The evaluation of the function [tex]f(x)=e^x[/tex] at a=0 and x=5 by the taylor series will have a value 65.37.
What is taylor's series?We know the fromula of taylor series is given as:
[tex]f(x)=f(a)+\dfrac{f'((a)}{1!}(x-a)+\dfrac{f''(a)}{2!}(x-a)^2+\dfrac{f'''(a)}{3!}(x-a)^3.................[/tex]
Now for the function [tex]f(x)=e^x[/tex] the taylor's series will become.
[tex]f(x)=e^a+e^ax+\dfrac{e^ax^2}{2!}+\dfrac{e^ax^3}{3!}+\dfrac{e^ax^4}{4!}[/tex]
[tex]f(x)=1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\dfrac{x^4}{4!}[/tex]
So at x=5 the values will become
[tex]f(x)=1+5+12.5+20.83+26.04=65.37[/tex]
hence the evaluation of the function [tex]f(x)=e^x[/tex] at a=0 and x=5 by the taylor series will have a value 65.37.
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There are 20 students on the student council at Nina's school. Eight of the students are in Nina's math class, 6 of the students are in her science class, and 4 students are in both her math and science classes.
If 2 members of the student council are randomly chosen, what is the probability that both are in Nina's math or science class?
Step-by-step explanation:
out of the total possibilities of 20 student council members, 8 are in Nina's math class, and 6 are in Nina's science class.
as I understand the given information, out of these 14 council members, 4 are in her math and in her science class. but this is then irrelevant for the question (and do not add more possibilities), as these 4 are already covered by the 8 and 6 in her individual classes.
remember, a probability is always
desired cases / possible cases
so, let's pick the first random choice :
the probabilty to pick one that is either in her math or her science class is
14/20 = 7/10
because there are 20 total possibilities to pick from, and 14 of these 20 are in at least one of her classes.
now let's pick the second one.
I assume the first pick has not been returned to the pool and cannot be picked a second time.
so, this time we have therefore only 19 total choices, and 13 of them are in at least one of Nina's classes.
so, the probability for the second pick is
13/19
so, the probability that both picks are in at least one of her classes is then the combination of both probabilities (they have to happen together) :
7/10 × 13/19 = 91/190 = 0.478947368...
4. Find the value of x to the nearest tenth.
35
o
11
O
12.9
O
6.3
O
-10
Answer:
11
Step-by-step explanation:
I don’t understand what to do, it says to find the area of the figure and I don’t know what that means.
Answer:
area is length x width multiply one side by the other
Step-by-step explanation:
Answer the questions below.
asapppppppppppppppppp
Answer:
a. mode
b. median
c. median
Step-by-step explanation:
the mode is the most common number
the median is when you order the numbers in order and use the middle number
Need help on this question help please
Which triangle is not similar to the other two triangles?
Answer:
First choice top-down
Step-by-step explanation:
The Similarity Theorem Side-Angle-Side it can be checked here to see what triangles are similar.
All 3 triangles have 2 congruent sides so the triangles are all isosceles.
The base angles of isosceles triangles are congruent so knowing this and that the sum of angles in a triangle is 180° we can calculate the measure of all angles.
180-20 = 160; 160/2 = 80°
180-30 = 150; 150/2 = 75°
Now we can conclude that Δ JLK is not similar with Δ MNO ≈ ΔPRQ
I’ll give brainliest!
Answer:
y = -x + 4
Step-by-step explanation:
y = mx + b
m - since the line is going downwards. the slope is negative
slope = rise / run = 1 / 1 = 1 but negatuve siunce diwnawards
b - this the y - intercept (when x = 0), the point of intersect is (0, 4)
Please help I don’t know how to do this
Step-by-step explanation:
when 2 objects are similar, that means that all the angles of one object are the same as the angles in the other object. and - the scaling factor of one pair of correlating sides is the same for all pairs of correlating sides.
therefore,
x/2.7 = 4.8/3.6 = 4/3
x = 4×2.7/3 = 4×0.9 = 3.6 m
A circle has a diameter of 12 units, and its center lies on the x-axis. what could be the equation of the circle? check all that apply. (x – 12)2 y2 = 12 (x – 6)² y² = 36 x² y² = 12 x² y² = 144 (x 6)² y² = 36 (x 12)² y² = 144
The equation of a circle with radius of 6 units and center on the x axis could be (x - 6)² + y² = 36
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The circle has a diameter of 12 units. Hence, radius = 12/2 = 6 units.
