Step-by-step explanation:
Starting out with the Taylor series,
[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(a)}{n!}(x-a)^n[/tex]
where [tex]f^{(n)}[/tex] is the nth derivative of f(x) and if we set a = 0, we get the special case of the Taylor series called the Maclaurin series:
[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(0)}{n!}x^n[/tex]
Expanding this series up to the 1st 3 terms at a = 0,
[tex]f(x) = f(0) + \dfrac{f'(0)}{1!}x + \dfrac{f''(0)}{2!}x^2[/tex]
Let's find the derivatives of [tex]e^{\frac{x}{2}}[/tex]:
[tex]f'(x) = \frac{d}{dx} (e^{\frac{x}{2}}) = \frac{1}{2}e^{\frac{x}{2}} \Rightarrow f'(0) = \frac{1}{2}[/tex]
[tex]f''(x) = \frac{1}{4}e^{\frac{x}{2}} \Rightarrow f''(0) = \frac{1}{4}[/tex]
We can now write the Maclaurin series for [tex]e^{\frac{x}{2}}[/tex]as
[tex]e^{\frac{x}{2}} = 1 + \frac{1}{2} x + \frac{1}{8} x^2[/tex]
Alla and Balla together drink 750 milliliters (ml) of water. If Alla drinks 50% more than
Balla, how much does Alla drink?
Answer:
Step-by-step explanation:
A + B = 750
A = 1.5 B
~~~~~~~~~~~~~~
750-B = 1.5 B
750 = 1.5 B + B
750 = B(1.5 +1)
750 = B (2.5)
B = 300
A = 450
A.Calculate the mean,median and mode.(3 points each) 1.)1,2,3,4,5 2.)2,3,4,5,6,6 3.)6,7,5,4,5,6,2,5
Answer:
Step-by-step explanation:
1.)1,2,3,4,5
mean=sum of all values/number of values
=1+2+3+4+5/5
=15/5
mean=3
Mode :
In the given data, no observation occurs more than once.
Hence the mode of the observations does not exist, means mode=0.
Median
1,2,3,4,5
Middle value is 3 so the median is 3.
2.)2,3,4,5,6,6
mean=sum of all values/number of values
=2+3+4+5+6+6/6
=26/6
mean =4.33
Mode
is that value of the observation which occurs maximum number of times so here mode is 6.
Median
2,3,4,5,6,6
4+5/2
9/2
median=4.5
3.)6,7,5,4,5,6,2,5
mean=sum of all values/number of values
=6+7+5+4+5+6+2+5/8
=40/8
mean =5
Mode
is that value of the observation which occurs maximum number of times so here mode is 5
Median
2,4,5,5,5,6,6,7
5+5/2
10/2
median=5
if someone could help me i would aprshh
Answer:
Slope: -5/4
Step-by-step explanation:
Use slope (m) formula:
m = y2 - y1 / x2 - x1
m = 5 - 10 / 49 - 45
m = -5/4
Answer:
[tex]-\frac{5}{4}[/tex]
Step-by-step explanation:
Hi there!
Equation for the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
To find the slope of the line, plug in any two points given in the table. For example, we can use the points (49,5) and (53,0):
[tex]=\frac{5-0}{49-53}\\=\frac{5}{-4}[/tex]
Therefore, the slope of the line is [tex]-\frac{5}{4}[/tex].
I hope this helps!
Evaluate integral tan^6(2x) sec^4(2x) dx.
Answer:
Is the question original or you simply made it.
Find the value of each variable. PLEASE HELP ME
Given:
A quadrilateral DEFG inscribed in a circle.
[tex]m\angle D=60^\circ, m\angle E=m^\circ, m\angle F=2k^\circ, m\angle G=60^\circ[/tex]
To find:
The value of variables [tex]m[/tex] and [tex]k[/tex].
Solution:
If a quadrilateral is inscribed in a circle then it is a cyclic quadrilateral. The opposite angles of a cyclic quadrilateral angle supplementary angles.
Quadrilateral DEFG inscribed in a circle. So, quadrilateral DEFG is a cyclic quadrilateral.
