Answers
(i) The Maclaurin's series is:
1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
(ii) Integral of limit o to 1∫ e^sinx is 0
Maclaurin's expansion is as follows:
y(x) = y₀ ₊ x y₁(0) ₊ x²/2! y₂(0) ₊ x³/3! y₃(0) ₊ ........
y = e^sinx
y(0) = e^sin0
y(0) = 1
Differentiate y with respect to x
y₁(x) = e^sinx . cos x
y₁(0) = 1 [i.e y₁ = cosx.y]
y₁(0) = 1
Differentiate y₁ with respect to x
y₂(x) = cosc . y₁ ₋ sinx . y
∴ y₂(0) = 1 ₋ 0 = 1
Differentiate y₂ with respect to x
y₃ = cosx . y₂ ₋ (2 sinx ₊ cosx)y₁
y₃(0) = 1 ₋(0 ₊ 1)1
y₃(0) = 0
Differentiate y₃ with respect to x
y₄ = cosx . y₃ sinx . y₃ ₋ (2sinx ₊ cosx)y₂ ₋ (2cos x ₋ sinx) y₁
y₄(0) = 0 ₋ (3 . 0 ₊ 1)1 ₋ (2 ₋ o) 1
y₄(0) = -3
∴ From maclaurin's equation we get:
e^sinx = 1 ₊ x . 1 ₊ x²/2! . 1 ₊ x³/3! (0) ₊ x⁴/4! (₋3) ₊ ....
=1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
Hence we get the the series expansion as 1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
(ii) limit 0 to 1∫e^sinx
integration formula ∫e^x dx = e^x + c
limit 0 to 1 ∫e^sinx = [e^sinx + c ]limit 0 to 1
= e^sin0 ₋ e^sin1
= 1 ₋ 1
= 0
Hence we get the answer as 0
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Related Questions
Based on the graph of g(x), on which intervals
are the function's values negative? Select all that
applv.
Answers
Answer:
[tex]\text{B}) \text{ } -3 < x < -1\\\text{D}) \text{ } 2 < x < \infty[/tex]
Step-by-step explanation:
The graph lies below the x-axis.
Please help! Will give the brainliest :)
Answers
Answer:
First figure out the angle measure of CBA and DBE to find out what Angle measure of ABE is.
Angle CBA and DBE are vertical angles, meaning they are congruent.
so set the equation as:
(2x+21)=(5x)
21=5x-2x
21=3x
x=7
It doesn't matter in which angle you plug 7 you get the same angle measure, so : 5x=5(7)=35 degrees
So to find angle measure of ABE:
We know that ABE and DBE form linear pair, so
180-35=145 degrees
145 degrees is the answer.
Hope it helps!
Answer:
∠ABE = 145°
Step-by-step explanation:
because angle CBA and ABE form a straight line, we know that they must add together to 180 degrees
and because DBE and ABE also form a straight line/angle, they must add together to 180 degrees
we can set this up as a system of equations (I will be writing ABE as "y")
2x + 21 + y = 180
5x + y = 180
We can combine this to beL
2x + 21 + y = 5x + y
- 2x -2x
21 + y = 3x + y
- y - y
21 = 3x
x = 7
If we plug this back into our original equations (which is set to 180 degrees), we can find y
2(7) + 21 + y = 180
14 + 21 + y = 180
35 + y = 180
- 35 - 35
y = 145
(remember, "y" is angle ABE)
we can check this value (ABE = 145) by substituting our second equation
5(x) + ABE = 180
35 + 145 = 180
180 = 180
(TRUE)
so, the measure of ∠ ABE is 145°
hope this helps!!
Classify this triangle. (image down below)
(Acute scalene triangle. (Obtuse isosceles triangle. (Right isosceles triangle (Right scalene triangle?
Answers
Answer: Right iscoleces triangle
Step-by-step explanation: The square on the left bottom side means it is a right angle. The lines means that a side is congruent to the other side. By definition, iscoleces triangles have two congruent sides, so this must be it.
