Thus, the inverse Laplace transform is found as: f(t) = 1/4h(t-2) + (1/4 - 1/2e2ln(2))h(t) - 1/4h(t+ln(2)) + C, in which C is a constant.
To find the inverse Laplace transform of F(s) = 1e2/(s+2)(1+e-2s)2, we need to use partial fraction decomposition and the Laplace transform table.
First, let's rewrite F(s) using partial fraction decomposition:
F(s) = 1e2/[(s+2)(1+e-2s)2]
= A/(s+2) + (B + Cs)/(1+e-2s) + (D + Es)/(1+e2s)
where A, B, C, D, and E are constants to be determined.
To find A, we multiply both sides by (s+2) and then let s=-2:
A = lim(s→-2) [s+2]F(s)
= lim(s→-2) [s+2][1e2/[(s+2)(1+e-2s)2]]
= 1/4
To find B and C, we multiply both sides by (1+e-2s)2 and then let s=ln(1/2):
B + C = lim(s→ln(1/2)) [(1+e-2s)2]F(s)
= lim(s→ln(1/2)) [(1+e-2s)2][1e2/[(s+2)(1+e-2s)2]]
= 3/4
B - C = lim(s→ln(1/2)) [(d/ds)(1+e-2s)(1+e-2s)F(s)]
= lim(s→ln(1/2)) [(d/ds)(1+e-2s)(1+e-2s)][1e2/[(s+2)(1+e-2s)2]]
= -1/2
Solving for B and C, we get:
B = 1/4 - 1/2e2ln(2)
C = 1/2 + 1/2e2ln(2)
To find D and E, we repeat the same process by multiplying both sides by (1+e2s) and letting s=-ln(2):
D + E = lim(s→-ln(2)) [(1+e2s)F(s)]
= lim(s→-ln(2)) [(1+e2s)][1e2/[(s+2)(1+e-2s)2]]
= -1/4
D - E = lim(s→-ln(2)) [(d/ds)(1+e2s)F(s)]
= lim(s→-ln(2)) [(d/ds)(1+e2s)][1e2/[(s+2)(1+e-2s)2]]
= -1/2
Solving for D and E, we get:
D = -1/4 - 1/2e-2ln(2)
E = -1/4 + 1/2e-2ln(2)
Therefore, F(s) can be rewritten as:
F(s) = 1/4/(s+2) + (1/4 - 1/2e2ln(2))/(1+e-2s) + (-1/4 - 1/2e-2ln(2))/(1+e2s)
Using the Laplace transform table, we know that:
L{h(t-a)} = e-as
L{C-1} = C
Therefore, the inverse Laplace transform of F(s) is:
f(t) = L-1{F(s)}
f(t) = 1/4h(t-2) + (1/4 - 1/2e2ln(2))h(t) - 1/4h(t+ln(2)) + C
where C is a constant.
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polynomial>>>look at pick fundamental theorem
Answer:
1
Step-by-step explanation:
The factor (x³ - 1) is not repeated.
A man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66?
If x represents the number of 13 cent stamps and y the 18 cent stamps, which system represents the problem?
The system of equation which represent the scenario is;
x + y = 42
x + y = 420.13x + 0.18y = 6.66
Simultaneous equationlet
number of 13 cent stamps = xnumber of 18 cent stamps = yTotal cost of the stamps = $6.66Total number of stamps = 42x + y = 42
x + y = 420.13x + 0.18y = 6.66
Therefore, the equation which represent the problem is;
x + y = 42
0.13x + 0.18y = 6.66
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marca la respueta correcta el termino general de la sucesion 3,6,9,12,15, es.: a-2n b-3n c-n2 ayudaaaaa
Andy is collecting pocket change for a fundraiser. he begins with 102 coins in the cup, and their monetary value is $17.10. if he has a mix of dimes and quarters, how many of the coins are dimes?
If Andy has 102 coins mixed with dimes and quarters and monetary value of $17.10 then he has 56 dimes and 42 quarters.
Given number of coins Andy has is 102 and montary value of all coins is $17.10.
We have to determine number of dimes and quarters.
1 dime=$0.10
1 quarter=$0.25
Suppose the number of dimes be x and number of quarters be y.
The equations are:
0.10x+0.25y=17.10------------1
x+y=102-------------2
from equation 2, y=102-x
Put the value of y=102-x in equation 1
0.10x+0.25(102-x)=17.10
0.10x+25.5-0.25x=17.10
-0.15x=17.10-25.5
-0.15x=-8.4
x=8.4/0.15
x=56
Put the value of x in y=102-x
y=102-56
y=46
Hence Andy has 56 number of dimes and 46 quarters.
