Answer:
1/4
Step-by-step explanation:
it came to me in a dream.
1/4 or 25% is the probability that the randomly selected point is in the bullseye.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The area of the bullseye is the area of the inner circle with a radius of 4 cm. Similarly, the area of the entire target is the area of the outer circle with a radius of 8 cm.
The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
Therefore, the area of the bullseye is:
A_bullseye = π(4 cm)² = 16π cm²
And the area of the entire target is:
A_target = π(8 cm)² = 64π cm²
So, the probability that the randomly selected point is in the bullseye is the ratio of the area of the bullseye to the area of the target:
P(bullseye) = A_bullseye / A_target
P(bullseye) = (16π cm²) / (64π cm²)
P(bullseye) = 1/4
Therefore, the probability that the randomly selected point is in the bullseye is 1/4 or 25%.
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Michael read 135 pages in 90 minutes. Select all the rates that have the same constant rate of change as michael's
The same constant rate of change as Michael's is depicted in following ratio - 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.
The rate of reading Michael is -
Rate = 135/90
Rate = 3:2
Now, we will check the options to see if they have same ratio.
Option 1 180 page in 2 hours
As known about time conversion that 1 hour has 60 minutes, 2 hours = 120 minutes
So, Rate = 180/120
Rate = 3:2
Option 2 60 pages in 30 minutes
Rate = 60/30
Rate = 2:1
Option 3 108 pages in 2 and half hours
Time = 2.5 hours
Time = 150 minutes
Rate = 108/150
Rate = 18:25
Option 4 150 page in 1 hour
Rate = 150/60
Rate = 5:2
Option 5 225 pages in 150 minutes
Rate = 225/150
Rate = 3:2
Option 6 210 pages in 2 hour 20 minutes
Time = 140 minutes
Rate = 210/140
Rate = 3:2
Hence, the same rate options are 180 page in 2 hours, 225 pages in 150 minutes and 210 pages in 2 hour 20 minutes.
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The complete question is -
Michael read 135 pages in 90 minutes. Select all of the rates that have the same constant rate of change as Michael's rate. 180 pages in 2 hours, 60 pages in 30 minutes, 108 pages in 2 and half hours, 150 pages in 1 hour, 225 pages in 150 minutes, 210 pages in 2 hour 20 minutes
Noah spent $2.50 on 2 bags of peanuts and 1 bottle of water at a baseball game.
Emily spent $4.25 on 3 bags of peanuts and 2 bottles of water.
Lily bought 2 bottles of water and 1 bag of peanuts.
If they all paid the same amount for peanuts and water how much did lily spend?
The amount of money Lily spent on peanuts and water is 2.75 dollars.
How to find the amount Lily spent?Noah spent $2.50 on 2 bags of peanuts and 1 bottle of water at a baseball game.
Emily spent $4.25 on 3 bags of peanuts and 2 bottles of water.
Using equation,
where
x = cost of each bag of peanuty = cost of a bottle of waterTherefore,
2x + y = 2.50
3x + 2y = 4.25
multiply equation(i) by 2
4x + 2y = 5
3x + 2y = 4.25
x = 0.75 dollars
y = 2.50 - 2(0.75)
y = 2.50 - 1.5
y = 1 dollars
Therefore,
cost of Lily expenses = 2(1) + 0.75(1)
cost of Lily expenses = 2 + 0.75
cost of Lily expenses = 2.75 dollars
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What is the area of the base of this right rectangular prism?
plsss help
Step-by-step explanation:
Base area is 6 in x 4 in = 24 in^2
Now if you multiply by the height you will get the VOLUME in units of in^3
Over the course of a month, Santiago spoke to his mom on his cell phone for 45 minutes, his dad 30 minutes, and his friends for 110 minutes. What operation would you use to determine the total number of cell phone minutes that Santiago used?
Santiago used 185 cell phone minutes over the course of a month.
To determine the total number of cell phone minutes that Santiago used over the course of a month, you would use the operation of addition.
You would add up the number of minutes that Santiago spoke with his mom, dad, and friends:
Total cell phone minutes = 45 minutes + 30 minutes + 110 minutes
Total cell phone minutes = 185 minutes
Therefore, Santiago used 185 cell phone minutes over the course of a month.
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ANSWER THIS QUESTION QUICKLY PLS!
Nine people sit in chairs in a room.
