Answer:
45
Step-by-step explanation:
The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.
Answer:
45
Step-by-step explanation:
The final had an extra credit as 25, so without it it would be 135. Then, you would divide by three to find that the first test had 45 points.
I promise I will mark the brainiest
Answer:
[tex]\frac{9}{a - b}[/tex].
Step-by-step explanation:
a^2 - b^2 = 9
(a + b)(a - b) = 9
a + b = [tex]\frac{9}{a - b}[/tex].
ab = 3
a = 3/b
3/b + b = [tex]\frac{9}{\frac{3}{b} -b}[/tex]
3 + b^2 = [tex]\frac{9b}{\frac{3}{b}-\frac{b^2}{b} }[/tex]
3 + b^2 = [tex]\frac{9b}{\frac{3-b^2}{b} }[/tex]
3 + b^2 = [tex]9b * \frac{b}{-b^2 + 3}[/tex]
3 + b^2 = [tex]\frac{9b^2}{-b^2 + 3}[/tex]
(b^2 + 3)(-b^2 + 3) = 9b^2
-b^4 + 9 = 9b^2
b^4 + 9b^2 - 9 = 0
Let's say that b^2 = x
x^2 + 9x - 9 = 0
Hope this [somewhat] helps!
Answer:
Step-by-step explanation:
a²-b²=9
ab=3 then a=3/b
a²-b²=9
(a+b)(a-b)=9 ( the values has to b (3*3) or (9*1)
but since ab=3. so the value has to be (3*3)
(a+b)(a-b)=9
3*3=9
a+b=3
ab=3
(Dividing polynomials ick!) Please help I'm failing summer class:)
Answer:
The answer is 9 (D).
Step-by-step explanation:
Hope this helps!
Write these series with summation notation. 1,4,9,16...
Answer: [tex]\sum\limits_{i=1}^{n} n^2[/tex] , where n is a natural number.
Step-by-step explanation:
A series can be represented in a summation or sigma notation.
Greek capital letter, ∑ (sigma), is used to represent the sum.
For example: [tex]\sum\limits_{n=1}^{\infty} n=1+2+3+4+5+...[/tex], where n is a natural number.
The given series : 1,4,9,16 which can be written as [tex]1^2, 2^2, 3^2,...[/tex] .
So , we can write it as
[tex]\sum\limits_{n=1}^{\infty} n^2[/tex] , where n is a natural number.
Answer:
B=6
C=n^2
Just did the test
Step-by-step explanation:
Suppose that a bacterial culture was known to double every 2 days. After 46 days, it covered the entire surface area in the petri dish. When did it cover half the area? Explain.
Answer:
in day 44 it covered half the area.
Step-by-step explanation:
A bacterial culture doubles every two days, so if today it covers [tex]3 cm^2[/tex], in two days it will cover [tex]6cm^2[/tex]. In other words, if today it covered x space, two days ago it covered half the space [tex](\frac{x}{2})[/tex].
Now, following that reasoning, we have that after 46 days the bacterial culture covered the entire surface area in the Petri dish, therefore, two days ago it covered half the area and we can conclude that in day 44 it covered half the area.
. What is half the next number in the pattern 1, 3, 9, 27, 81
A. 234
B. 67
D c. 468
0 0.76
Answer:
A. 243
Step-by-step explanation:
just multiply the next number by 3
81*3= 243
Answer:
[tex]\boxed{243}[/tex]
Step-by-step explanation:
The ratio can be found by dividing a term in the sequence by the previous term.
[tex]\frac{27}{9} =3[/tex]
Each term gets multiplied by 3 to get the next term.
[tex]81 \times 3 = 243[/tex]
The following box plot shows the number of years during which 40 schools have participated in an interschool swimming meet: A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years. At least how many schools have participated for more than 1 year and less than 6 years?
Answer:
Step-by-step explanation:
The box encloses data between the two quartiles, namely at least half of the data. If there are 40 schools, then half of them would be in the box, between 1 and 6.
see attached plot.
