The total number of ways by words are formed is 35 ways.
According to the statement
We have given that the 5 letters and we have to make word from them and the letters are repeated as equal to letters in given words.
And we have to find the possible ways.
So, The given words are:
TEXAS and MEXICO
Here X = 2 and E = 2 and all other words are one time used words.
We can find possible ways by use of combination and permutation.
So,
Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]
here 3 because three letters are not repeatable and 2 letters are repeated for 2 times.
So,
Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]
Total number of ways = [tex]3(\frac{5!}{1!} ) + 2(\frac{5!}{2!*3!} )[/tex]
Total number of ways = [tex]3(5) + 2(10)[/tex]
Total number of ways = 15 + 20
Total number of ways = 35.
So, The total number of ways by letters are formed is 35 ways.
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A fruit basket contains only apples and bananas. If there are 8 apples and 13 bananas, what is the ratio of bananas to fruit? Select all that apply.
13:8
13:21
StartFraction 8 Over 13 EndFraction
21 to 13
StartFraction 13 Over 21 EndFraction
The ratio of bananas to fruit is 13 : 21
How to determine the ratio of bananas to fruit?The given parameters are
Banana = 13
Apple = 8
The total number of fruits is
Fruit = Banana + Apple
Substitute the known values in the above equation
Fruit = 13 + 8
Evaluate the sum
Fruit = 21
The ratio of bananas to fruit is then represented as:
Ratio = Banana : Fruit
Substitute the known values in the above equation
Ratio = 13 : 21
Hence, the ratio of bananas to fruit is 13 : 21
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13. The average of 15, 19, 23, 41, and x is 20. What is the value of x? (A) 2 (B) 20 (C) 23.6 (D) 31
Answer:
A
Step-by-step explanation:
(x + 15 + 19 + 23 + 41) / 5 = 20
x + 15 + 19 + 23 + 41 = 100
x + 98 = 100
x = 2
Answer: it’s 2 (A)
Step-by-step explanation:
20 * 5 = 100
15 + 19 + 23 + 41 = 98
100-98=2
If a1=6 and a5=12, what does a3=?
a3=9
assuming the pattern is constant, a3 is right in the middle of a1 and a5 so the answer would be right in the middle of 6 and 12. the average of 6 and 12 is 9, so a3=9.
hope this helps!
A small pizza has an area of 730 square centimeters.
Write an inequality that describes p, the area of a
pizza that is larger than a small pizza.
The inequality that describes p, the area of a pizza that is larger than a small pizza 730 < p
How to determine the inequality
From the information given, we have that;
Area of the small pizza = 730 square centimeters
p = area of the larger pizza
In writing inequality, we have to use the signs
< less than
> greater than
Since p has greater area, we have
730 < p
Thus, the inequality that describes p, the area of a pizza that is larger than a small pizza 730 < p
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Answer:
the answer is actually p > 730
Step-by-step explanation:
i juts checked on Kahn academy and i got it right..
The graph of the step function g(x) = –⌊x⌋ + 3 is shown.
On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 2, 5) to (negative 1, 5). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, negative 1) to (5, negative 1).
What is the domain of g(x)?
{x| x is a real number}
{x| x is an integer}
{x| –2 ≤ x < 5}
{x| –1 ≤ x ≤ 5
Using it's concept, the domain of the function is given as follows:
{x| –2 ≤ x <= 5}
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function, that is, the values for which the function is defined.
The function described in this problem is defined from x = -2 until x = 5 hence the domain of the function is given as follows, by the interval:
{x| –2 ≤ x <= 5}
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Answer:
So I got 64 on my test, but it doesn't let you see what was right and what was wrong, so I guess we will never know☹️☹️☹️☹️.
BTW in was on edge
Which graph represents the equation y2 = –4x?
On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 1, 0), and a directrix at x = 1.
On a coordinate plane, a parabola opens down. It has a vertex at (0, 0), a focus at (0, negative 1), and a directrix at y = 1.
On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 4, 0), and a directrix at x = 4.
On a coordinate plane, a parabola opens down. It has a vertex at (0, 0), a focus at (0, negative 4), and a directrix at y = 4.
Answer:
its A
Step-by-step explanation:
Answer: The first one (A)
Step-by-step explanation:
Consider this equation.