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Please help!!! due today. Find the surface area of the triangular prism.
The surface area of the shape is 168 square cm
Surface area of triangular prismThe surface area of a figure is the area of the faces of the given figure.
For the given figure, the area will be the sum of area of 2 triangles and 3 rectangles.
Area = (6*3) +(10*6)+(6+10) +(10*3)
Surface area = 18 + 120 + 30
Surface area = 168 square cm
Hence the surface area of the shape is 168 square cm
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Find the measure for the unknown angle.
Answer:
49°
Step-by-step explanation:
Right angled triangle:
This is a type of triangle with one of the angle as 90°
Sum of angles in a Right angled triangle is 90°
Therefore,
y + 41° = 90°
collecting like terms
y = 90 - 41 = 49°
Therefore,
y = 49°
How many 3-coin combinations exist if we can choose from
pennies, nickels, dimes, and quarters?
select one:
a. 20
b. 4!
o
c.4.
o
d. 12
There are four numbers of 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars.
How to solve probability combinations?The coins to select from are nickels, dimes, quarters, and half-dollars;
Thus;
Coins (n) = 4
The number of coin to select is:
Coin (r) = 3
The coin combination is then calculated using:
Combination = ⁴C₃
Apply the combination formula, we have;
Combination = 4
Thus, there are four number 3-coin combinations if we can choose from nickels, dimes, quarters, and half-dollars.
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Answer:
12
Step-by-step explanation:
took the exam
6,000 people voted in a town election. Of the two candidates, the winning candidate received 4,000 more votes than the losing candidate. How many votes did the winner get?
Answer:
Step-by-step explanation:
let x = the number of votes of the first person
winner = x + 4000
x+ x+4000 = 6000
2x=2000
x=1000
first person = x = 1000
winner = x+4000 = 5000
The winner got 5000 votes
What ia an equation of the line that is parallel to y=3x-8 and passes through the point (4,-5)?
Answer:
y = 3x - 17
========================
Given liney = 3x - 8Parallel lines have equal slopes, so its equation is in the form of:
y = 3x + bSince it passes through the points (4 , - 5), find the value of the y-intercept b by substituting x- and y- coordinates into this equation:
- 5 = 3*4 + b- 5 = 12 + bb = -5 - 12b = - 17The equation of the parallel line is:
y = 3x - 17someone please help asap.. what even is this. ill give brainliest
Given: line AC is perpendicular to line BC
Prove: the slopes of lines AC and BC is -1
Complete the Proof.
first blank: angle addition; definition of perpendicular lines; definition of congruent angles; definition of a straight angle.
second blank: addition property of equality; subtraction property of equality; transitive property of equality; substitution property of equality.
third blank: transitive property of equality; substitution property of equality; definition of slope; corresponding sides of similar triangles are proportional.
fourth blank: multiplication property of equality; substitution property of equality; addition property of equality; transitive property of equality.
Congruency property relates to two or more triangles with similar dimensions, and internal angles. So that the required statements to complete the proof are:
1. definition of a straight angle.
2. subtraction property of equality
3. corresponding sides of similar triangles are proportional
4. transitive property of equality.
The intersection of two or more lines forms a number of angles which depends on the number of lines involved. These angles formed may have similar or different properties.
When two or more triangles have similar lengths of sides and measure internal angles, it can be said that they are congruent. Thus they have some common properties.
Therefore, the appropriate statements to answer the given question are stated below:
Definition of a straight angle.Subtraction property of equality.Corresponding sides of similar triangles are proportional.Transitive property of equality.For more clarifications on the properties of congruent triangles, visit: https://brainly.com/question/15835221
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Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection
The probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.
What is probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection:
Given that Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. We are to calculate the probability that Rita will need to pick at least 5 beads before she picks a grey bead from her collection.Prob for drawing at least 5 beads before she picks a grey bead from her collection= 1-Prob for drawing at least one grey beed in the first 5 draws.(Because these two are complementary events)number of grey beads drawn in the first 5 trials is[tex](5, \frac{80}{80+160+240} ) = (5,\frac{1}{6} )[/tex]Prob for drawing at least one grey beed in the first 5 draws.=1-Prob of no greyHence required prob=P(X=0 in the first 5 draws)[tex](1-\frac{1}{6})^{5}\\0.4018[/tex]The 6th beeds onwards can be grey also.The nearest answer is (C) 0.45Therefore, the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.