Answer:
really hard to tell what the box plot is like without an attachment so im gonna help u find it out anyway
Step-by-step explanation:
basically when u look at a box plot and the range the line in the middle is the median and then the max the lowest range the lower quartile and then the higher quartile you can find ur anser, simply find the median first, find where the lower quartile is and then the lowest number in the group thats in betweeen 1 and 6
Julio’s rotation maps point K(–6, 9) to K’(9, 6). Which describes the rotation? 90 degrees clockwise rotation 180 degrees rotation 90 degrees counterclockwise rotation 270 degrees clockwise rotation
Answer: 90 degrees clockwise rotation
Step-by-step explanation:
Common rotations about Origin :
90° clockwise (x,y)→(y,-x)
90° counterclockwise (x,y)→(-y,x)
180° (x,y)→ (-x,-y)
270° clockwise (x,y)→(-y,x)
Given: Julio’s rotation maps point K(–6, 9) to K’(9, 6).
Rotation corresponding to this is (x,y) → (y,-x) since K(–6, 9) → K’(9, -(-6)) = K(9,6).
Therefore, Julio’s rotates 90° clockwise to map point K(–6, 9) to K’(9, 6).
so , correct answer is "90 degrees clockwise rotation".
Answer:
90 degrees clockwise
Step-by-step explanation:
EDGE2020
I need help ASAP thank you!!
Answer:
Step-by-step explanation:
Hello!
a)
You have three triangles and you have to find the ratio of the adjacent sides to the angle 23.1º
Remember, considering a specific angle ∠, "the adjacent sides" are those that make contact with the angle and the "opponent side" is the one that is in the opposite side of the angle and the hypotenuse is the longest side of the right triangle, always opposed to the right angle.
First triangle, the adjacent sides, are
JL= 20.17m (hypotenuse)
JK= 18.55m
Ratio: [tex]\frac{JK}{JL}= \frac{18.55}{20.17}= 0.9196= 0.92[/tex]
Second triangle, adjacent sides:
PR= 141.19m (hypotenuse)
PQ= 129.85m
Ratio: [tex]\frac{PQ}{PR} = \frac{129.85}{141.19}= 0.9196= 0.92[/tex]
Third triangle, adjacent sides:
XZ= 181.53m (hypotenuse)
XY= 166.95m
Ratio: [tex]\frac{XY}{XZ} = \frac{166.95}{181.53} = 0.9196= 0.92[/tex]
b)
Using the calculator you have to calculate the trigonometric ratios of 23.1º:
sin(23.1º)= 0.392= 0.39
cos(23.1º)= 0.9198= 0.92
tan(23.1º)= 0.426= 0.43
c)
To calculate the trigonometrical ratios manually you have to do as follows:
Consider the angle A
[tex]sinA= \frac{opposite}{hypotenuse}[/tex]
[tex]cosA= \frac{adjacent}{hypotenuse}[/tex]
[tex]tanA= \frac{opposite}{adjacent}[/tex]
In item a) you calculated the ratios of the adjacent sides of the angle by the hypotenuse, this is equal to the cosine of the given angle.
I hope this helps!
What is the solution to this equation?
X +8=-3
A. x=-11
B. x= 11
c. x= -5
D. x = 5
Answer:
Option A
Step-by-step explanation:
x + 8 = -3
x + 8 - 8 = -3 - 8
x = - 11
Answer:
A. x= -11
Step-by-step explanation:
We want to solve for x. Therefore, we must get x by itself on one side of the equation.
x+8= -3
8 is being added to x. The inverse of addition is subtraction. So, subtract 8 from both sides of the equation.
x+8-8=-3-8
x= -3-8
x= -11
Now let’s check our solution. Plug -11 in for x in the original equation.
x+8=-3
-11+8=-3
-3=-3
This checks out, so we know our solution is correct and A. x= -11 is the correct choice.
A spherical mirror gives an image magnified 5 times at a distance 5 m. determine whether the mirror is convex or concave? How much will be the focal length of the mirror?
Answer:
a) The mirror is concave
b) The focal length of the mirror = -1.25m or -5/4 m
Step-by-step explanation:
a) Determine whether the mirror is convex or concave?
A concave mirror is a spherical mirror that it's magnification is equal to, less than or more than 1 while a convex mirror is a mirror whereby it magnification is always less than one.
From the above question we are told that the spherical mirror is magnified 5 times.
Hence, because the spherical mirror is magnified 5, it is a concave mirror.
b) Magnification = - image distance/ object distance
Magnification = 5
Image distance = 5m
Object distance = ???