Use the graph to find the approximate solutions to this equations
The equation be 2(x-2)-5=√x+3-1 then the graphical solution of the equations exists approximately x = 3 and x = 6.
What is the solution of the equation?The solution of an equation creates that equation true.
The equation of can be simplified, therefore:
2(x-2)-5=√x+3-1
simplifying the above equation, we get
2x -9 =√x+2
4 x²-37x + 79 = 0
The graphical solution of the equations exists at approximately x = 3 and
x = 6
In ending, the solution of an equation makes the equation true.
Therefore, the graphical solution of the equations exists approximately x = 3 and x = 6
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for f(x) = x+1 and g(x)= 2x+3, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.(gof)(2)
Answer:
a) 2x + 4
b) 2x + 5
c) 8
d) 9
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}[/tex]
Function composition is an operation that takes two or more functions and combines them into a single function.
(f o g)(x) means find g(x) first and then substitute the result into f(x).
(g o f)(x) means find f(x) first and then substitute the result into g(x).
Part (a)
[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}[/tex]
Part (d)
[tex]\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}[/tex]
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(fog)(x)
f(g(x))f(2x+3)2x+3+12x+4(gof)(x)
g(f(x))g(x+1)2x+2+32x+5(fog)(2))
2(2)+48(gof)(2)
2(2)+59use the fact that there are 2pi radians in each circle to find another angle, smaller than 2pi, that is equivalent to 17pi/6. with detailed steps pleasee
The equivalent angle in the interval [0, 2pi] is 5pi/6.
How to find the equivalent angle?
Remember that for any given angle θ in radians, we define a family coterminal or equivalent angles as:
A = θ + n*(2pi)
Where n is a whole number.
Now we want to find an angle equivalent to 17pi/6 that is on the range between 0 and 2pi.
Then we can write:
A = 17pi/6 + n*(2pi)
If we use n = -1, then we get:
A = 17pi/6 - 2pi = 17pi/6 - 12pi/6 = 5pi/6
This is the equivalent angle in the desired range.
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An isosceles triangle has a perimeter (9y-15)cm. what is the length of the remaining equal sides of it's third side is (3y-7) cm.
The length of each of the equal sides is become x = (3y-4) cm
According to the statement
we have given that the perimeter of the isosceles triangle and length of third side. and we have to find the length of same side of triangle.
So,
An isosceles triangle is a triangle that has two sides of equal length.
Let the equal sides of isosceles triangle be x cm each.
We know that the
Sum of sides of a triangle = perimeter
x+x+(3y-7) = 9y-15
2x = 9y-3y-15+7
After solving the equation it become
2x= 6y-8
x=(6y-8)/2
Now the length of equal sides is x=3y-4
So, The length of each of the equal sides is become x = (3y-4) cm
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Solve for x: 12x2 – 6 (a2 + b2)x + 3a2b2 = 0
Answer:
x:12×2−6(a2+b2)x+3a2b2=0
Step-by-step explanation:
equation
Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table. A 2-column table with 4 rows is shown. The first column is labeled Blood Type with entries O, A, B, AB. The second column is labeled Number of People with entries 22, 20, 6, 2. Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
The length of a rectangular field is 9m longer than its width, if the perimeter of the field is 270m find its width.
==================================================
Work Shown:
width = w
length = w+9
perimeter = 2*(length + width)
P = 2(w+9+w)
P = 2(2w+9)
P = 4w+18
4w+18 = P
4w+18 = 270
4w = 270 - 18
4w = 252
w = 252/4
w = 63 meters is the width
w+9 = 63+9 = 72 meters is the length
Check:
perimeter = 2*(length + width)
perimeter = 2*(72 + 63)
perimeter = 2*(135)
perimeter = 270
The answer is confirmed.
Suppose A and B are points on the number line. If AB = 8 and B lies at −7, where could A be located?
The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.
According to the statement
We have given that the
AB = 8 and B lies at −7, and we have to find the position of the A on the number line.
Let a be a point on number line and b be the second point on number line.
And The distance between two numbers on number line is calculate by subtracting the smaller number from larger number.
Here
AB = 8
B = -7
We have to look at the options one by one.
For A = -1
As A>B
AB = -1-(7) = -1+7 = 6
For A = 1
As A>B so
AB = 1-(-7) = 8
So with A = 1 , AB = 8
This is one of the right answers.