Answer:
right isosceles
Step-by-step explanation:
the right angle and the two sides that are equal make the triangle a right isosceles
What is the equation of the parabola? (3 points)
A) y = -1/8x^2 +5
B) y = 1/8x^2 +5
C) y = 1/8x^2 - 5
D) y = -1/8x^2 -5
Answers
Answer:
A.
Step-by-step explanation:
The parabola opens down, so the "a" value (the number in front of x^2) must be negative. The y-intercept is (0, 5) so the constant must be positive 5.
Which of the following is the number if sides a polygon can have to form a regular tessallation?
A. 5
B. 9
C. 3
D. 7
Answers
None of the options is true.
Three Different, Regular tessellation is formed 1. if we join regular polygons of side 3, called equilateral triangle,2. Regular polygon of side 4, called Square, and 3. Regular polygon of side,6 called hexagon,
to form a pattern.
What is the polygon?A polygon is said to be regular if all interior angles and all sides are equal.
The regular polygon of side 3, when joined together can be named: 3.3.3.
The regular polygon of side 4, when joined together can be named 4.4.4.
The regular polygon of side 6, when joined together can be named 6.6.6.
So, a regular tessellation is formed, from a regular polygon having,3,4, and 6 Sides.
None of the sides of the polygon, which is given in the option, can be used to form a regular tessellation.
None of the options is true.
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a) Write VW as a column vector.
b) Write WV as a column vector.
c) Write a sentence to explain what you notice about
your answers.
W
V
Answers
Answer:
vector VW= w - v
vector WV= v - w
Step-by-step explanation:
there are no figures to solve the question so i'll just write the formula..
vector VW= w - v
vector WV= v - w
62. The width of a rectangle is 3 cm less than its length. The perimeter of the rectangle is 30 cm. Find the length and width of the rectangle.
Answers
Answer: Length = 9 cm, Width = 6 cm
Step-by-step explanation:
L - 3 + L - 3 + L + L = 30
2L - 6 + 2L = 30
4L - 6 = 30
4L = 36
L = 9
Length = 9 cm
Width = 9-3 = 6 cm
5
14
6
3
1
2
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If
it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a
probability of winning.
B. Yes. Each friend has a
probability of winning.
C. No. Andrew has a probability of winning and Liz has a
probability of winning.
D. No. Andrew has a probability of winning and Liz has a
probability of winning.
Answers
The question is incomplete. Below you will find the missing figure.
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a 1/4 probability of winning.
B. Yes. Each friend has a 1/6 probability of winning.
C. No. Andrew has a probability of 1/4 winning and Liz has a probability of 1/6 winning.
D. No. Andrew has a probability of 1/3 winning and Liz has a probability of 1/4 winning.
The correct option is Option A: Yes. Each friend has 1/4 probability of winning.
Probability is the possibility of an event to happen which is the ratio of no. favorable outcomes and no. of total outcomes.
P = no. of favorable outcome/ total no. of outcome
Here given in the question,
If the spinner touches region 2 or 3, Andrew wins
If the spinner touches region 4, Liz wins.
This is fair play because both have the same size of region for winning.
If we cut the circle into 8 pieces,
as region 1 is the sum of 2 sub-parts of the circle,
possibility of spinner touching region 1= 2/8= 1/4
possibility of spinner touching the small region = 1/8
So the possibility of the spinner touching the region 2or 3= 1/8+1/8= 2/8= 1/4
Hence the possibility of Andrew wins= possibility of the spinner touching region 1= 1/4
possibility of Liz wins= possibility of the spinner touching the region 2 or 3= 1/4
Therefore the correct option is Option A: Yes. Each friend has 1/4 probability of winning.
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Find the volume of a cylinder that has a diameter of 7 and a height of 8.
