The displacements are 2.84 cm, 2.77 cm, 2.83 cm and 2.83 cm respectively.
Instantaneous velocity of the particle at t =,1 is 0.72 cm/s.
How to calculate displacement and velocity?a. To find the displacement of the particle at various times t, we can simply plug the given value of t into the equation s = 2 sin(t) + 3 cos(t) and evaluate:
[1, 2]: s = 2 sin(1) + 3 cos(1) = 2.84 cm
[1, 1.1]: s = 2 sin(1.1) + 3 cos(1.1) = 2.77 cm
[1, 1.01]: s = 2 sin(1.01) + 3 cos(1.01) = 2.83 cm
[1, 1.001]: s = 2 sin(1.001) + 3 cos(1.001) = 2.83 cm
b. To find the instantaneous velocity of the particle when t = 1, we need to find the derivative of the equation for displacement with respect to time, which will give us the velocity. The derivative is given by:
v(t) = ds/dt = 2 cos(t) - 3 sin(t)
Plugging in t = 1 into this equation, we find:
v(1) = 2 cos(1) - 3 sin(1) = 0.72 cm/s
So, the instantaneous velocity of the particle at t = 1 is approximately 0.72 cm/s.
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Desmond is making chocolate chip pancakes for his whole family. He uses 3 cups of flour to make 20 equal -sized pancakes. How many cups of flour will be in each pancake?
0.15 cups of flour will be in each pancake.
As per the given data:
Desmond is making chocolate chip pancakes for his whole family.
He uses 3 cups of flour to make the 20 equal-sized pancakes.
Here we have to determine that how many cups of flour will be in each pancake.
Here we use the unitary method to find the number of cups of flour will be in each pancake.
Unitary method: The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Number of cups of flour in each pancake = [tex]$\frac{3}{20}[/tex]
= 0.15
Therefore 0.15 cup of flour in each pancake.
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f (x )equals fraction numerator 2 over denominator s plus 5 end fraction use the inverse laplace transform to find f (t ).
The inverse Laplace transform of (2/(s+5)) is f(t) = 2 * e^(-5t)u(t).
To find the inverse Laplace transform of F(s) = (2/(s+5)), we can use partial fraction expansion and then use a table of Laplace transforms to identify the inverse transforms.
Step 1: Perform partial fraction expansion on the fraction:
(2/(s+5)) = (2/5) * (1/(1+(s/5))) = (2/5) * (1/1 + (s/5))
Step 2: Recognize the form of the partial fraction as a geometric series, and use the formula for the sum of a geometric series to find the inverse Laplace transform:
The sum of this geometric series is
(2/5) * (1/(1-(-s/5)))
= (2/5) * (1/(1+s/5))
= (2/5) * (5/5+s)
= (2/(5+s))
Step 3: Use the table of Laplace transforms to find the inverse transform of (2/(5+s)):
f(t) = 2 * e^(-5t)u(t)
where u(t) is the unit step function.
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To save for retirement, starting from her 30th birthday (t = 0), Miss Saver will invest
some money each year in a 30-year deposit in her bank saving account. The first
payment of $1000 will be made at the beginning of the first year. Every subsequent
payment increases by 5%.
She will retire at age 60, and will withdraw $X each year from her bank saving account
from then. The first withdrawal will be made at age 60. After 20 years (i.e. after the
20th withdrawal), she will have taken out all the money she had saved.
Assuming the effective annual interest rate is 2% perpetually, compute the value of X.
Give your answer to the nearest integer.
Answer:
To calculate the value of X, we first need to calculate the total amount of money Miss Saver will have saved by the time she retires at age 60.
We know that her first payment is $1000, and that every subsequent payment increases by 5%. Using this information, we can calculate the total payments made during the 30 years:
$1000 x (1 + 0.05)^30 = $1000 x 3.3201 = $3320.1
This is the total amount of money Miss Saver will have saved by the time she retires at age 60.