The center of the circle is at x axis (*, 0), the equation could be:
(x - 6)² + (y - 0)² = 6²
(x - 6)² + y² = 36
The equation of a circle with radius of 6 units and center on the x axis could be (x - 6)² + y² = 36
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Angelo can run 3 miles in 22
minutes. At this rate, how many
miles could she run in 33 minutes?
Answer: 4.52 miles
Step-by-step explanation:
Which expression is a factor of 12x2 29x – 8? x – 8 2x – 1 3x 8 4x 1
The factorization of the given expression is:
p(x) = (x - 2.66)*(x - 0.25)
Which expression is a factor?We have the quadratic equation:
12x^2 + 29x - 8
To get the factors we need to find the roots, then we use Bhaskara's formula:
[tex]x = \frac{-29 \pm \sqrt{29^2 - 4*(-8)*12} }{2*12} \\\\x = \frac{-29 \pm 35}{24}[/tex]
Then the solutions are:
x = (-29 + 35)/24 = 0.25
x = (-29 - 35)/24 = -2.66
Then the factors of the expression are:
(x - 2.66) and (x - 0.25)
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Triangle fgh is an isosceles right triangle with a hypotenuse that measures 16 units. an altitude, line segment g j, is drawn from the right angle to the hypotenuse. what is the length of line segment g j? 2 units 4 units 6 units 8 units
The square of the altitude is equal to the product of the base of the triangles
Triangular altitude theoremThe square of the altitude is equal to the product of the base of the triangles. The length of line segment GJ is 8units
According to the theorem;
GJ² = HJ*JF
Determine the value of x using the pythagorean theorem
[tex]x^2+x^2=16\\2x^2=16\\x^2=8\\x=\sqrt{8}\\x=2\sqrt{2}[/tex]
According to the theorem;
GJ² = HJ*JF
HJ + JF = 16
Since HJ = JF, hence
HJ = JF = 8
Substitute
GJ² = HJ*JF
GJ² = 8 * 8
GJ² = 64
GJ = 8units
Hence the length of line segment GJ is 8units
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Answer:
8
Step-by-step explanation:
Can someone help me on this, please?
convert both heights to inches:
Jack = 12 x 6 = 72 + 3 = 75 inches tall
Hill = 12 x 5 = 60 + 8 = 68 inches tall
now subtract:
75-68 = 7 inches
Jack is 7 inches taller
Step-by-step explanation:
here is your answer, step by step
Answer the two questions down below
Answer:
Step-by-step explanation:
a) Reflection over the x axis then a translation directly to the right
b) All the figures are conrguent since only rigid motions were used.
Find the slope of the line that passes through (3, 6) and (8, 7)
Answer:
The slope of this line is 1/5
Step-by-step explanation:
You can find the answer easily by graphing the problem. In doing so, you will find the slope (rise over run) to be one over five. This is because you rise one unit, and run five.
You're learning yoga in a fitness center which charges a $200 registration fee plus $12 per lesson. If an equation is made to
calculate the total charge you need to pay,
What would be the value of the slope?
What would be the value of the y - intercept? (0,blank)
The slope of the equation will be 12 and the y-intercept of the equation will be 200.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
You're learning yoga in a fitness center that charges a $200 registration fee plus $12 per lesson.
If an equation is made to calculate the total charge you need to pay.
Let y be the total amount and x be the number of the lesson. Then we have
y = 12x + 200
Then the slope of the equation will be 12 and the y-intercept of the equation will be 200.
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Complete the vector to fully describe the single transformation which takes shape a to shape b translate shape a by the sector.
The single transformation that maps shape a onto shape b is [tex]\left[\begin{array}{c}-5&-5\end{array}\right][/tex]
How to determine the vector transformation?From the figure, we have the following highlights
Both triangles are congruentTriangle B is 5 units down from triangle ATriangle B is 5 units left of triangle AThe above highlights mean that the triangle A must be translated 5 units left and 5 units down to get triangle B.