28 Pi
392 Pi
448 Pi
98 Pi
Answers
Therefore,
Radius (r) = d / 2Radius (r) = 7/2We know that :
V = πr^2hSubstituting the values :
>> V = π × (7 / 2)^2 × 8
>> V = π × (49 / 4) × 8
>> V = π × 49 × 2
>> V = 98π
Henceforth,
98 pi is the answer.We know , the volume of a cylinder is given by the formula – πr²h, where r is the radius of the cylinder and h is the height.
Diameter - 7Height - 8radius = 7/2Therefore, putting the values, we get,
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: {r}^{2}h[/tex]
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \times \: \bigg(\frac{7}{2} \bigg)^{2} \: \times \: 8 \\ [/tex]
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{2} \: \times \: 8 \\ [/tex]
[tex] \Large \mathcal \purple {Volume } \large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{ \cancel2} \: \times \: \cancel{8} \: ^{ \orange4} \\ [/tex]
[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{ \cancel2} \: \times \: {7} \: \times \: \cancel4 \: ^{ \orange2} \\ [/tex]
[tex] \\ \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: 7 \: \times \: 7 \: \times \: 2[/tex]
[tex]\Large \mathcal \purple {Volume }\ \large\red\implies \tt \large \:\pi \: \times \: 49 \: \times \: 2[/tex]
[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:98 \:\pi[/tex]
Hence , the volume of cylinder is 98 pi
Which graph best represents the equation shown below? 3x + y = 2 A. B. C. D.
Answers
Answer:
The plots are (0,2) (1,-1)
Step-by-step explanation:
a slanted line starting from top left corner ending in the bottom right
The function f(x) = x2 + 6x +7 is graphed below.
Drag the correct word and the the appropriate value to the box with each given interval to indicate whether the function is increasing or decreasing on that interval
Answers
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the function f(x) = x² + 6x + 7. This is a quadratic equation,that is of degree two.
The function f(x) = x² + 6x + 7 is increasing over the interval x > -3 and decreasing over the interval x < -3.
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Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]
Answers
The area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.
What is quadrilateral?It is defined as the four-sided polygon in geometry having four edges and four corners. It has one pair of opposite congruent angles and the diagonals of a kite are perpendicular.
We have a quadrilateral shown in the picture.
The diagonal divides the quadrilateral into two triangles
The area of the quadrilateral = area of the triangle ADC + area of the
triangle ADB
= (1/2)3.42×4.39 + (1/2)5.44×3.42
= 7.5069 + 9.3024
= 16.80 square units
Thus, the area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.
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Algebra 2 help needed image below
Answers
Answer:
8x + 100
Step-by-step explanation:
Your answer is correct! But because the equation is already set to "y =", you do not need the "f(x)" in your equation.
a. The Gap purchased inventories totaling $10,392 million for the fiscal year ended February 2, 2019. Use the financial statement effects template to record cost of goods sold for The Gap's fiscal year ended February 2, 2019. (Assume accounts payable is used only for recording purchases of inventories and all inventories are purchased on credit.)
b. What amount did the company pay to suppliers during the year? Record this with the financial statement effects template.
I'm not sure how to show these amounts on the financial statement effects template.
Answers
The cost of goods sold is $10,258 million and the Cash paid to supplier is $10,447 million.
Cost of goods solda. Cost of goods sold
Cost of Goods Sold=Beginning Inventories + Purchases – Ending Inventories
Cost of goods sold = $1,997 + $10,392 - $2,131
Cost of goods sold = $10,258
b. Cash paid to supplier
Cash paid=2015 Beginning balance + Purchases - 2015 Ending balance
Cash paid = $1,181 + $10,392 - $1,126
Cash paid = $10,447
Therefore the cost of goods sold is $10,258 million and the Cash paid to supplier is $10,447 million.
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Here is the histogram of a data distribution. All class widths are 1.
SO
4
3
2-
2 3
Which of the following numbers is closest to the mean of this distribution?