Next, we need to calculate the value of each annual withdrawal over the 20 years of withdrawals.
We know that the effective annual interest rate is 2% perpetually, so we can use the formula for the future value of an annuity:
FV = X * ((1 + r)^n - 1) / r
where X is the annual withdrawal, r is the interest rate (0.02), and n is the number of years (20).
We can use this formula to solve for X:
3320.1 = X * ((1 + 0.02)^20 - 1) / 0.02
X = 3320.1 * 0.02 / (1.02^20 - 1)
X = 3320.1 * 0.02 / 0.1135 = $292.36
Therefore, Miss Saver needs to withdraw $292.36 each year for 20 years to deplete her savings account.
Rounded to the nearest integer, the value of X is $292.
Please help me solve this
Extra points
Answer:
D
Step-by-step explanation:
bc -1+27 =26
X
0
8
y
1
5
7
A parabola contains the points in the table.
a) Graph the points on the next DESMOS scre
b) Find the equation that models the quadratic
regression.
Answer:
Step-by-step explanation:
I need help pleaseeeeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation: [-2.19] = -3
[3.67] = 3
[-0.83] = -1
The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.
This can be generalized as given below:
[x] = -2, -2 ≤ x < -1
[x] = -1, -1 ≤ x < 0
[x] = 0, 0 ≤ x < 1
[x] = 1, 1 ≤ x < 2
Answer:
y = - [tex]\frac{3}{2}[/tex] x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line
m = [tex]\frac{0-3}{0-(-2)}[/tex] = [tex]\frac{-3}{0+2}[/tex] = - [tex]\frac{3}{2}[/tex] , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (0, 0 )
0 = - [tex]\frac{3}{2}[/tex] (0) + c = 0 + c , so
c = 0
y = - [tex]\frac{3}{2}[/tex] x + 0 , that is
y = - [tex]\frac{3}{2}[/tex] x
Aaron used the scaled picture on his jigsaw puzzle box as a guide for putting the puzzle together. Both the picture and the scale used to make it are shown below. According to the scale, what will the length of the finished puzzle be, in inches? A. inch B. inch C. 16 inches D. 32 inches
1. The receipt is for lunch for five students. Each student will pay 1/5 of the bill.
What will each student pay, excluding taxes and tip?
The required, each student will pay $10, as per the given condition.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The question seems to be incomplete,
Let's assume that the bill is of $50 excluding taxes
Now, each student has to pay = 50 / 5
= $10 per head
Thus, the required, each student will pay $10, as per the given condition.
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Determine if the following equation is an identity equation, a conditional equation, or an inconsistent equation. −2x+4−7x=−4+5−9x
The equation −2x+4−7x=−4+5−9x is an inconsistent equation.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is −2x+4−7x=−4+5−9x
Add the like terms on both sides
-9x+4=1-9x
inconsistent equation.
A system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system
Hence, the equation −2x+4−7x=−4+5−9x is an inconsistent equation.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The instantaneous rate of change of g(x) = 2/(x + 6) at x = 3 is given as follows:
g'(3) = -0.025.
How to obtain the instantaneous rate of change?The function for this problem is defined as follows:
g(x) = 2/(x + 6).
The instantaneous rate of change at x = a is defined as follows:
g'(a).
In exponent format, the function is defined as follows:
g(x) = 2(x + 6)^(-1).
Applying the chain rule, the derivative of g(x) is given as follows:
g'(x) = -2(x + 6)^(-2)[x + 6]'
g'(x) = -2/(x + 6)².
At x = 3, the numeric value of the derivative is given replacing the lone instance of x by 3, hence:
g'(3) = -2/(3 + 6)²
g'(3) = -2/81
g'(3) = -0.025.
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$4,640
$10,304
$2,500
$3,998
$3,000
$700
Part A
Based on the table, which college expenses would you consider fixed and which expenses would you consider variable?
Why?