For A=15
As A>B
AB = 15-(-7) = 22
For A=-15
As B>A
AB = -7 -(-15) = 8
As with A=1 and A=-15, the distance between AB is 8 so these are the correct answers.
So, The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Suppose A and B are points on the number line. If AB = 8 and B lies at −7, where could A be located?
Select ALL that apply.
A −1
B 1
C 15
D −15
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Una estrategia de cálculo mental con
números decimales consiste en buscar
parejas de números cuya suma sea un
número entero. Aplica esta estrategia para
calcular mentalmente:
a. 15,75 + 1,2 + 0,25
b. (–1,8) + 2,45 + (–0,20)
c. 3,5 + 11,8 + 12,5
d. 7,38 – 1,5 + 2,62
Esta estrategia se puede aplicar sumando 15,75 + 0,25, –1,8 + –0,20, 3,5 + 12,5 y 2,62 + 7,38 antes de sumar el tercer número dado en cada caso.
¿En qué consiste está estrategia?La estrategia propuesta consiste en sumar dos números decimales que den como resultado un número entero antes de sumar el tercer número decima. Por ejemplo si teneos 1,4 + 0,6 + 1,2, se debe sumar primero 1,4 + 0,6 lo que es igual a 2 antes de sumar el 1,2.
¿Por qué utilizar esta estrategia?Este estrategia es beneficiosa porque facilita sumar números decimales.
¿Cómo aplicar está estrategia?15,75 + 1,2 + 0,25 = 16 (0,25+15,75) + 1,2 = 17,2 (–1,8) + 2,45 + (–0,20) = -2 (-1,8-0,20) + 2,45 = 0,453,5 + 11,8 + 12,5 = 16 (12,5+3,5) +11,8 = 27.87,38 – 1,5 + 2,62 = 10 (7,38+2,62) + 2,62 = 12,62Aprenda más sobre números decimales en: https://brainly.com/question/24620232
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If a sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years.Find the rate of interestsl
The rate of interest applied on the amount is 15%.
According to the statement
we have given that the sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years.
And we have to find the rate of interest on this money.
So, For this purpose,
The given equation is:
Money in 3 years = 2175
Money in 5 years = 2625
Amount increased in 2 years = 2625-2175
Amount increased in 2 years = 450
And amount increased per year = 450/2
Amount increased per year = 225.
SI in 3 years=450/2 *3=Rs. 675
Principal amount= 2175-675=1500
so again,
R=(I*100)/(P*T)
R=15%
So, The rate of interest applied on the amount is 15%.
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________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
What is DPU?Defects per unit (DPU) can be defined as the number of defects divided by the number of opportunities
It is also seen as the universal measure of quality.
For example, if there are 100 defects in 1,000 units produced, then the defects per unit will be 0.01.
Defects per million opportunities can be defined as a mathematical calculation of the estimated quality of a process
From this information, we can conclude that DPU and DPMO are measure of defects in a sample.
Thus, DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
Complete question is;
________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
a. DPMO, DPU
b. DPU, DPMO
c. RTY, FTY
d. FTY, RTY
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Analyze the diagram below and answer the question that follows. If 2004-02-01-02-00_files/, what is 2004-02-01-02-00_files/? A. 2004-02-01-02-00_files/ B. 2004-02-01-02-00_files/ C. 2004-02-01-02-00_files/ D. 2004-02-01-02-00_files/
Option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively. This can be obtained by knowing what similar triangles are and finding which sides are proportional.
Find the correct option:Similar triangles: If two triangles have proportional sides the are similar.
For example, if ΔABC and ΔDEF are similar then
[tex]\frac{AB}{DE}= \frac{BC}{EF} =\frac{AC}{DF}[/tex]
∠ABC = ∠DEF and ∠ACB = ∠DFE
Then we can write that, ΔABC ~ ΔDEF
Here in this question,
Since A, Y, Z are midpoints of sides XW, VW, XV
XA = AW
WY = VY
XZ = VZ
To consider sides AY and XV we should take triangles ΔWAY and ΔWXV
[tex]\frac{WX}{WA} =\frac{2WA}{WA} = 2[/tex] (since A is the midpoint of WX)
[tex]\frac{WV}{WY} =\frac{2WY}{WY} = 2[/tex] (since Y is the midpoint of WV)
∠AWY = ∠XWV (reflexive property)
Therefore ΔWAY and ΔWXV are similar triangles
[tex]\frac{WX}{WA}= \frac{XV}{AY} =\frac{WV}{WY}[/tex] = 2
∠WAY = ∠WXV and ∠AYW = ∠XVW
Hence,
AY || XV option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Analyze the diagram below and answer the question that follows. If Z, Y and A are midpoints of ΔVWX what is true about AY and XY?