In how many ways can four of these people be chosen to stand up?
Enter your answer in the box.
Step-by-step explanation:
Assuming the order matters....i.e. they stand up one at a time
(question does not state how the 4 are chosen)
9 choices for first
8 choices for second
7 choices for third
6 choices for fourth
9 x 8 x 7 x 6 = 3024 ways
this is 9 P 4 = 9!/5! = 3024
the domain of function f is (-oo, oo). the value of the function what function could be f
The domain of rational function f(x) = (x² - 36) / (x - 6) is x ∈ (- ∞, + ∞).
How to find a function associated with a given domain
In this question we must determine what function has a domain, that is, the set of all x-values, that comprises all real numbers. According to algebra, polynomic functions have a domain that comprises all real numbers.
Herein we need to determine what rational function is equivalent to a polynomic function. Polynomic functions are expression of the form:
[tex]y = \sum\limits_{i = 0}^{n} c_{i}\cdot x^{i}[/tex]
Where:
[tex]c_{i}[/tex] - i-th Coefficient of the polynomial.[tex]x^{i}[/tex] - Power of the i-th term of the polynomial.y - Dependent variable.Now we check the following expression by algebra properties:
f(x) = (x² - 36) / (x - 6)
f(x) = [(x - 6) · (x + 6)] / (x - 6)
f(x) = x + 6
The rational function f(x) = (x² - 36) / (x - 6) is equivalent to polynomial of grade 1 and, thus, its domain comprises all real numbers.
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HELP FAST. 2
If Tom travels 3 and 2/5 of a mile in 5 hours on his skateboard. How far will he travel in 1 hour?
Group of answer choices
17/25 miles per hour
15 miles per hour
1 and 8/17 miles per hour
25/17 miles per hour
Answer: 17/25 miles per hour
Step-by-step explanation:
In order to find your answer, you will need to divide 3 and 2/5 by 5 hours
or (3.4/5) which equals 0.68.
As a fraction, 0.68 is 17/25 which is your answer :)
And if you want to check your work, simply multiply 0.68 x 5 and you get 3.4 (which is 3 and 2/5's)!
Good Luck!
The number of people who visited a winter carnival
during the first 7 hours of a day was recorded, as
shown.
79, 83, 50, 69, 86, 77, 88
It was later found that the number of people who
visited during 4th hour was incorrectly recorded. It
should have been 96. Enter a number in each box
to make the statements true.
The range of the incorrectly recorded data is
The actual range of the data is
Answer: The range of the incorrectly recorded data is:
96 - 50 = 46
The actual range of the data is:
96 - 50 = 46
The range is not affected by the correction of the 4th hour data because the range only depends on the difference between the highest and lowest values, which remains the same.
Step-by-step explanation:
Find m∠D and m∠C in rhombus BCDE.
In the rhombus, m<D is 16^o and m<C is 164^o.
What is a rhombus?A rhombus is a quadrilateral which has equal length of sides, but stands on one of its edges. One of its major properties is that the measure of opposite internal angles are congruent.
The sum of the internal angles of a rhombus gives 360^o.
So that in the given diagram, we can deduce that;
y + y + (4y + 100) + (4y + 100) = 360^o
2y + 8y + 200 = 360
10y = 360 - 200
= 160
y = 160/ 10
= 16
y = 16^o
So that;
(4y + 100) = 4*16 + 100
= 64 + 100
= 164^o
Therefore, m<D is 16^o and m<C is 164^o.
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(e) A company has 8000 employees. 3600 of them belong to a certain labour union. A
committee of 20 people must be selected. If the selection is random, what is the probability
that 12 of the selected people belong to the labour union?
The probability that exactly 12 of the selected people belong to the labor union is approximately 0.167 or 16.7%.
To solve this problem, we can use the binomial probability formula:
[tex]P(X = k) = (n choose k)p^{k}(1 - p)^{(n - k)}[/tex]
where:
- P(X = k) is the probability of getting k successes (12 in this case)
- n is the number of trials (20 in this case)
- p is the probability of success (belonging to the labor union, which is 3600/8000 or 0.45)
- (n choose k) is the number of ways to choose k items from a set of n items, which is given by the binomial coefficient formula (n! / (k! (n-k)!))