Answer:Fixed expenses are those that do not change regardless of the level of production or consumption. Variable expenses are those that change in proportion to the level of production or consumption.
Based on the table provided, the following expenses can be considered fixed:
$4,640
$10,304
$2,500
$3,998
These expenses could be considered fixed because they do not appear to be directly related to the level of production or consumption. For example, $4,640 could be tuition fees, which remain the same regardless of how many classes a student takes or how much they use campus facilities.
The following expenses can be considered variable:
$3,000
$700
These expenses could be considered variable because they may be directly related to the level of production or consumption. For example, $3,000 could be the cost of books, which may change depending on the number of classes a student takes. $700 could be spending money for daily needs like food, transportation, or entertainment, which would likely vary depending on how much a student spends.
In conclusion, the distinction between fixed and variable expenses is based on the relationship between expenses and the level of production or consumption. The expenses listed above have been categorized as fixed or variable based on this relationship.
Karissa purchased a set of LED lights online that normally sells for $90 but was marked down to $67.60 what is the discount rate karissa received
The discount rate Karissa received is 12% discount.
What is discount rate?In a discounted cash flow (DCF) analysis, the interest rate used to calculate the present value of future cash flows is known as the discount rate. This aids in determining if the present-day capital outlay required to fund a project or investment will be greater than the value of the projected future cash flows from that project or investment.
The WACC and adjusted present value are the two main formulas for calculating the discount rate (APV).
WACC = E/V x Ce + D/V x Cd x (1-T) is the formula for the WACC discount, and
APV = NPV + PV of the impact of financing is the formula for the APV discount.
Take the change in price
65 - 57.20 =7.80
And divide by the original price
7.80/65=.12
Change to percent form
12%
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HELP FAST WILL MARK BRAINLYIST !!! You are a realtor who is preparing a brochure for future clients. You review a list of houses you recently sold in a particular neighborhood. The selling prices were as follows: $125,000, $125,000, $178,000, $190,000, $216,000, $225,000, and $890,000 Which measure best describes the typical selling price for a house in this neighborhood?
mode
median
mean
weighted mean
spread
The mode, median, mean ,weighted mean, spread of the set of data are: 125, 190, 278429, 765 respectively
What is Measure of central tendency?We are asked to find the following
Mode: This is the highest occurred frequency in a set of data and the mode here is 125
The median is the middle frequency when arranged in an order of magnitude the the set of data is $125,000, $125,000, $178,000, $190,000, $216,000, $225,000, and $890,000. the median is 190
The mean is the average of the data that is: ( $125,000,+$125,000+$178,000+$190,000+$216,000+$225,000+$890,000)/7 = 1949000/7 = 279429
the spread is the range which is the highest frequency minus the lowest frequency = $890,000 -$125,000= 765000
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Answer:
median
Step-by-step explanation:
Need help please, fast, here i screenshot!!
The equation g(x) = (x - 4) (x + 2) is in the factored form.
The x-intercepts are x = -2 and x = 4.
The axis of symmetry is x = 1.
Vertex is (1, -9).
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
g(x) = (x - 4) (x + 2)
This is in the factored form.
Now,
From the graph,
The x-intercepts are x = -2 and x = 4.
The axis of symmetry.
x = -b/2a
x = 2/2
x = 1
i.e
g(x) = (x - 4) (x + 2)
g(x) = x² + 2x - 4x - 8
g(x) = x² - 2x - 8
a = 1, b = -2, and c = -8
Now,
g(x) = x² - 2x - 8
g(x) = x² - 2x + 1 - 1 - 8
g(x) = (x² - 2x + 1) - 9
g(x) = (x - 1)² - 9
This is in the form of f(x) = a(x - h)² + k
So,
Vertex = (h, k) = (1, -9)
Thus,
The statements are completed above.
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What's the sum of this?
Answer:
sum = (m+n)(n-m +1)/2
Step-by-step explanation:
You want an expression for the sum of the numbers from m to n.