A. AY || XV
B. 1/2 AY = XV
C. AY = XV
D. AY ≅ XV
Answer:
A
Step-by-step explanation:
Which number is equivalent to (1/3)^-4
A 81
B −1/81
C −1/12
D 12
The fraction (1/3)⁻⁴ is equal to 81.
Given that:
Fraction: (1/3)⁻⁴
Rewrite the expression by applying the rule that states a negative exponent is equal to the reciprocal of the positive exponent:
(1/3)⁻⁴= 1 / (1/3)⁴
Now, let's simplify (1/3)⁴:
(1/3)⁴ = (1/3) × (1/3) × (1/3) × (1/3)
(1/3)⁴ = 1/81
So, the expression becomes:
1 /(1/3)⁴ = 1 / (1/81)
Now, dividing by a fraction is equivalent to multiplying by its reciprocal:
1 / (1/81) = 1 × 81 = 81
Therefore, the fraction (1/3)⁻⁴ is equal to 81.
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Expand 10a(2a-7) pls its very urgent
Answer:
[tex]20a^2-70a[/tex]
Step-by-step explanation:
1) Expand by distributing terms.
[tex]10\times2a+10a\times-7[/tex]
2) Take out the constants.
[tex](10\times2)aa+10a\times-7[/tex]
3) Simplify [tex]10\times2[/tex] to [tex]20.[/tex]
[tex]20aa+10a\times7[/tex]
4) Use Product Rule:[tex]x^ax^b=x^{a+b}[/tex].
[tex]20a^2+10a\times-7[/tex]
5) Simplify [tex]10a\times-7[/tex] to [tex]-70a.[/tex]
[tex]20a^2-70a[/tex]
Thank you,
Eddie
Answer:
20a² - 70a
Step-by-step explanation:
(10a)(2a-7)
= 10a*2a + 10a*-7
= 20a² - 70a
If you want to connect your home network to the internet, you will need a ________ in addition to a modem.
Answer:
landline
hshdjdh
dbbdhdhdh
bdbdhdhdhe
Answer:
Router
Step-by-step explanation:
Hope this helps
Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).
4x − y = −6
x + 4y = 7
x − 4y = −9
4x + y = 2
Answer:
x + 4y = 7
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 ) = (- 1, 2 ) and (x₂, y₂ ) = (3, 1 )
m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 1, 2 )
2 = [tex]\frac{1}{4}[/tex] + c ⇒ c = 2 - [tex]\frac{1}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex]x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form
multiply through by 4 to clear the fractions
4y = - x + 7 ( add x to both sides )
x + 4y = 7 ← equation in standard form
equation of line in two point form is needed here.
(y - y1) = [ (y2 - y1)/(x2-x1) ] (x - x1)y - (2) = [ (1 - 2)/(3 - (-1)) ] (x - (-1))y - 2 = [ -1/4 ] (x + 1)y = -(x/4) -1/4 + 2y = -x/4 + 7/44y = -x + 7x + 4y = 7If a polynomial function, f(x), with rational coefficients has roots 0, 4, and 3 startroot 11 endroot, what must also be a root of f(x)? 3 i startroot 11 endroot negative 3 i startroot 11 endroot 3 minus startroot 11 endroot negative 3 minus startroot 11 endroot
Answer:
C
Step-by-step explanation:
C
Answer:
Step-by-step explanation:
its c
give me some questions of grade 7
Q1: For 30 minutes, a person jogged 10 times along the perimeter of a rectangular field at 12 kilometers per hour. Find the square meters of the field if its length is twice its width.
Q2: A car is traveling at a speed of 75 kilometers per hour. In one minute, how many meters does the car travel?
Q3: What is the length of 2000 millimeters in inches? Round your answer to the nearest hundredth.
Hope this helps =)
A and B are two cylinders that are mathematically similar.