So, plugging in the values we get:
[tex]P(X = 12) = (20 choose 12) (0.45)^{12} (1 - 0.45)^{(20 - 12)}\\ = (167,960)(0.45)^{12}(0.55)^{8}\\ = 0.167[/tex]
Therefore, the probability that exactly 12 of the selected people belong to a labor union is approximately 0.167 or 16.7%.
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Year-round-Recreation sells recreation vechiles (cross country motorcycles to snowmobiles) and has total costs given by
C(e) 2750+30x+2
and the total revenues for Year-round-Recreation is given by
R(z) = 135x
Find the x-values of the break-even points.
The break-even x-value(s) are (separate by commas - order does not matter)
The break-even x-value for Year-round-Recreation is approximately 26.19.
To find the break-even points for Year-round-Recreation, we need to set the total costs equal to total revenues and solve for x. In this case, the total costs are given by C(x) = 2750 + 30x + 2, and the total revenues are given by R(x) = 135x.
The break-even point is when C(x) = R(x), so:
2750 + 30x + 2 = 135x
Now, we need to solve for x:
1. Subtract 30x from both sides:
2750 + 2 = 105x
2. Subtract 2 from both sides:
2750 = 105x
3. Divide both sides by 105:
x = 2750 / 105
x ≈ 26.19
The break-even x-value for Year-round-Recreation is approximately 26.19.
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Determine the intervals on which the function is concave up or down and find the value at which the inflection point occurs. Y = 8x' – 3x+ (Express intervals in interval notation. Use symbols and fractions when needed)
The value of the inflection point is 1/10, and the intervals on which the function is concave up or down are (0, 1/10) and (1/10, ∞).
Taking the second derivative of y(x), we get:
y''(x) = 240x³ - 24x²
Setting y''(x) equal to zero and solving for x, we get:
x = 0 or x = 1/10
These critical points divide the real line into three intervals:
(-∞, 0), (0, 1/10), and (1/10, ∞)
We evaluate the sign of y''(x) on each of these intervals to determine where the function is concave up or down:
For x < 0: y''(x) < 0, so y(x) is concave down.
For 0 < x < 1/10: y''(x) > 0, so y(x) is concave up.
For x > 1/10: y''(x) > 0, so y(x) is concave up.
Therefore, the function is concave down on the interval (-∞, 0) and concave up on the intervals (0, 1/10) and (1/10, ∞).
To find the inflection point, we set y''(x) equal to zero and solve for x:
240x³ - 24x² = 0
Factor out 24x²:
24x²(10x - 1) = 0
So either x = 0 or x = 1/10.
Since the second derivative changes sign at x = 1/10, this is an inflection point.
Therefore, the inflection point occurs at x = 1/10.
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The question is -
Determine the intervals on which the function is concave up or down and find the value at which the inflection point occurs.
Y = 8x^5 - 3x^4
(Express intervals in interval notation. Use symbols and fractions when needed)
point of influence at x = __________
interval on which function is concave up = ____________
interval on which function is concave down = ___________
Write a Ratio
Samantha has 6 apples and 5 bananas in a fruit basket.
RATIOS
as a fraction using a colon
with words
apples to
bananas
bananas to
total fruit
total fruit to
apples
5 to 11
6:5
5:11
6 to 5
5
11
11
6
Un lo
11:6
11 to 6
In a case whereby Samantha has 6 apples and 5 bananas in a fruit basket,the ratio of apple to banana is 6:5, the ratio of banana to total fruit is 5:11
How can the rato be calculated?A ratio can be desribed as the the quantitative relation that is been established when dealing with two amounts showing the number of times onethe first value contains compare to another value.
It should be noted that the total number of the fruit is (6+5)= 11
the ,the ratio of apple to banana is 6:5, the ratio of banana to total fruit is 5:11
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Which table shows a linear function
The table that shows a linear function include the following: B. table B.
What is a linear function?In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
In this context, we have:
Slope = (0 - 2)/(-3 + 5) = (2 - 0)/(-3 + 1) = -1
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14. Divide (x4 - 5x² + 2x-8) + (x+2)
Answer: Dividing (x⁴ - 5x² + 2x - 8) by (x + 2) using polynomial long division:
x³ - 2x² - x + 4
________________________
x + 2 | x⁴ - 5x² + 2x - 8
| x⁴ + 2x³
| _____________
-2x³ + 2x²
-2x³ - 4x²
_____________
6x² + 2x
6x² + 12x
_____________
-10x - 8
Therefore, the quotient is x³ - 2x² - x + 4 and the remainder is -10x - 8.