This is represented as:
(x,y) -> (x - 5, y - 5)
By vector representation, we have:
[tex]\left[\begin{array}{c}-5&-5\end{array}\right][/tex]
Hence, the single transformation that maps shape a onto shape b is [tex]\left[\begin{array}{c}-5&-5\end{array}\right][/tex]
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A rectangular garden measures by 30ft and 40ft. Surrounding (and bordering) the garden is a path 3ft wide. Find the area of this path. Be sure to include the correct unit in your answer
Answer:
312 ft²
Step-by-step explanation:
Area of the garden = Length x Width
Area of the garden = 30 x 40 = 1200ft²
Length of the garden and path = Length of the garden + 3 ft on both sides
Length of the garden and path = 30 + 3 + 3 = 36 ft
Width of the garden and path = Width of the garden + 2 ft on both side
Width of the garden and path = 40 + 3 + 3 = 46 ft
Area of the garden and path = Length x Width
Area of the garden and path = 36 x 46 = 1512 ft²
Area of the path = Area of the garden and path - Area of the garden
Area of the path = 1512 - 1200 = 312 ft²
Answer: 312 ft²
what is the value of 5 in 564,242
Answer:
The value of 5 is 500,000
Step-by-step explanation:
becuse their is 5 numbers behind it making it equivilant to 500,000
Hey there!
EXPANDED FORM:
500,000
+ 60,000
+ 4,000
+ 200
+ 40
+ 02
WORD FORM:
Five hundred 6
Sixty four thousand, two hundred forty two
PLACE VALUE FORM
5: 500,000 (hundred thousand)
6: 60,000 (ten thousand)
4: 4,000 (thousand)
,
2: 200 (hundreds)
4: 40 (tens)
2: 02 (ones)
To sum it is all up {5} is in the: [hundred thousands] place
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
The eccentricity of the conic section
graphed is:
a. Zero
b. Between 0 and 1
c. One
d. Greater than 1
The eccentricity of the conic section that is graphed is C. One.
What is eccentricity?It should be noted that the eccentricity of the clinic section simply means the distance from the point to its focus.
In this case, the eccentricity of the conic section that is graphed is one. The eccentricity value is usually constant for any conics.
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Answer:
The answer is B. Between 0 and 1
Step-by-step explanation:
What is (m - 5) divided by 4 where m = 17
Please help thanks!!!!!! I really appreciateeeee it!!!!!!!
Problem 7 (a)
Pick any two values you want for the radius and height (r and h). Repeats are allowed.
I'll go with r = 1 and h = 1
Compute the surface area of the cylinder with these parameters.
SA = 2pi*r^2 + 2*pi*r*h
SA = 2pi*1^2 + 2pi*1*1
SA = 2pi + 2pi
SA = 4pi
Now double the radius. We go from r = 1 to r = 2. Keep the height the same and compute the new surface area.
SA = 2pi*r^2 + 2*pi*r*h
SA = 2pi*2^2 + 2*pi*2*1
SA = 8pi + 4pi
SA = 12pi
The jump from 4pi to 12pi is "times 3".
Answer: The surface area triples========================================================
Problem 7 (b)
Let's go back to r = 1 and h = 1 again.
LSA = lateral surface area of the cylinder
LSA = 2*pi*r*h
LSA = 2*pi*1*1
LSA = 2pi
Now double r, but keep h the same
LSA = 2*pi*r*h
LSA = 2*pi*2*1
LSA = 4pi
Going from 2pi to 4pi is a jump of "times 2"
Answer: The lateral area doubles========================================================
Problem 7 (c)
We'll go back to r = 1 and h = 1.
Compute the volume of this cylinder.
V = pi*r^2*h
V = pi*1^2*1
V = pi
Then compute the volume with double the radius, but the same height
V = pi*r^2*h
V = pi*2^2*1
V = 4pi
The volume has quadrupled since we have gone from pi to 4pi.
Answer: Volume quadruples========================================================
Problem 8
The volume of the block, before the half cylinders are removed, is 10*3*8 = 240 cubic inches.