5 = -5/Object distance
Object distance = -5/5
= -1m
Formula for focal length =
1/f = 1/v + 1/u
v = image distance = 5
u = object distance = -1
1/f = 1/5 +1/-1
1/f = 1/5 - 1
1/f = -4/5
f = -5/4
f = -1.25m
The focal length of the mirror = -1.25m
Overnight the temperature in Alaska dropped from 3%
degrees Fahrenheit to twelve and a quarter degrees
Fahrenheit below zero. By how many degrees did the
cemperature drop overnight?**
A. 8 3/4 degrees
B. 9 3/4 degrees
C. 15 1/2 degrees
D. 15 3/4 degrees
Answer:
A. 8 3/4 degrees
Step-by-step explanation:
Alaska temperature dropped from 3 degrees Fahrenheit to twelve and a quarter degrees Fahrenheit below zero
12 1/4°F - 3°F
=8 3/4°F
The temperature dropped by 8 3/4°F
Please answer this question now
Answer:
825 or 500
Step-by-step explanation:
Depends, if it is talking about just an up-down, it is 500, but if it is just distance in general, it would be 825 because 325+500=825
Hope this will help
10.
Find the length of the arc on a circle of radius r intercepted by a central angle 0.
r=20 cm,
e
1/4 radian
Answer:
Length of arc = 5 cm (Approx)
Step-by-step explanation:
Given:
Radius of circle = 20 cm
Angle = 1/4 radian
Find:
Length of arc
Computation:
Angle in degree = 1/4 radian × 180°π
Angle in degree = 1/4 × 180° / 22/7
Angle in degree = 14.31° Approx
Length of arc = (Ф / 360)2πr
Length of arc = (14.31 /360)2(22/7)(20)
Length of arc = 4.997 cm
Length of arc = 5 cm (Approx)
Music CD's cost $9 each, and movies cost $10 each. If you
spend $78 and buy 8 items, how many of each did you buy?
Answer:
2 CDs and 6 movies
Step-by-step explanation:
Let the number of CD you bought be x, and the number of movies you bought be y.
Since you bought 8 items in total,
x + y = 8 ______(1)
The sum of money spent is 78, so
9x + 10y = 78 ________(2)
From equation (1),
x = 8 - y ________(3)
Substitute (3) into (2),
9 (8-y) + 10y = 78
72 - 9y + 10y = 78
- 9y + 10y = 78-72
y = 6
Now substitute y=6 into (3).
x = 8 - y
x = 8-6
x = 2
Therefore, you bought 2 CDs and 6 movies.
Mr.lopez wrote the equation 32g+8g-10g=150
Answer:
g=5
Step-by-step explanation:
32g+8g-10g=150
30g=150
g=5
Does anyone know the answer
Solution: C
Explanation:
Use the cosine rule
A^2=B^2+C^2-2BCcos a
5^2=8^2+8^2-2×8×8cos a
cos a=(25-64-64)÷(-2×64)
a=36.419°
approx = 36
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.) 40
Answer:
Probability of selecting none of the correct six integers:
a) 0.350
b) 0.427
c) 0.489
d) 0.540
Step-by-step explanation:
a) 40
Given:
Number of integers in a lottery 6
Order in which these integers are selected does not matter
To find:
Probability of selecting none of the correct six integers
Solution:
When the order of selection does not matter then we use Combinations.
Given integers = 40
Number of ways to choose 6 from 40.
Let A be the sample space of choosing digits 6 from 40.
Then using Combinations:
(n,k) = n! / r! (n-r)!
n = 40
r = 6
40C6
=(40,6) = 40! / 6! ( 40 - 6)!
= 40! / 6!34!
= 40*39*38*37*36*35*34! / 6!34!
= 2763633600 / 720
= 3838380
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 40
n = 40 - 6 = 34
r = 6
34C6
=(34,6) = 34! / 6! ( 34 - 6)!
= 34! / 6! 28!
= 34 * 33 * 32 * 31 * 30 * 29 * 28! / 6! 28!
=968330880 / 720
= 1344904
Probability of selecting none of the correct six integers:
P(E) = E / A
= 1344904 / 3838380
= 0.350
Probability of selecting none of the correct six integers is 0.350
b) 48
Following the method used in part a)
(n,k) = n! / r! (n-r)!
n = 48
r = 6
48C6
=(48,6) = 48! / 6! ( 48 - 6)!