Step-by-step explanation:
PLEASE ANSWER QUICK!!!!! 25 POINTS
find the probability of exactly one successes in five trials of a binomial experiment in which the probability of success is 5%
The probability of one success in five trials in the binomial experiment with a success probability of 5 % is 20. 4 %.
How to find the probability of success ?The formula for calculating the likelihood of one success in a binomial probability with a 5% chance of success is:
P ( X = 1) = (5 choose 1) x ( 0.05 ) x (0.95 ) ⁴
Solving for this success would give :
= ( 0.05 ) x ( 0. 95 ) ⁴
= 0.05 x 0.8145
= 0.040725
Then we multiply both sides to get :
P(X = 1) = 5 x 0.040725
= 0.203625
= 20. 4 %
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A student designed a flag for the school's Gaming Club. The design is rectangular with vertices at (3, 7), (11, −9), and (3, −9). Find the missing vertex and the area of the flag in square inches?
The missing vertex is (−9, 7) with an area of 16 in2.
The missing vertex is (7, 11) with an area of 16 in2.
The missing vertex is (−9, 11) with an area of 128 in2.
The missing vertex is (11, 7) with an area of 128 in2.
Answer:
(11, 7) with an area of 128 in2.
Step-by-step explanation:
Find the missing side. Round
to the nearest tenth.
Х
у
39°
57
y=[?]
For a right angled triangle with side length 57, x and y, the missing sides lenths x and y are equal to the 73.1 and 46.17 respectively.
See the above figure, we have a right angled triangle. Let the be say ABC with measure of angle B be 90°, and the three sides of triangle are defined as length of base of triangle, BC = 57
height of triangle, AB = y
length of hypothonous, AC = x
measure of angle C = 39°
measure of angle B = 90°
So, measure of angle of A = 180° - 90° - 39° = 51°
We have to determine the missing length of sides. Using the trigonometry functions, for determining the value x and y. So, [tex]Cos(39°) = \frac{ 57} {x} [/tex]
=> [tex]x = \frac{ 57} {Cos(39°)} [/tex]
=> x = 57/0.78 = 73.1
Similarly,
[tex]tan(39°) = \frac{y} {57} [/tex]
=> y = 57 × tan(39°)
=> y = 0.81 × 57 = 46.17
Hence, required value is 46.17.
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Complete question:
The above figure complete the question.
A triangle has sides with lengths of 5 feet 11 feet and 13 feet is it a right triangle
Answer:
no
Step-by-step explanation:
to be a right triangle it must satisfy the Pythagoras theorem. 5-12-13 works
Answer:
Yes.
Step-by-step explanation:
29,61,90 are right triangles
15+11+13 is 29 therefor its a right triangle
pls help with this question fast
The slope of any line parallel to the given line is also 9.
The slope of any line perpendicular to the given line is -1/9.
We have,
The given line is y = 9x - 6
This is in the form of y = mx + c.
So,
The slope of the line is 9.
Now,
Parallel lines have the same slope,
So the slope of any line parallel to the given line is also 9.
Perpendicular lines have negative reciprocal slopes,
So the slope of any line perpendicular to the given line is -1/9.
Thus,
The slope of any line parallel to the given line is also 9.
The slope of any line perpendicular to the given line is -1/9.
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Carlos has a square tablecloth with a total area of 48
square feet. Which measurement is closest to the length of each side of the tablecloth in feet?
The measurement which is closest to the length of each side of the tablecloth is 6.9 feet.
Which measurement is closest to the length of each side of the tablecloth in feet?It follows from the task content that the measurement which is closest to the length of each side of the tablecloth in feet.
Total area of the square tablecloth = 48 square feet
Area of a square = Side length²
48 = Side length²
Find the square root of both sides
Side length = √48
= 6.928203230275
Approximately,
Side length = 6.9 feet
Therefore, the side length of the table cloth is 9.6 feet.