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The question you are looking for is given below.
Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection?
(A) 0.05
(B) 0.10
(C) 0.45
(D) 0.55
What is the length of an edge of a cube whose total surface area is equal to 150 square feet?
The length of an edge of a cube is 5 feet.
What is cube?In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Total surface area of a cube = 6[tex]l^{2}[/tex]
Given that,
Total surface area of a cube = 150 square feet
Total surface area of a cube = 6[tex]l^{2}[/tex]
[tex]\Rightarrow[/tex] 150 = 6[tex]l^{2}[/tex]
[tex]\Rightarrow[/tex] [tex]l^{2}[/tex] = [tex]\frac{150}{6}[/tex]
[tex]\Rightarrow[/tex] [tex]l^{2}[/tex] = 25
[tex]\Rightarrow[/tex] l [tex]=\sqrt{25}[/tex]
[tex]\Rightarrow[/tex] l = 5 feet
Hence, the length of an edge of a cube is 5 feet.
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David has kept track of his family’s grocery bills for the past 10 weeks, as shown in the table.
Week 1 2 3 4 5 6 7 8 9 10
Bill ($) 92 106 129 115 100 84 110 156 98 87
Would you choose to use a histogram, a circle graph, or a line graph to display the data? Explain your choice. Then make a display.
The preferred choice would be a line graph (drawn in the figure attached) for displaying the data.
Why a line graph is the preferred option here?
For displaying the data of David's family's grocery bills for the past 10 weeks, a line graph is the most preferable choice since it would display the data's trend for us. This is similar to how we would notice times when there were huge costs.Another reason for choosing a line graph is that it is very easy to comprehend. It is simple to observe how the data are related and how they have changed.What is a line graph?
An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.
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The greatest question: what is the square root of nine. i don't know the answer:)
3 is the square root of nine.
The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } square root of, end square root . Finding the square root of a number is the opposite of squaring a number.
To find the fraction square root, first, find the square root of the numerator and then find the square root of denominator. After finding the square root values, simplify the fraction. For example, √(4/16), can be written as √4/√16.
(3)^2 = 9
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Given startlayout enlarged left-brace first-row startfraction x cubed minus 1 over x squared minus 1 endfraction, for x less-than 1 second row startfraction 3 over x minus 1 endfraction, for x greater-than-or-equal-to 1 endlayout. what is limit of f (x) as x approaches 1 minus? negative three-halves 0 three-halves dne
The limit of f(x) as it approaches -1 is given as 3/2
What is limit in mathematics?In mathematics and computation, the limit can be described to be the value that a sequence is going to approach in such a way that the input would approach or tend towards a given value
The unit is used to assign values to numbers at certain points where there are no defined values.
How to solve the limitwe have 3/x-1
We have to take the value of x here to be three as the equation tends to 1.
Then we apply it in the formula
3/3-1
= 3/2
Hence the limit of f(x) is given as 3/2
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Are the ratios 2:1 and 14:6 equivalent?
yes
no
A supermarket increases the prices of some grocery items by 10%.
(a) What will be the new price of a loaf of bread marked at $1.80.
(b) What will the price of a packet of cereal that has a price tag of $4.20, but already discounted by 50%
Answer:
(a) $1.98
(b) $6.30
Step-by-step explanation:
(a)
The new value =
1.80 + The value of the percentage increase =
1.80 + (10% × 1.80) =
1.80 + 10% × 1.80 =
(1 + 10%) × 1.80 =
(100% + 10%) × 1.80 =
110% × 1.80 =
110 ÷ 100 × 1.80 =
110 × 1.80 ÷ 100 =
198 ÷ 100 =
1.98
Calculate the actual change (the absolute difference) between the two values
The actual change =
The new value - 1.80 =
1.98 - 1.80 =
0.18
Proof of calculation.
Calculate the percentage increased value...
... and see if we get as a result...
... the actual change (the absolute difference).
Calculate the percentage increased value:
The value of the percentage increase =
10% × 1.80 =
10 ÷ 100 × 1.80 =
10 × 1.80 ÷ 100 =
18 ÷ 100 =
0.18
So we have proven that the calculations are correct.
For positive numbers
The actual change =
The value of the percentage increase
The answer:
1.80 increased by 10% = 1.98
The actual change:
1.98 - 1.80 = 0.18
(b)
Calculate the New value
The new value =
42.0 + The value of the percentage increase =
4.20 + (50% × 4.20) =
4.20 + 50% × 4.20 =
(1 + 50%) × 4.20 =
(100% + 50%) × 4.20 =
150% × 4.20 =
150 ÷ 100 × 4.20 =
150 × 4.20 ÷ 100 =
63,000 ÷ 100 =
630
(but its as a dollar so its 6.30)
Calculate the actual change (the absolute difference) between the two values
The actual change =
The new value - 4.20 =
6.30 - 4.20 =
2.10
Proof of calculation.