The area of the cross-section
of cylinder A is 18 cm².
Work out the volume of cylinder B.
+
18 cm²
A
5 cm
1
B
61%
10 cm
The Volume of the Cylinder B is gotten as; 720 cm³
What is the Volume of the Cylinder?We are given 2 similar cylinders with;
ratio of heights = a : b
Thus;
ratio of areas = a² : b²
We are given that;
Height of A is 5cm.
Height of B is 10cm.
Thus;
Ratio of heights = 5 : 10 = 1 : 2
Therefore;
ratio of areas = 1² : 2² = 1 : 4
The cross sectional area of B is 4 times the cross sectional area of A. Thus;
Cross sectional area of B = 4 × 18 = 72 cm²
Volume of cylinder = cross section area × height
Volume of cylinder B = 72 × 10 = 720 cm³
The complete question is;
A and B are two cylinders that are mathematically similar.
The area of the cross-section of cylinder A is 18cm².
Height of A is 5cm.
Height of B is 10cm.
Work out the volume of cylinder B
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please help i need
this asap!! drag each measure to the correct location on the table classify each measure as a measure of center or a measure or variation
The measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.
what is measure centre and measure of variation?A measure of central tendency (measure of centre) is a value that attempts to describe a set of data by identifying the central position of the data set.
The measure of central tendency includes the mean, median and mode.
The measure of variation describes the amount of variability or spread in a set of data.
The common measures of variability are the range, the interquartile range (IQR), variance, and standard deviation.
Therefore, the measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.
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which expression shows how the distribuive property can be used to multiply 8x29?
The expression which shows how the distributive property of the can be used to multiply 8×29 as in the task content is; 8(20 + 9).
Which expression can be used to show how the distributive property can help multiply 8×29?It follows from the task content that the given product to be multiplied is; 8×29.
Consequently, it follows from convention that the distributive property of multiplication allows that the multiplication in this case can be rewritten as follows;
8×29 = 8 (20 + 9)
Hence, we have; (8×20) + (8×9).
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The water usage at a car wash is modeled by the equation w(x) = 4x3 6x2 − 11x 7, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 4x3 4x2 − 11x 8 c(x) = 3x3 4x2 − 11x − 8 c(x) = 3x3 4x2 − 11x 8 c(x) = 4x3 4x2 − 11x − 8
A function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.
What is an equation?A relationship between two variables is defined as an equation; if we plot the graph of the linear equation, we will get a straight line.To find a function, C(x), to model the water used by the car wash on a shorter day:
Given information -
The water usage at a car wash is modeled by the equation W(x) = 4x³ + 6x² − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open.The amount of decrease in water used is modeled by D(x) = x³+ 2x² + 15, where D is the amount of water in cubic feet and x is time in hours.Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.
We are trying to find:
C(x) = W(x) - D(x)C(x) = (4x³ + 6x²− 11x + 7) - (x³ + 2x² + 15)C(x) = 4x³ - x² + 6x² - 2x³ - 11x + 7 - 15C(x) = 3x³ + 4x² - 11x - 8Therefore, a function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.
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The correct question is given below:
The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day
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A package is oscillating on a spring scale with a period of 5.00 s. at time t = 0.00 s the package has zero speed and is at x = 8.50 cm. at what time after t = 0.00 s will the package first be at x = 4.50 cm?
Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.
How to analyze an object on simple harmonic motion
Simple harmonic motion is a kind of periodic motion represented by sinusoidal functions. Physically speaking, it is a good approximation for periodic motion due to small perturbations and with absence of frictions and viscous forces on the system.
The position of an object under simple harmonic motion is described by the following equation:
x (t) = A · cos (2π · t / T + Ф) (1)
Where:
A - Amplitude, in centimetersT - Period, in secondsФ - Angular phase, in radiansx(t) - Position, in centimetersIf we know that T = 5 s, A = 8.50 cm, Ф = 0 rad and x = 4.50 cm, then the time when the package will reach x = 4.50 cm is:
4.50 = 8.50 · cos (2π · t / 5)
9 / 17 = cos (2π · t / 5)
0.322π = 2π · t / 5
t = 0.805 s
Under the assumption of simple harmonic motion, the package will be at x = 4.50 centimeters at a time of 0.805 seconds.
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