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3 2. Find y' when x' - xy + y = 4 and y = f(x).
y' = f'(x) = (4 - C1e^x)/(1 - x)^2
Differentiate the given equation with respect to x:
x' - xy + y = 4
Differentiating both sides with respect to x using the product rule, we get:
x'' - y - xy' + y' = 0
Simplifying, we get:
x'' + (y - 1)y' = 0
Now, since y = f(x), we can write y' as f'(x). Substituting in the above equation, we get:
x'' + (f(x) - 1)f'(x) = 0
This is a first-order linear differential equation, which we can solve using an integrating factor. The integrating factor is e^(-x). Multiplying both sides by e^(-x), we get:
e^(-x)x'' + e^(-x)(f(x) - 1)f'(x) = 0
Using the product rule on the left-hand side, we can rewrite this as:
(e^(-x)x')' + e^(-x)f'(x) - e^(-x)f'(x) = 0
Simplifying, we get:
(e^(-x)x')' = 0
Integrating both sides with respect to x, we get:
e^(-x)x' = C1
where C1 is a constant of integration. Solving for x', we get:
x' = C1e^x
Substituting this into the original equation, we get:
C1e^x - xy + y = 4
Solving for y, we get:
y = (C1e^x + 4)/(1 - x)
Now, since y = f(x), we can write:
f(x) = (C1e^x + 4)/(1 - x)
To find y', we differentiate this expression with respect to x:
f'(x) = [(C1e^x)(-1) - 4(-1)]/(1 - x)^2
Simplifying, we get:
f'(x) = (4 - C1e^x)/(1 - x)^2
Now, substituting this expression for f'(x) into the earlier equation, we get:
x'' + (f(x) - 1)f'(x) = 0
x'' + [(C1e^x + 4)/(1 - x) - 1][(4 - C1e^x)/(1 - x)^2] = 0
Simplifying, we get:
x'' - (3C1e^x + 4)/(1 - x)^2 = 0
Thus, the expression for y' is:
y' = f'(x) = (4 - C1e^x)/(1 - x)^2
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if two numbers have a difference of 56 and we let x represent the smaller of these two numbers, then the larger of these two numbers is given by the following.
If x represents the smaller of the two numbers, then the larger number can be represented as x + 56 (since the difference between the two numbers is 56).
Large numbers are numbers that are larger than those used in everyday life, such as simple calculations or currency operations, and often appear in fields such as mathematics, cosmology, cryptography, and similar mathematical machine. These are usually good numbers or more likely really good numbers, but there may be other numbers in other situations.
Given that the difference between the two numbers is 56, and x represents the smaller number, the larger number can be represented as x + 56.
This is because the larger number is 56 units greater than the smaller one (x). So, the larger number is given by the expression: x + 56.
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Archie invests $27000 into his savings account with an interest rate of 2. 25% compounded monthly. What’s Archie’s balance of his savings account after 8 years?
Archie's balance in his savings account after 8 years with an interest rate of 2. 25% is approximately $33,030.19.
To calculate the balance of Archie's savings account after 8 years, we can use the formula:
[tex]A = P(1 + r/n)^{(nt)}[/tex]where A is the final amount, P is the principal (initial amount invested), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Substituting the given values, we get:
A = 27000(1 + 0.0225/12)⁽¹²ˣ⁸⁾
Simplifying, we get:
A = 27000(1.001875)⁹⁶
A = 27000(1.22034)
A = 33030.19
Therefore, Archie's balance in his savings account after 8 years is approximately $33,030.19.
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Please help ASAP! I need to finish this TODAY
The school which is a better choice is sea side.
We are given that;
The plot
Now,
If you are interested in a smaller class size, Seaside School is a better choice for you because it has a smaller mean and median class size than Bay Side School. This means that on average and in general, Seaside School has fewer students per class than Bay Side School. Also, Seaside School has a smaller maximum class size than Bay Side School (both have a minimum of zero), so you are less likely to encounter a very large class at Seaside School.
Therefore, by algebra the answer will be sea side.
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PLS HELP ASAP THANKS
Answer:−
2x2−8x−9
Step-by-step explanation:
Use the table of values to calculate the linear correlation coefficient r. X 4,53,86,162 Y 5,1,13,16
5 and 1 is a negative
The rank correlation is 1, this means that the two variables being compared are monotonically related, even if their relationship is not linear.
Given the data
X, ...rankX.....Y.....rankY......d=rx-ry........d²
4.........4...........-5......4................0..............0
53.......3.........-1........3................0...............0
86.......2.........13.......2................0................0
162......1..........16.......1.................0...............0
Then, using the rank correlation formula
p = 1 — 6•Σd² / n(n²—1)
p = 1 - 6• 0 / 4(4²-1)
p = 1 - 0
p = 1
So, the rank correlation is 1, this means that the two variables being compared are monotonically related, even if their relationship is not linear.