TotalsAs the example shows, the sums of the numbers written forward and backward will be the sum of the numbers at the ends of the range:
m +n
CountThe number of times this sum is repeated is equal to the number of numbers in the range:
n -m +1
Sum of rangeThe sum of the numbers in the range will be half the product of these values:
sum = (m+n)(n-m +1)/2
.The cost c of fish varies directly as its wieght w in kilograms.
a.Direct variation b.joint variation c.combined variation
2.The number of men n needed to do a job varies inversely as the number of days d to finish the job.
a.Direct variation b.Joint variation C.combined variation
The cost c of fish varies directly as its weight w in kilograms.
a.Direct variation
b.joint variation
c.combined variation
A SIMPLE RELATIONSHIP BETWEEN TWO VARIABLES IS DESCRIBED AS A DIRECT VARIATION.
When c=kw, where k is the variational constant, we say that c directly varies with w.
2. The quantity of men (n) required to complete a task varies inversely with the duration (d) of the task.
INVERSE VARIATION: Inverse variation occurs when the product of two variables (n and d) ALWAYS equals a fixed value (k). Example,
N=k/d states that the required number of men (n) varies inversely with the number of days (d) required to complete the task.
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At the dog park, there are several dogs with their owners. Counting heads, there are 20; counting legs, there are 62. How many dogs and owners are there?
What is the simplified form of this expression?
(5x2 + 2x + 11) − (7 + 4x − 2x2)
Answer:
Below
Step-by-step explanation:
(5x2 + 2x + 11) − (7 + 4x − 2x2) = 5x^2 + 2x + 11 - 7 - 4x + 2x^2 =
(5x^2 + 2x^2 ) + ( 2x-4x) +(11-7) =
7x^2 - 2x + 4
Sketch a cylinder with a diameter of 6 centimeters and a volume of 36 pay cubic centimeters. Then find its radius and height.
Label your sketch with the cylinder's radius and height
The radius of the cylinder is 3 cm and the height of the cylinder is 1.27 cm.
What is the radius of the cylinder?
The radius of the cylinder is half of the diameter of the cylinder and the value of the radius is calculated as follows;
r = d / 2
where;
d is the diameter of the cylinderr = ( 6 cm ) / ( 2 )
r = 3 cm
The height of the cylinder is calculated as follows;
V = πr²h
where;
h is the height of the cylinderr is the radius of the cylinderh = ( V ) / ( πr² )
h = ( 36 ) / ( π x 3² )
h = 1.27 cm
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You are choosing between two different cell phone plans. The first plan charges a rate of 24 cents per minute. The second plan charges a monthly fee of $29.95 plus 9 cents per minute.
Let
be the number of minutes you talk and
and
be the costs (in dollars) of the first and second plans. Give an equation for each in terms of t, and then find the number of talk minutes that would produce the same cost for both plans.
c1=
c2=
If you talk for ____ minutes the two plans will cost the same. (round your number to one decimal place)
Equation for charges of first plan
C₁ = 24.t
Equation for charges of second plan
C₂ = 9t + 2995
If we talk for _199.7__ minutes the two plans will cost the same.
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Given,
First plan charges rate of 24 cents per minute
C₁ = 24.t
C₁ is the charge of first plan
t is the number of minutes
Second plan charges $29.95 plus 9 cents per minute.
C₂ = 9t + $29.95
1 dollar = 100 cents
C₂ = 9t + 2995
Where C₂ is the charge of first plan
t is the number of minutes.
Let after x minutes the cost of both plans will be same
C₁ = C₂
24x = 9x + 2995
24x - 9x = 2995
15x = 2995
x = 2995/15
x = 199.667 ≈ 199.7 minutes
Hence, C₁ = 24.t and C₂ = 9t + 2995 are the equations for the charges of first plan and second plan respectively.
After talking 199.7 minutes the cost of two plans will be same.
