3 cm²
Step-by-step explanation:
Recall: Area Scale Factor = (Linear Scale Factor)²
Area scale factor = surface area of bigger cone/surface area of smaller cone
Let the surface area of the smaller cone be represented as x
Therefore,
Area scale factor = 75/x
Linear scale factor = radius of bigger cone/radius of smaller cone = 3/2
Thus:
75/x = (3/2)²
75/x = 9/4
Cross multiply
x*9 = 75*4
9x = 300
Divide both sides by 9
x = 300/9
x = 33.3 cm² (nearest tenth)
Find the measure of 0. Round answer to the nearest tenth. Pleas help
Answer:
[tex]\theta=36.43^{\circ}[/tex]
Step-by-step explanation:
Given that,
Base = 42
Perpendicular height = 31
We need to find the value of [tex]\theta[/tex]. It can be calculated using trigonometry as follows :
[tex]\tan\theta=\dfrac{P}{B}\\\\\theta=\tan^{-1}(\dfrac{P}{B})[/tex]
Put all the values,
[tex]\theta=\tan^{-1}(\dfrac{31}{42})\\\\\theta=36.43^{\circ}[/tex]
So, the value of [tex]\theta=36.43^{\circ}[/tex].
A soccer team has 15 players and needs to choose a captain and an assistant captain. How many ways can those positions be selected?
Select one:
105
50
30
Answer:
30?
Step-by-step explanation:
I think its 30 because 15*2 is 30 but I really don't know im sorry
Please answer number 5 I’ll give brainliest thanks
Answer:
Hello! answer: C
Hope that helps!
Answer:
b
Step-by-step explanation:
Experimental - 5 choices, 1 is Q = 1/5
Theoretical - 5 choices, landed on Q 4 times =4/5
Five times the sum of 4 and some number is 40.
Answer:
5 × 4 = 20 not 40
Step-by-step explanation:
Which inequality can be used to represent this scenario?
Mikael needs to rent a scooter to get to work. The scooter charges $1.85 to activate it and $0.50 per mile Mikael has a gift card for
$10 and he can not spend more on the scooter
O 10 < 0.502 +1.85
O 10 < 1.85.1 +0.50
O 10 > 1.852 +0.50
O 10 > 0.503 +1.85
Answer:
[tex]10 > 1.85 + 0.5m[/tex]
Step-by-step explanation:
Price of the scooter:
Fixed price of $1.85 to activate plus $0.50 for each mile. This situation can be represented by a linear function, and it is given by:
[tex]P(m) = 1.85 + 0.5m[/tex]
Mikael has a gift card for $10 and he can not spend more on the scooter.
The spendings have to be less than 10. So
[tex]10 > P(m)[/tex]
[tex]10 > 1.85 + 0.5m[/tex]
A system of equations is created by using the line represented by2x+4y=0And the line represented by the data in the table below
What is the X value of the solution to the system if x -1 and y is 8
Answer:
x = 2
Step-by-step explanation:
From the data, we obtain the slope :
-1, 8 ; 3, - 4
Slope = Rise / run
Rise = y2 - y1 = (-4 - 8) = - 12
Run = x2 - x1 = (3 - (-1)) = 4
Slope, m = - 12 / 4 = - 3
Recall:
Equation of line :
y - y1 = m(x - x1)
y - 8 = - 3(x + 1)
y - 8 = - 3x - 3
y = - 3x - 3 + 8
y = - 3x + 5
Substituting y = - 3x + 5 into the equation 2x+4y= 0
2x + 4(-3x + 5) = 0
2x - 12x + 20 = 0
-10x = - 20
x = 2
brainliest eeeeeeeeeeeeee
Answer:
3 / 4
Step-by-step explanation:
We can realize that both the numerator and denominator have a common factor of 9. We can divide them both by 9 to get:
3 / 4
This fraction is in simplest form.
Answer:
3/4
hope this helps
have a good day :)
Step-by-step explanation:
what is the volume of the cube I'm confused (look at the picture to see)
Answer: D (64)
Step-by-step explanation:
My answer is correct because, it's showing that 4 is the length, width, and height. So it bassically 4 x 4 x 4 in other words 4 exponent 3. And 4 exponent 3 would equal 64.
Hope This Helps!
Connor made 16 brownies. He put nuts on 6 brownies. Write
the simplified fraction of the brownies that had nuts.
6/16 = 3/8
hope this helps
graph your linear equation. y=x÷3
When there are 24 cars in the parking lot, the lot is ⅜ full. What is the maximum capacity (total number of cars) that the parking lot can hold? Show your work.
not really tricky just a little thing I needed help with
Answer:
64 cars
Step-by-step explanation:
total number of cars that the parking lot can hold = 8/3 × 24 = 64 cars
Help pls!
(The question are in the image)
A. -1/p
B. 0
C. 1
D. p
PLssssssssssssss help..