A. 2
OB. 3
O C. 10
OD. 5
5 6 7 8 9 10
E. 4
Answers
The correct answer is option B which is 3
What is mean?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Given data:-
4,3,2
The mean will be calculated as:-
Mean = (4 + 3 + 2) / 3
Mean = 9 / 3
Mean = 3
Therefore the correct answer is option B which is 3
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the perimeter of a rectangle is 70 cm . if the ratio of the width to the length is 2:5 what is the width ?
Answers
Answer:
width = 10 cm
Step-by-step explanation:
the ratio of width to length is 2 : 5 = 2x : 5x ( x is a multiplier )
the perimeter (P) of a rectangle is calculated as
P = 2 × width + 2 × length
given P = 70 then
2(2x) + 2(5x) = 70
4x + 10x = 70
14x = 70 ( divide both sides by 14 )
x = 5
Then
width = 2x = 2 × 5 = 10 cm and length = 5x = 5 × 5 = 25 cm
Thanks
solve for x
[tex]\bold{x {}^{2} + 5x + 6 = 0}[/tex]
ty! ~
Answers
Answer:
x = -2x = -3Step-by-step explanation:
[tex] \bf {x}^{2} + 5x + 6 = 0[/tex]
Write the equation in factored form.
[tex]\bf (x + 2)(x + 3) = 0[/tex]
Separate equations, and set each factor to zero.
[tex]\bf x + 2 = 0[/tex]
[tex]\bf x + 3 = 0[/tex]
Rearrange and isolate the variable to find the solutions
[tex]\bf x = - 2[/tex]
[tex]\bf x = - 3[/tex]
------------------------------------
Answer:
x=-3 x=-2
Step-by-step explanation:
x^2 +5x+6 =0
We need to factor the equation
What two numbers multiply to 6 and add to 5
3*2 = 6
3+2 =5
(x+3)(x+2)
Using the zero product property
x+3 =0 x+2 =0
x=-3 x=-2
NEED HELP ASAP !!!
Simplify: √16r
O 47²
O 473
87²
O 8-3
Answers
Answer:
4 r^3
Step-by-step explanation:
sqrt ( 16 r^6 ) = sqrt ( 4^2 * (r^3)^2 ) = 4 r^3
A count of patients needing a blood transfusion in the emergency room at a city hospital would best be modelled by what
distribution?
A. geometric
B. continuous
C. normal
D. Poisson
Answers
The count of patients needing a blood transfusion can be modelled as a continuous distribution.
What is a continuous distribution?
A continuous distribution is a distribution that can take on an infinite number of possible values. A continuous distribution is not defined at specific values. The number of patients can be 1 or 10 or 50 or even 0.
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probability of independent events: decimal answers (probability and counting)
Answers
The probability that both are smokers is 6903/180000
How to determine the probability?The given parameters are:
Male smoker = 177
Female smoker = 78
Total student = 78 + 522 = 600
The probability of a male smoker is
P(Male) = 177/600
The probability of a female smoker is
P(Female) = 78/600
The probability that both are smokers is
P(Smoker) =P(Male) *P(Female)
So, we have:
P(Smoker) = 177/600 * 78/600
Simplify
P(Smoker) = 177/600 * 39/300
Evaluate the product
P(Smoker) = 6903/180000
Hence, the probability that both are smokers is 6903/180000
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whats the GCF of x^6 and x^4
Answers
no cap in my rap im da mf truth + yb better + ratio bozo
Which expression is equivalent to...
Answers
Answer:
first option
Step-by-step explanation:
[tex]\frac{(2g^5)^3}{(4h^2)^3}\\= \frac{8g^1^5}{64h^6} \\= \frac{g^1^5}{8h^6}[/tex]
Step-by-Step Solution:
= (2g^5)^3 / (4h^2)^3
= 8g^15 / 64h^6
=> g^15 / 8h^6
NEED HELP ASAP !!
Which equations are equivalent to 2 + 2 12-x1=1? Check all that apply.