= 48! / 6! ( 42 )!
= 48*47*46*45*44*43*42! / 6!42!
= 8835488640 / 720
= 12271512
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 48
n = 48 - 6 = 42
r = 6
42C6
= (42,6) = 42! / 6! ( 42 - 6)!
= 42! / 6! 36!
= 3776965920
= 5245786
P(E) = E / A
= 5245786/12271512
= 0.427
c) 56
(n,k) = n! / r! (n-r)!
n = 56
r = 6
56C6
=(56,6) = 56! / 6! ( 56- 6)!
= 56! / 6! ( 50 )!
= 56*55*54*53*52*51*50! / 6! 50!
= 23377273920/6
= 32468436
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 56
n = 56 - 6 = 50
(50,6) = 50! / 6! ( 50- 6)!
= 50*49*48*47*46*45*44! / 44! 6!
= 11441304000 / 6
= 15890700
P(E) = E / A
= 15890700 / 32468436
= 0.489
d) 64
(n,k) = n! / r! (n-r)!
n = 64
r = 6
64C6
=(64,6) = 64! / 6! ( 64 - 6)!
= 64! / 6! ( 58 )!
= 64*63*62*61*60*59*58! / 6! 58!
= 53981544960 / 720
= 74974368
Let E be the event of selecting none of the correct six integers.
So using combinations we can find the total number of ways of selecting none of 6 integers from 64
n = 64 - 6 = 58
(58,6) = 58! / 6! ( 58- 6)!
= 58*57*56*55*54*53*52! / 52! 6!
= 29142257760/ 6
= 40475358
P(E) = E / A
= 40475358/ 74974368
= 0.540
The probability of selecting none of the correct six integers in a lottery is, 0.350.
Number of integers given = 40
So, Total outcomes for choosing 6 from 40 integers.
Number of arrangements [tex]=_{6}^{40}\textrm{C}[/tex]
[tex]=\frac{40!}{6!*34!} =3838380[/tex]
Since, we have to find probability of selecting none of the correct six integers in a lottery.
Remaining integer = 40 - 6 =34
Let favourable outcomes is selecting none of the correct six integers.
So, number of arrangements, = [tex]=_{6}^{34}\textrm{C}[/tex]
= [tex]\frac{34!}{6!*28!}=1344904[/tex]
Probability is defined as, divide favourable outcomes by total outcomes.
So, The probability of selecting none of the correct six integers in a lottery,
[tex]P=\frac{1344904}{3838380}=0.35[/tex]
Learn more:
https://brainly.com/question/13604758
How many minutes are in 324 hours?
Answer: 19440 minutes
Step-by-step explanation:
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------
Answer: There are 19440 minutes in 324 hours.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Since there are 60 minutes in each hour, we need to multiply the time value by 60. Like this:
324 x 60 = 19440.
2. Susan wants to use blue, yellow, green, and pink paint to decorate her house. She needs 3 times as much blue paint as yellow paint and ½ much yellow paint as green paint. She needs 3 ¼ gallons of pink paint, which is ¾ of a gallon more than the green paint she needs. How much paint does Susan need in all?
Answer:
B = Blue
Y = Yellow
G = Green
P = Pink
The info that we have is:
3*B = Y
(1/2)Y = G
P = (3 + 1/4) gal
P = G + 3/4 gal.
So we have 4 equations. The first step is replacing the third equation into the fourth equation, and get:
G + 3/4 gal = (3 + 1/4) gal
G = (3 + 1/4) gal - 3/4 gal = (2 + 2/4) gal
Now we can replace this into the second equation ((1/2)*Y = G) to find the value of Y.
(1/2)Y = (2 + 2/4) gal
Y = 2*(2 + 2/4) gal = (4 + 1)gal = 5 gal.
Now we can replace this into the first equation and get:
3*B = 5gal
B = 5/3 gal = (1 + 2/3)gal
So the total amount of paint used is:
T = P + G + Y + B = (3 + 1/4) gal + (2 + 2/4) gal + 5gal + (1 + 2/3)gal
T = (11 + 3/4 + 2/3)gal
T = (11 + 9/12 + 8/12)gal = (11 + 17/12)gal = (11 + 1 + 5/12)gal = (12 + 5/12) gal.