[tex]m\angle D+m\angle F=180^\circ[/tex] [Supplementary angle]
[tex]60^\circ+2k^\circ=180^\circ[/tex]
[tex]2k^\circ=180^\circ-60^\circ[/tex]
[tex]2k^\circ=120^\circ[/tex]
Divide both sides by 2.
[tex]k^\circ=\dfrac{120^\circ}{2}[/tex]
[tex]k^\circ=60^\circ[/tex]
[tex]k=60[/tex]
Similarly,
[tex]m\angle E+m\angle G=180^\circ[/tex]
[tex]m^\circ+60^\circ=180^\circ[/tex]
[tex]m^\circ=180^\circ-60^\circ[/tex]
[tex]m^\circ=120^\circ[/tex]
[tex]m=120[/tex]
Therefore, the values of the variables are [tex]m=120[/tex] and [tex]k=60[/tex].
holaaaaaaaaaaaaaaaaa plz help i need this quick :)
Quadrilateral ARMY is rotated 90 degrees about the origin. Draw the image of this rotation.
Answer:
Step-by-step explanation:
If a point (x, y) is rotated 90° counterclockwise about the origin, rule for the rotation will be,
(x, y) → (-y, x)
Therefore, coordinates of the image point after the rotation will be (-y, x).
Following this rule,
Image points of the quadrilateral will be,
A(3, 3) → A'(-3, 3)
R(5, 7) → R'(-7, 5)
M(7, 5) → M'(-5, 7)
Y(5, 1) → Y'(-1, 5)
By graphing the image points we can get the graph of the image quadrilateral A'R'M'Y'.
Answer:
I got my answer on Khan Academy:
Kelly used the vertical line test to determine whether or not the curve that she had been given is a function. After conducting the vertical line test, Kelly determined that the curve is a function. Which of the following choices represents the result of Kelly’s vertical line test?
Answer:
0 or 1
Step-by-step explanation:
Given that Kelley is tasked with having to use vertical line test to determine whether or not a curve is a function. Each vertical line that Kelly draws through her curve must intersect the curve at maximum one point only in order for thecurve to be a function
Answer is 0 or 1 point
which of the following is a geometric sequence?
Answer:
The right answer is a.
Step-by-step explanation:
PLEASE MARK ME AS A BRAINLIEST
Is it true or false that for all sets A, B, and C, A U (B - C) = (A U B) - C?
Answer:yes
Step-by-step explanation:66
The given statement A U (B - C) = (A U B) - C is true.
What is a set ?A set is collection of well defined objects.
According to the given question we have to state whether A ∪ ( B - C ) = ( A ∪ B ) - C.
Lets consider we have three sets A, B and C and we also consider they intersect each other.
( B - C ) represents the elements which belongs to B but not in C.
∴ A ∪ ( B - C ) represents the no. of elements which belongs to the set B but not in C union the no. of elements which belongs to A.
AND
( A ∪ B ) - C represents no. of elements which belongs to A or B but not in C.
learn more about sets here :
https://brainly.com/question/8053622
#SPJ2
Help help help help help
Answer:yo we talking the same test
Step-by-step explanation:
Insta= santiagorez
Answer:
Radius , r = 5 units
Step-by-step explanation:
The standard form of a circle's equation:
[tex](x-a)^2 + (y -b)^2 = r^2 \ , \ where \ (a , b) \ is \ the \ centre\ and\ r \ is \ the \ radius.[/tex]
Given equation :
[tex]x^2 - 2x + y^ 2- 4y = 20\\\\[/tex]
Find radius .
Convert the given equation into standard form.
[tex](x - 1)^2 = x^ 2 - 2x + 1 \\\\(y - 2) ^2 = y^ 2 - 4y + 4\\\\[/tex]
Now add both equations :
[tex](x - 1)^2 + (y - 2)^2 = r^2[/tex]
[tex](x ^ 2 - 2x + 1) + (y^2 - 4y + 4 ) = r^2\\\\(x^2 -2x + y^2 - 4y ) + 1 + 4 = r^2\\\\20 + 1 + 4 = r^2[/tex] [tex][ \ given : \ x^2 - 2x + y^ 2 - 4y = 20 \ ][/tex]
[tex]25 = r^2 \\\\5 = r[/tex]
The system of equations Y equals -1/5 X -6 and Y equals negative 2X +3 is shown on the graph below
Answer:
The solution of the system is (5, -7)
Step-by-step explanation:
Here we have the system:
y = (-1/5)*x - 6
y = -2*x + 3
We know that this system is graphed below, and the question is incomplete, but I assume that we want to find the solution to this system. If you can see the graph, the solution is just the point where both graphs intersect, but we can find the solution analytically.