Answers
Answer:
[tex]\frac{2}{3}|2-x|=\frac{1}{15}[/tex]
Step-by-step explanation:
[tex]\frac{1}{5} + \frac{2}{3} |2-x| = \frac{4}{15} \\\\\frac{1}{5}*(\frac{3}{3}) = \frac{3}{15}\\\\\frac{3}{15}-\frac{3}{15} + \frac{2}{3}|2-x| =\frac{4}{15}-\frac{3}{15}\\\\\frac{2}{3}|2-x|=\frac{1}{15}[/tex]
The tables represent the functions f(x) and g(x).
Which input value produces the same output value for the two functions?
x = –12
x = –9
x = –6
x = –3
Answers
A function assigns the values. The correct option is C, x=-6.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) When the value of x is -12,
f(-12) = 2/3(-12) + 7 = -1
g(-12) = 2(-12) + 15 = -9
B.) When the value of x is -9,
f(-9) = 2/3(-9) + 7 = 1
g(-9) = 2(-9) + 15 = -3
C.) When the value of x is -6,
f(-6) = 2/3(-6) + 7 = 3
g(-6) = 2(-6) + 15 = 3
D.) When the value of x is -3,
f(-9) = 2/3(-3) + 7 = 5
g(-9) = 2(-2) + 15 = 11
Hence, the correct option is C, x=-6.
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What’s the vertex of this graph??
Answers
Answer:
(4, -3)
Step-by-step explanation:
A vertex is just a point at which 2 lines going in different directions meet, hence (4, -3)
Determine the area of a sector with√20 radius meters, and central angle 30°.
I will mark brainliest!
Answer Options:
20πm²
5π/3m²
30πm²
π/3²
Answers
Answer: [tex]\frac{5\pi}{3}[/tex]
Step-by-step explanation:
[tex]A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}[/tex]
Please answer this question i really want answers :(
Answers
Step-by-step explanation:
[tex] \sqrt{10} = 3.2 \\ then \: the \: sign \: there \: is \: = \\ \sqrt{10 } = 3.2 \\ \\ \: \sqrt{12} = 3.5 \\then \: the \: sign \: there \: is \: = \\ \: \sqrt{12} = 3.5 \\ \\ 6 \frac{1}{3} = 6.3 \: and \: \sqrt{40 } = 6.3 \\ therefore \: 6 \frac{1}{3} = \sqrt{40} \\ \\ 2 \frac{2}{5} = 2.4 \: and \: \sqrt{5.76} = 2.4 \\ then \: \: 2 \frac{2}{5} = \sqrt{5.76} \\ \\ 5 \frac{1}{6} = 5.16 \: and \: 516 \: \: therefore \: \\ 5 \frac{1}{6} = 5.16 \\ \\ \sqrt{6.2} = 2.5 \\ and \: 2.4 \: therefore \: \\ \sqrt{6.2} > 2.4[/tex]
(6-^8)^4 please helpppp
Answers
[tex](6^-^8)^4[/tex]
[tex]=6^-^2^4[/tex]
[tex]=\frac{1}{6^2^4}[/tex]
Construct a linear equation for the linear data presented in the table
Answers
Answer:
y = -7x
Explanation:
Take two points from table: (-4, 28), (-3, 21)
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope\ (m): \dfrac{21-28}{-3-(-4)} = -7[/tex]
Now find equation:
[tex]\sf y - y_1 = m (x - x_1)[/tex]
[tex]\rightarrow \sf y - 21 = -7(x - (-3))[/tex]
[tex]\rightarrow \sf y = -7(x +3) + 21[/tex]
[tex]\rightarrow \sf y = -7x -21 + 21[/tex]
[tex]\rightarrow \sf y = -7x[/tex]
Slope
m=y/xm=14/-2m=-7Equation of line
y=mx+0y=-7xHelp me with this question please!! :)
Answers
Answer: 4.2%
Step-by-step explanation:
The probability the first response is correct is 1/6.The probability the second response is correct is 1/4.Multiplying these, we get (1/6)(1/4), which is about 4.2%