Calculate the percentage increased value...
... and see if we get as a result...
... the actual change (the absolute difference).
Calculate the percentage increased value:
The value of the percentage increase =
50% × 4.20 =
50 ÷ 100 × 4.20 =
50 × 4.20 ÷ 100 =
21,000 ÷ 100 =
210
(but its as a dollar so its 2.10)
So we have proven that the calculations are correct.
For positive numbers
The actual change =
The value of the percentage increase
The answer:
4.20 increased by 50% = 6.30
The actual change:
6.30 - 4.20 = 2.10
The volume of a box without a lid is given by the formula v = 4x(10-x)^2, where x is a length in inches and v is the volume in cubic inches. what is the volume when x = 5
The volume of the box without the lid is 500 cubic inches.
What is volume?The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim.
Another way to think of volume is as the amount of space a three-dimensional object takes up.
Calculation for the volume of the box-
The volume of a box without a lid is given by the formula v = 4x(10-x)².
Where,
'x' is a length in inches, and
'v' is the volume in cubic inches.
The volume when x = 5 inches.
Substitute the value of 'x' in the formula of volume;
v = 4×5(10-5)²
= 20×5²
v = 500
Therefore, the volume of a box without a lid is 500 cubic inches.
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MATH HELP!!! 100PTS!!!
Write the parametric equations
x=5sinθ,y=3cosθ,0≤θ≤π
in the given Cartesian form.
(y^2)/9=
with x≥0.
Answer:
[tex]\dfrac{y^2}{9}=1-\dfrac{x^2}{25}[/tex]
Step-by-step explanation:
When converting parametric equations that involve trig functions to Cartesian equations, use trig identities to eliminate the parameter.
Given parametric equations:
[tex]x=5 \sin \theta, \quad y=3 \cos \theta, \quad 0\leq \theta\leq \pi[/tex]
Square the equation for x:
[tex]\implies x^2=(5 \sin \theta)^2=25 \sin^2 \theta[/tex]
Use the identity [tex]\sin^2 x+\cos^2x =1[/tex] to write [tex]x^2[/tex] in terms of cos:
[tex]\implies x^2=25(1-\cos^2 \theta)[/tex]
Isolate [tex]\cos^2 \theta[/tex] :
[tex]\implies \dfrac{x^2}{25}=1-\cos^2 \theta[/tex]
[tex]\implies \cos^2 \theta=1- \dfrac{x^2}{25}[/tex]
Square the equation for y:
[tex]\implies y^2=(3 \cos \theta)^2=9 \cos ^2 \theta[/tex]
Replace [tex]\cos^2 \theta[/tex] with the found equation involving [tex]x^2[/tex] :
[tex]\implies y^2=9\left(1-\dfrac{x^2}{25}\right)[/tex]
Divide both sides by 9:
[tex]\implies \dfrac{y^2}{9}=1-\dfrac{x^2}{25}, \quad \textsf{with }x\geq 0[/tex]
What is the scale factor for Triangle XYZ to Triangle UVW?
A. 1/2
B. 2
C. 1/4
D. 4
If 4x² = 16, then x =
A20
B12
C4
D2
Michael collects 45 trays of eggs every week . how many trays does he collect in two months?
The answer is C, how is it solved?
Answer:
(C) 0
Step-by-step explanation:
As always, the first step is to read and understand the question. You are asked to find the smallest number in the set {M₁, M₂, M₃}. Each of these values is defined to be the largest number in the corresponding sets S₁, S₂, S₃.
Set MThe numbers in each set are ordered smallest to largest, so the largest number in each set is the one on the right.
The largest number in S₁ is 8, so M₁ = 8.
The largest number in S₂ is 6, so M₂ = 6.
The largest number in S₃ is 0, so M₃ = 0.
This means the set M is ...
M = {M₁, M₂, M₃} = {8, 6, 0}
The question asks for the smallest number in set M. Clearly, it is 0.
The smallest number in the set is 0.
Kelly is 5'4" tall. She measured her shadow one morning to be 8'7". She then measured the shadow of her house. The house shadow was 42'3". How tall is the
actual house? (inches rounded to the hundredths.)
The height of the actual house is 26'.26" .