We know that:
y = (-1/5)*x - 6
y = -2*x + 3
Then, we can write:
y = (-1/5)*x - 6 = y = -2*x + 3
This leads to:
(-1/5)*x - 6 = -2*x + 3
Now we can solve this for x.
(-1/5)*x + 2*x = 3 + 6
(-1/5)*x + (10/5)*x = 9
(9/5)*x = 9
x = (5/9)*9 = 5
x = 5
now that we know the value of x, we can input this in one of the two equations above to find the correspondent value of y, we will get:
y = -2*x + 3 = -2*5 + 3
y = -10 + 3 = -7
y = -7
Then the solution is:
x = 5 and y = -7, or (5, -7)
What is a cubic function
Answer:
In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d where the coefficients a, b, c, and d are real numbers, and the variable x takes real values, and a ≠ 0. In other words, it is both a polynomial function of degree three, and a real function.
If the circumference of the circle is 88 cm, then its radius is 14 cm.
true or false?
Answer:
The radius is approximately 14 cm
Step-by-step explanation:
The circumference
C = 2 * pi *r
88 = 2 * pi *r
Divide by 2
44 = 3.14 *r
Divide by 3.14
44/3.14 = r
14.01273885=r
Of the following fractions: 9/19, 5/11, 7/15, and 11/23, which is the largest?
Answer:
silly question...I used technology to "cheat"
it is 11/23
34155 32775 33649 34485
72105 72105 72105 72105
Step-by-step explanation:
Review the graph.
On a coordinate plane, a circle has center (1, 0) and radius 5. Another circle has center (0, negative 4) and radius 4. Everything inside the second circle and between the first circle is shaded.
Which system of inequalities has the solution set shown in the graph?
25 < (x – 1)2 + y2 and 16 > x2 + (y + 4)2
25 > (x – 1)2 + y2 and 16 > x2 + (y + 4)2
25 < (x – 1)2 + y2 and 16 < x2 + (y + 4)2
25 > (x – 1)2 + y2 and 16 < x2 + (y + 4)2
Answer:
second option
Step-by-step explanation:
[tex]shaded~area\\(x-1)^2+y^2<25\\and\\(x+4)^2+y^2<16[/tex]
Answer:
A
Step-by-step explanation:
edge
not sure if this is the right question so i dont know if we're thinking about the same question...
de moirve's
(√3-i ÷ √3+i)^6 = 1
(√3 - i ) / (√3 + i ) × (√3 - i ) / (√3 - i ) = (√3 - i )² / ((√3)² - i ²)
… = ((√3)² - 2√3 i + i ²) / (3 - i ²)
… = (3 - 2√3 i - 1) / (3 - (-1))
… = (2 - 2√3 i ) / 4
… = 1/2 - √3/2 i
… = √((1/2)² + (-√3/2)²) exp(i arctan((-√3/2)/(1/2))
… = exp(i arctan(-√3))
… = exp(-i arctan(√3))
… = exp(-iπ/3)
By DeMoivre's theorem,
[(√3 - i ) / (√3 + i )]⁶ = exp(-6iπ/3) = exp(-2iπ) = 1
The probability of spinning blue on a spinner is 0.3. If the spinner is spun 40 times, estimate how many times you would spin blue. A 3-sided sninner is snun 10 time 1
Answer:
12 times.
Step-by-step explanation:
That would be 40 * 0.3 = 12.
Layers of rock wear off during which of the following processes?
A: Expansion B: Contraction C: Exfoliation D: Pressure
Answer:
Exfoliation
Step-by-step explanation:
Changes in temperature cause rock to expand (with heat) and contract (with cold). As this happens over and over again, the structure of the rock weakens. Over time, it crumbles.