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Full Question: Use the table of values to calculate the linear correlation coefficient r.
X Y
4 -5
53 -1
86 13
162 16
use law of sines to solve triangle with B=52 C=15 b=43
Using the Law of Sines, we can solve the given triangle with B = 52, C = 15, and b = 43. The three angles of the triangle are approximately A = 112.94°, B = 52°, and C = 15°, and the lengths of the sides opposite these angles are approximately a = 28.29, b = 43, and c = 8.11.
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all sides and their opposite angles. Therefore, we can use the Law of Sines to solve the given triangle as follows
sin(A)/a = sin(B)/b = sin(C)/c
We are given B = 52, C = 15, and b = 43, so we can use the Law of Sines to find a
sin(A)/a = sin(B)/b
sin(A)/a = sin(52)/43
sin(A) = a sin(52)/43
a = 43 sin(A)/sin(52)
Similarly, we can use the Law of Sines to find c
sin(A)/a = sin(C)/c
sin(A)/a = sin(15)/c
sin(15)c = a sin(A)
c = a sin(A)/sin(15)
Now, we can substitute the expressions for a and c into the equation sin(A)/a = sin(B)/b and solve for sin(A)
sin(A)/(43 sin(A)/sin(52)) = sin(52)/43
sin(A) = (43 sin(52) sin(15))/c
Substituting the expression for c, we get
sin(A) = (43 sin(52) sin(15))/(a sin(A)/sin(15))
Simplifying, we get
sin²(A) = (43²sin²(52) sin²(15))/(a²sin²(A))
Multiplying both sides by a^2 sin^2(A), we get
a²sin⁴(A) = 43^2 sin²(52) sin²(15)
Taking the square root of both sides and solving for a, we get
a = √((43² sin₂(52) sin²(15))/(sin⁴A)))
Substituting the given values and solving for A, we get
a = 28.29 (approx)
A = 112.94° (approx)
c = 8.11 (approx)
Therefore, the three angles of the triangle are approximately A = 112.94°, B = 52°, and C = 15°, and the lengths of the sides opposite these angles are approximately a = 28.29, b = 43, and c = 8.11.
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Question 8(Multiple Choice Worth 3 points)
(07.04 MC)
Given u = -7i - 5j and v= -10i - 9j, what is projvu?
O-9.9371-8.943j
O-6.956i-4.968j
O-6.354i-5.718j
-4.448i-3.177j
The projection of vector u in the direction of vector v is equal to P = - 6.354 i - 5.718 j.
How to find the projection of a vector with respect to other vector
In this problem we need to determine the expression of the projection of vector u in the direction of vector v, whose formula is now introduced:
P = [(u • v) / ||v||²] · v
Where:
u, v - Vectors||v|| - Norm of vector v.If we know that u = - 7 i - 5 j and v = - 10 i - 9 j, then the projection of the vector is:
u • v = 70 + 45
u • v = 115
||v||² = 100 + 81
||v||² = 181
P = (115 / 181) · (- 10 i - 9 j)
P = - (1150 / 181) i - (1035 / 181) j
P = - 6.354 i - 5.718 j
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The distance of a swinging pendulum from its resting position is given by the function d(t)=
5.5cos(8t), where the distance is in inches and the time is in seconds. Once released, how
long will it take the pendulum to reach its resting position? Round your answer to the near-
est hundredth.
It will take the pendulum approximately 0.20 seconds to reach its resting position.
We have,
The resting position of the pendulum is when d(t) = 0.
So we need to solve the equation:
5.5cos(8t) = 0
We know that cos(0) = 1 and that cos(π) = -1, and that the cosine function has a period of 2π.
Therefore, the first time the pendulum will reach its resting position is at
t = 0, and then it will reach its resting position again at t = π/8.
However, we are interested in the time it takes for the pendulum to go from its starting position to its resting position, which is half of its period.
So the time it takes for the pendulum to reach its resting position is:
t = π/8 / 2
t = π/16
Using a calculator, we can approximate this value to the nearest hundredth:
t = 0.20 seconds
Therefore,
It will take the pendulum approximately 0.20 seconds to reach its resting position.
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