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Di {XER} R: {YeR [122] gu)--(2-x-1 g(x)=2x g(x)--2x 9(*)-(2)^-1+2
base graph is correct
vertical reflection/stretch/compression (if any)
horizontal and vertical translation (if any)
Step-by-step explanation:
No vertical reflection, stretch, or compression has been applied.
Horizontal translation: The graph has been shifted to the right by 122 units.
Vertical translation: The graph has been shifted up by 2 units.
The charge for a taxi ride in New York City is $2.50 upon entry and $0.40 for each 1/5 of a mile traveled (rounded up to the nearest 1/5 mile), when the taxicab is traveling at 6 mph or more. In addition, a New York State Tax Surcharge of $0.50 is added to the fare. What is the cost of a taxi ride that is 14.3 miles?
Find the equation for the circle with a diameter whose endpoints are (-4,-3) and (-1,1).
write the standard equation for the circle
The equation of the circle will be x² +y² +7x +11.
What is the equation of a circle?A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).
The fixed point is referred to as the circle's origin or center, and the fixed distance between each point and the origin is referred to as the radius.
The general form of the equation of a circle is x² + y² + 2gx + 2fy + c = 0.
The equation can be written as:-
( x - x₁)( x - x₂) + ( y - y₁) ( y - y₂)
( x + 4 ) ( x + 3) + ( y + 1) ( y -1)
x² +7x +12 + y² - 1
x² + 7x + y² +11
Hence, the equation of the circle is x² + 7x + y² +11.
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Solve the system by elimination. b= 2x-y=14 "-3x+y=-6"
Answer:
below
Step-by-step explanation:
2x-y =14
-3x+y = -6 add these two equations together....this will 'eliminate' y
-x = 8
x = -8 use this value of x in one of the equations to find y = -30
Calculate the length w in the shape below.
Give your answer in centimetres to 2 d.p.
Answer:
w ≈ 12.14 cm
Step-by-step explanation:
using the tangent ratio in the right triangle on the left.
let vertical height be x
tan56° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{3.2}[/tex] ( multiply both sides by 3.2 )
3.2 × tan56° = x , then
x ≈ 4.744
using the cosine ratio in the right triangle on the right
cos67° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{w}[/tex] = [tex]\frac{4.744}{w}[/tex] ( multiply both sides by w )
w × cos67° = 4.744 ( divide both sides by cos67° )
w = [tex]\frac{4.744}{cos67}[/tex] ≈ 12.14 cm (to 2 decimal places )
Answer:
w = 12.14 cm
Step-by-step explanation:
See the attached image. Trigonometric functions will be used
Express the desired quantity as a definite integral and evaluate the integral using Theorem 2 .
Find the distance traveled by a train moving at 87 mph from 8:00 A.M. to 11:00 A.M.
Let t be the time elapsed in hours, starting at 8:00 A.M. So t = 0 at 8:00 A.M. and t = 3 at 11:00 A.M. The distance traveled by the train can be expressed as the definite integral of its velocity with respect to time:
distance = ∫(87 mph) dt from t = 0 to t = 3
Since mph is a unit of speed, we need to convert it to a unit of velocity (feet per second) in order to evaluate the integral:
87 mph = 87 miles/hour × 5280 feet/mile = 454840 feet/hour
distance = ∫(454840 ft/hr) dt from t = 0 to t = 3
distance = 454840 ft/hr * t from t = 0 to t = 3
distance = 454840 ft/hr * 3 hours
distance = 1364520 feet
So, the train travels a distance of 1364520 feet from 8:00 A.M. to 11:00 A.M.
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in this line of circles
Answer:
11
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.
Currently, there is 1 red circle and 3 blue circles, making the ratio 1: 3.
Adding 1 red circle would make the ratio 2: 3.Adding 8 circles would make the ratio 9: 3.Adding 11 red circles would make the ratio 12: 3.The ratio 12:3 can be simplified to get 4:1.