The two half cylinders removed can be rearranged to combine to a full cylinder. This empty space cylinder has a radius of 8/2 = 4 inches and height 3 inches. This means we'll be kicking out the volume of pi*r^2*h = pi*4^2*3 = 48pi cubic inches of empty space.
The resulting volume of this weird looking solid is 240-48pi cubic inches.
--------------
The front panel is a 3 in by 10 in rectangle. It has area of 3*10 = 30 square inches. The same goes for the back wall.
The top or ceiling panel is going to involve us first finding the area of the 8 by 10 rectangle (if you didn't remove those circular portions). So we have 8*10 = 80 square inches to start with. Then we kick out the circle of radius 4. So the top and bottom panels have area of 80 - 16pi square inches each.
The left and right curved walls are the lateral sides of a full cylinder of radius 4 inches and height 3 inches. This is when we combine the two curved sides to form one cylinder.
LSA = 2*pi*r*h = 2*pi*4*3 = 24pi
This means each curved wall is 24pi/2 = 12pi square inches in surface area
Now add up the 6 sides mentioned
(front)+(back)+(top)+(bottom)+(left)+(right)
(30)+(30)+(80 - 16pi)+(80 - 16pi)+(12pi)+(12pi)
220-8pi
--------------
Answers:Surface area = 220-8pi square inchesVolume = 240-48pi cubic inches.2
What value of x makes the equation below true?
3.3x + 3.0 = 16.2
A 9.9
B. 5.82
C. 4
D. 1.64
The surface area of a cube is 328.56 square inches. How long are it’s sides?
Answer:
7.4 in
Step-by-step explanation:
Surface area of a cube = 6s²
(where s is the side length)
Given:
SA = 328.56 in²Substituting the given value into the formula and solving for s:
⇒ 328.56 = 6s²
⇒ 328.56 ÷ 6 = 6s² ÷ 6
⇒ 54.76 = s²
⇒ s = √54.76
⇒ s = 7.4 in
TSA of a cube=328.56
Side be x
6x²=328.56x²=54.76x=√54.76x=7.4inBananatown is 75 miles due east of
Appleton. The distance from
Bananatown to Cherryville is 83 miles.
How far is Appleton from Cherryville?
Answer:
8 miles
Step-by-step explanation:
because 83-75=8 miles
Please help!
Select the correct answer. What are the factors of this quadratic function? the graph of a quadratic function with a maximum value at the point (3,4) and zeros at 1 and 5 A. (x − 1) and (x − 5) B. (x + 1) and (x + 5) C. (x − 1) and (x + 5) D. (x + 1) and (x − 5)
The factor of the quadratic equation will be (x − 1) and (x − 5). Then the correct option is A.
What is a quadratic equation?It's a polynomial with a value of zero. There exist polynomials of variable power 2, 1, and 0 terms. A quadratic equation is an equation with one statement in which the degree of the parameter is a maximum of 2.
The graph of a quadratic function with a maximum value at the point (3,4) and zeros at 1 and 5.
Then the factor of the quadratic equation will be (x − 1) and (x − 5).
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Answer:
A.
Step-by-step explanation:
A basketball player can make 25 free throws in 3.5 minutes. How
many free throws can he make in 12 minutes?
An isosceles triangle is such that each of the base angles is twice the vertical angle. find the angles of the triangle
Answer:
2x + 2x + x =180
x = 36 degree
Step-by-step explanation:
.
Which statement is a TRUE statement about rectangles?
The angles in a rectangle are all different.
All the sides in a rectangle are equal.
The sides in a rectangle are not parallel.
The opposite sides in a rectangle are equal.
Answer:
the opposite sides in a rectangle are equal
∠A and \angle B∠B are supplementary angles. If m\angle A=(3x+9)^{\circ}∠A=(3x+9)
∘
and m\angle B=(6x+27)^{\circ}∠B=(6x+27)
∘
, then find the measure of \angle A∠A.
78 is the answer
Step-by-step explanation:
The two angles are complementary so m<A + m<B = 90
we are given m<A = 3x + 9 and m<B = x - 11
substituting we get 3x + 9 + x - 11 = 90
4x - 2 = 90
4x = 92
x = 23
m<A = 3x + 9 = 3(23) + 9 = 78