Answer:
141.4
Step-by-step explanation:
i think
solve the given system of equations 2x + 8y= 5 and 24x - 4y = -15
9514 1404 393
Answer:
(x, y) = (-1/2, 3/4)
Step-by-step explanation:
A graphing calculator does a nice job of finding the solution.
(x, y) = (-1/2, 3/4)
__
You can eliminate y by adding twice the second equation to the first.
(2x +8y) +2(24x -4y) = (5) +2(-15)
50x = -25
x = -1/2 . . . . . . divide by 50
__
24(-1/2) -4y = -15 . . . . .substitute for x in the second equation
-4y = -3 . . . . . . . . . add 12
y = 3/4 . . . . . . . . . divide by the coefficient of y
The solution is (x, y) = (-1/2, 3/4).
Rodas is standing 100 feet from the Eiffel Tower and sees a bird land on the top of the tower (he has really good eyes!). If the angle of elevation from Rodas to the top of the Eiffel Tower is close to 84.6°, how tall is the tower? Round to two decimal places.
Answer:
1057.89 feet
Step-by-step explanation:
Trig time! Start with a diagram and listing out your trig functions, either mentally or on paper. SOH CAH TOA
The best trig function for this problem is likely tan:
tan84.6 = height / 100
100 * tan 84.6 = height
height = 1057.89 feet
Pllssss somebody help me fast pllls!!!
Answer:
Yes; That what I got In my studies and lessons
These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two yellow
marbles if the first one is NOT placed back into
the bag before the second draw?
Give your answer as a rational number, reduced to
simplest terms.
1
[ ?
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.
Answer: 1/45
Step-by-step explanation:
If a vertical angle has 74 degree and also opposite angle is 2x degree ,what is value of x?
Answer:
x = 37
Step-by-step explanation:
Well if you didn't know vertical angles are congruent ( or equal to each other )
Which means that 74 = 2x
If we want to find the value of x, then we need to get rid of the "2" on 2x
To do so we can divide each side by 2
74 / 2 = 37
2x / 2 = x
we would be left with x = 37
Emma buys two bus tickets to Bradford. She pays with a £10 note. How much change will she get?
Hello there I hop you are having a good day :)
So, if she brought 2 tickets an they cost £4.00 you would add £4.00 + £4.00 = £8.00 and then you would take that away from the £10.00 - £8.00 = £2.00 so Emma would get £2.00 change :) hopefully that helps you.
Mandy and Jordan each bought some of the same notebook and the same three-ring
binder. Mandy paid $11.20 for 2 notebooks and 2 binders. Jordan paid $10.50 for 3
notebooks and 1 binder. What is the price of one of the notebooks?
Answer:
$11.20 + 2 = 1122 1050 +3 = 1053 hope this help .
What are the vertices of AA'B'C'if AABC is dilated by a scale factor of 5?
Answer:
B
Step-by-step explanation:
multiply each coordinate by 5
solve if h=5 and y=8 7hy^2+y
Step-by-step explanation:
h = 5
y = 8
=> 7hy² + y
=> 7 × 5 × 8² + 8
=> 35 × 64 + 8
=> 2240 + 8
=> 2248
5 pennies as a fraction
Answer:
5/100
Step-by-step explanation:
each penny = 1/100
If using the method of completing the square to solve the quadratic equation x² - 16x - 38 = 0, which number would have to be added to "complete the square"?
Answer:64
Step-by-Step
Image
You roll 2 dice. What is the probability of getting two 5's?
A multiple choice test contains questions
with four options each: A, B, C, or D. If
Natalie randomly guesses on the last three
questions, what is the probability that she
gets all three correct?
Answer:
Probability of getting all three correct answer = [tex]\frac{1}{64}[/tex]
Step-by-step explanation:
Given - A multiple choice test contains questions with four options each: A, B, C, or D. If Natalie randomly guesses on the last three questions.
To find - what is the probability that she gets all three correct.
Proof -
Given that, question has 4 options.
And 1 option can be correct,
Let
x be that Natalie gives correct answer.
So,
Probability of getting, correct answer, P(x) = [tex]\frac{1}{4}[/tex]
So,
Probability of getting, incorrect answer, P(x') = 1 - [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex]
Now,
Given that, she guess the 3 questions.
All correct means,
first, second, third question answer is correct.
So,
Probability of getting all three correct answer = [tex]\frac{1}{4}[/tex]×[tex]\frac{1}{4}[/tex]×[tex]\frac{1}{4}[/tex] = [tex]\frac{1}{64}[/tex]
Please I need help badly please no links or I will report you
Answer:
17.5 is going to be your answer
help me plzzzzzz!!!!!!!
Help pls. No links. Thank you :)
Answer:
784
Step-by-step explanation:
Mark as Brainliest
P.S
other person is wrong