Rocky desert landscapes are particularly vulnerable to thermal stress. The outer layer of desert rocks undergo repeated stress as the temperature changes from day to night. Eventually, outer layers flake off in thin sheets, a process called exfoliation.
The perimeter of the figure below is 41.6 in. Find the length of the missing side. (Note: diagram is NOT to scale)
Answer:
[tex]{ \tt{let \: that \: unknown\: side \: be \: x}} \\ { \boxed{ \tt{perimeter = (8 \times side)}}} \\ 41.6 = (3.2 \times 2) + (5.9 \times 5) + x \\ x = 5.7 \:in \\ { \bf{answer : 5.7 \: inches}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]
Help me pleaseeeeeeeeeeeeeeeeeee
Answer:
Always a parabola or U Shaped
U shaped or by rotating U it will be like intersect symbol.. You can see it in attached file
Take the area calculate the area of the circle around the answer to the nearest hundredth
Step-by-step explanation:
we cannot see anything, and you did not describe anything. so, there is nothing to calculate.
If you put 5 things in your mouth and take 3 out and put them in another hole, how much things are inside of you?
Answer:
2
Step-by-step explanation:
5-3=2 it's simple really
Answer:
5-3=2
Hope This Helps!!!
please help
Yaritza finds some nickels and pennies in her change purse. How many coins does she have if she has 140 nickels and 130 pennies? How many coins does she have if she has
n
n nickels and
p
p pennies?
Total coins, 140 nickels and 130 pennies: 270
Total coins,
n
n nickels and
p
p pennies:
Submit Answer
Answer:
270 coins
n + p
Step-by-step explanation:
Given that :
Number of nickels = 140
Number of pennies = 130
The total numbers coins had:
Number of Nickel + number of pennies
140 + 130 = 270 coins
If Number of nickels = n ; number of pennies = p
The total number of coins :
Number of Nickel + number of pennies
n + p
find the equation of the line shown
y =6 x=4
y - 6 = 0 ................ equation 1
x - 4 = 0 ................ equation 2
How would this quadrilateral be best classified, and what is the measure of Angle B?
Answer:
The quadrilateral is Rhombus
B=70°
Step-by-step explanation:
110+110+z+z=360
220+2z=360
2z=360-220
2z=140
z=140/2
Therefore, z=70
So Angle B=70
Since z= Angle B=Angle D
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Answer:
Undefined
Step-by-step explanation:
Lim x - - > 1(1 /In(2-x) + 1/(x-1))
To find the limit as x tends to 1
Substitute x = 1 into the function ;
(1 / In(2 - 1) + 1 / (1 - 1))
(1 / In 1) + (1 / 0)
1 / 0 + 1 / 0
Undefined
Find the midpoint of the line segment.
Answer:
-2,-3
Step-by-step explanation:
8)
8x + 6
14x - 2
A) 11
C) 8
B) -9
D) -7
Answer:
C) 8
Step-by-step explanation:
Consecutive angles are equal to 180. So 22x+4+180. Solve that to get x=8. Hope I helped and post more questions :)
What is the area of the figure below
Answer:
the answer for that is 61.
Step-by-step explanation:
Below is the frequency distribution of the score of 40 learners. COMPUTE THE mean,median and mode. (10 points)
Class interval: frequency
56-63 1
48-55 10
40-47 12
32-39 6
24-31 3
16-23 8
Answer:
Mean = 6.66
Median = 7
Mode = 7.68
Step-by-step explanation:
According to the Question,
Given That, the frequency distribution of the score of 40 learners.Class interval frequency
56-63 1
48-55 10
40-47 12
32-39 6
24-31 3
16-23 8
1). Mean = (Sum of all Observation) / (number of observation)
Mean = 40/6 = 6.66
2) For Median, If there are two number in the middle then you need to find their mean. 1 3 6 8 10 12 middle numbers are 6 and 8.
Median = (6+8) / 2 = 7
3) Mode = 3 × Median - 2 × Mean
Mode = 3×7 - 2×6.66
Mode = 7.68