How to find the height of the house using ratio?A ratio indicates how many times one number contains another.
Therefore, the heights will form a similar length. Therefore, the corresponding length have the same ratios.
Therefore,
height of Kelly / x = height of Kelly shadows / height of house shadow
Hence,
where
x = actual height of the house
5.4 / x = 8.7 / 42.3
cross multiply
42.3 × 5.4 = 8.7x
Therefore,
228.42 = 8.7x
divide both sides by 8.7
228.42 / 8.7 = 8.7x / 8.7
x = 26.2551724138
Therefore, the height of the actual house is 26'.26"
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Determine the equation of the parabola whose graph is given below. Write your answer in General Form. A parabola on a coordinate plane.
The equation of parabola becomes y = -2/25(x-3)^2 + 4.
According to the statement
we have given a graph and from this graph we have to find the equation of parabola in the general form.
So,
we know that the equation of parabola in general form is
y = a(x-h)^2 +k - (1)
From the graph we have:
a point on the graph is (x,y) = (-2,2)
the vertex of the graph is (h,k) = (3,4)
Now, substitute these values in the equation number (1)
Then
y = a(x-h)^2 +k
2 = a(-2-3)^2 +4
2 = a(-5)^2 +4
2 = a(25) +4
25a = -2
a = -2/25.
Now put a = -2/25 and (h,k) = (3,4) in the equation(1).
Then
the equation of parabola becomes y = -2/25(x-3)^2 + 4
So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.
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P(Music/Drama) round to the nearest percent
Using it's concept, the probability that a randomly selected student is in music/drama is: 25%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Hence, in this problem, the probability will be found dividing the number of students that are in music or drama by the total number of students.
These data is given in a table, which is not given in this exercise. Researching this problem on the internet, we have that there are 20 + 7 + 3 + 20 + 13 + 2 + 25 + 5 + 5 = 100 students, of which 7 + 13 + 5 = 25 are in music/drama, hence the probability is:
P = 25/100 = 25%.
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40 points+Brainliest
Can someone please help me asap?? I really appreaciate it. I have to select more than one
Answer:
Your correct
Step-by-step explanation:
x = 36
x/3 = 12
x = 12(3)
x = 36
If tan(t)=4/9 what is tan(t−π)
The value of tan(t−π) is 4/9.
According to the statement
we have given that tan(t)=4/9 and we have to find the value of tan(t−π).
So,
tan(t−π) -(1)
take negative sign common from equation (1) it then
tan(t−π) = -tan(-t+π)
and we know that the according to the mathematics formula it become
tan(-t+π) is -tan t
then
tan(t−π) = -(-tan t)
it becomes
tan(t−π) = tan t
then its value becomes
tan(t−π) = tan(t)=4/9.
because we have given that the value of tan t is tan(t)=4/9.
So, The value of tan(t−π) is 4/9.
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Jake tossed a paper cup 50 times and recorded how it landed. the table shows the results:
position
open side up closed side up landing on side
1
5
44
number of times landed in position
based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). show your work
2
xd
c
e!
23
3
12 source vc
bius x, xi :-
29
ee
styles
normal
. ?
The experimental probability of each event is as follows:
Landing open side up = 1/50 = 0.02 = 2%.Landing closed side up = 5/50 = 1/10 = 0.1 = 10%.Landing on its side = 44/50 = 0.88 = 88%.The experimental probability of an event is the ratio of the number of outcomes that favored the event to the total number of outcomes in the experiment.
In the question, we are given that Jake tossed a paper cup 50 times and recorded the position how it landed, which is shown in the table:
Open-sided up: 1
Closed side up 5
On the side: 44.
We are asked to determine the experimental probability of each outcome.
The number of outcomes, when the landing is open-sided up is 1.
The number of outcomes, when the landing is closed-sided up is 5.
The number of outcomes, when the landing is on the side up is 44.
The total number of times the experiment took place is 50.
Thus, the experimental probability of each event is as follows:
Landing open side up = 1/50 = 0.02 = 2%.Landing closed side up = 5/50 = 1/10 = 0.1 = 10%.Landing on its side = 44/50 = 0.88 = 88%.Learn more about the experimental probability at
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Which formula gives the zeros of y = sin(x)? k pi for any positive integer k k pi for any integer k StartFraction k pi Over 2 EndFraction for any positive integer k StartFraction k pi Over 2 EndFraction for any integer k
Answer:
y =sin(x)
Step-by-step explanation:
small brain
Answer:
B: k pi for any integer k
Step-by-step explanation:
I took the test