12 ÷ 3 = 43 ÷ 3 = 1Therefore, you will need to add 11 red circles to get the ratio 4: 1.
the passenger section of a train has width 2x-7, length 2x+3, and height x-2, with all dimensions in meters. solve a polynomial equation to determine the dimensions of the section of the train if the volume is 117m3
The dimensions of width, length and height of the passenger section of the train are 3 meters, 13 meters and 3 meters respectively.
What are the dimensions of the passenger section of the train?The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
Given that;
Width of the section = 2x - 7Length of the section = 2x + 3Height of the section = x - 2Volume = 117 m³First, plug in the given values into the above formula and solve for x.
V = w × h × l
117 = ( 2x - 7 )( 2x + 3 )( x - 2 )
Expand using FOIL method
( 2x - 7 )( 2x + 3 )( x - 2 ) = 117
( 2x(2x) + 2x(3) - 7(2x) - 7(3) )( x - 2) = 117
( 4x² - 8x - 21 )( x - 2 ) = 117
Expand
4x³ - 16x² - 5x + 42 = 117
4x³ - 16x² - 5x + 42 - 117 = 0
4x³ - 16x² - 5x - 75 = 0
Using rational roots text
(x - 5)(4x² + 4x + 15 ) = 0
( x - 5 ) = 0
x - 5 = 0
x = 5
4x² + 4x + 15 = 0
x = -1±i√14 / 2
Since dimensions are real and positive numbers, we use;
x = 5
To determine the dimensions of the passenger section of the train, plug in x = 5 and simplify.
Width = 2x - 7 = 2( 5 ) - 7 = 10 - 7 = 3 meters
Length = 2x + 3 = 2( 5 ) + 3 = 10 + 3 = 13 meters
Height = x - 2 = 5 - 2 = 3 meters
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which of the following decimal numbers can be represented accurately with a finite number of binary bits in the binary system?
Among the given, only 0.5 can be exactly represented in binary notation with a finite number of bits
Hence, option (d) is the correct choice.
Binary is a base-2 number system in which a number is represented by two states: 0 and 1. We can also refer to it as a true and false condition. A binary number is constructed in the same manner as a decimal number.
Binary data is information expressed or displayed using the binary number system. Binary data is the only type of data that a computer can directly understand and execute. It is represented numerically as a series of zeros and ones.
The binary representation of 0.5 is 0.1_2, and it is the only terminating fraction among the available possibilities.
As a result, it is the only fraction that can be expressed precisely.
All of the other possibilities have a non-terminating fraction portion and hence cannot be expressed accurately with a limited amount of bits.
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The complete question may be:
Which of the following decimal numbers can be exactly represented in binary notation with a finite number of bits?
(a) 0.1
(b) 0.2
(c) 0.4
(d) 0.5
(e) All the above
How many terminating zeros are at the end of 6311! ,when this number is multiplied out?
The number of terminating zero when the number 6311! is multiplied out is 252
What it terminating zeros?In mathematics, trailing zeros are a series of digits (usually 0) that follow a number's decimal form or, more broadly, any positional representation.
In mathematics, the term "factorial" refers to the product of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point.
Thus, factorial five is denoted by the symbol 5!, which stands for 1 * 2 * 3 * 4 * 5. Factorial 0 is equivalent to 1 by definition.
For the problem 6311! has 252 trailing zeros
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Answer:
1576 terminating zeros---------------------------
Terminated zeros at the end of number n! is found as the sum of the whole quotients of n and powers of 5 less than n.
Given:
n = 6311.This is greater than 5⁵ = 3125 but less than 5⁶ = 15625.
Find each quotient of 6311 and 5¹ through 5⁵ :
6311/5¹ = 1262,6311/5² = 252,6311/5³ = 50,6311/5⁴ = 10,6311/5⁵ = 2.Sum of the quotients is the number of terminating zeros:
1262 + 252 + 50 + 10 + 2 = 1576