Use cubic regression to find a function that fits the following points.
Answer:
Step-by-step explanation:
To use the regression function on your calculator, first hit STAT then choose 1:Edit by pressing ENTER. Then a table pops up. If it's not clear, arrow up to L1, hit CLEAR then ENTER and the table empties. Do the same with L2. Arrow left and right as needed to get from one column to the other. Then in L1 enter the x values one at a time, hitting ENTER after each. When all the x values are in, arrow over to L2 and enter the y values in the same way.
Next, hit STAT again, then right arrow over to CALC. Choose 6:CubicReg by either arrowing down to it or by pressing 6. If you have a TI 83+, the equation comes right up for you; if you have a TI 84+ or 84+CE, you have to arrow down to CALCULATE and hit ENTER to get your equation. The equation is
[tex]-2x^3+2x^2-4x+3[/tex] with a coefficient correlation (r-squared) value of 1 which means this is a perfect equation for this data and all the points you entered into the table fall perfectly on this curve.
Please answer the question correct only if you know the answer
Use the law of cosines to solve for side g.
g^2 = e^2 + f^2 - 2*e*f*cos(G)
g^2 = 10^2 + 8^2 - 2*10*8*cos(57)
g^2 = 76.85775 ... make sure your calc is in degree mode
g = sqrt(76.85775)
g = 8.766855
g = 8.8
A box of 15 cookies costs $ 9 What is the cost for 1 cookie?
Answer:
60 cents or $0.60
Step-by-step explanation:
9.00/15 = 0.6
Answer:
$.60
Step-by-step explanation:
This is just 9 divided by 15 which is $.60
In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer: 16,384
Step-by-step explanation:
The seven marbles have different colours, so we can differentiate them.
Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.
For the first marble, we have 4 options ( we have 4 jars)
For the second marble, we have 4 options.
Same for the third, for the fourth, etc.
Now, the total number of combinations is equal to the product of the number of options for each selection.
We have 7 selections and 4 options for each selection, then the total number of combinations is:
C = 4^7 = 16,384
Answer:
the answer is 16384
Step-by-step explanation:
have a nice day.
What is the explicit formula for this sequence?
Greetings from Brasil...
With the recursive formula, lets build the sequence:
A1 = 4
A2 = A1 - 7
A3 = A2 - 7
A4 = A3 - 7
A5 = A4 - 7
(...)
But pay attention to A3....
A3 = A2 - 7 but A2 = A1 - 7 , so rewriting A3
A3 = (A1 - 7) - 7 ⇒ A3 = A1 + 2.(- 7)
A4 = A3 - 7 ⇒ A4 = [(A1 - 7) - 7] - 7 = A1 + 3.(- 7)
A5 = {[(A1 - 7) - 7] - 7} - 7 = A5 + 4.(- 7)
so
An = A1 + (n - 1).(- 7)In a school, the ratio of students of class 9 to that of class 10 is 3:2. 30% of the students of class 9 and 10%of the students of class 10 were elected to the school student committee. What fraction of the total number of students of the two classes was selected to the school student committee?
Answer:
22% of the two classes were elected to the student committee
Step-by-step explanation:
Given
class 9 : class 10 = 3:2 = 60% : 40%
Total fraction = 60% * 30% + 40% * 10% = 18% + 4% = 22%
dentify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. To determine her air qualityair quality, MirandaMiranda divides up her day into three parts: morning, afternoon, and evening. She then measures her air qualityair quality at 33 randomly selected times during each part of the day. What type of sampling is used?
Answer:
The sampling method used is a stratified sampling method
Step-by-step explanation:
sampling is the selection of a predetermined representative subpopulation from a larger population, to estimate the characteristics of the whole population.
Stratified sampling: Here, the total population are divided into subcategories (strata) before sampling is done. The strata are formed based on some common characteristics. In our example, the times of the day (morning, afternoon and evening) has widely varying atmospheric conditions which will add biases to the measurement of air quality. For example, the air in the morning if compared to the afternoon in an industrial area may be purer because of minimal industrial activity, hence effective comparison will be made by stratification.
what is this expression in rational exponent form cuberoot√5xy^2
Answer:
[tex]5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex].
Step-by-step explanation:
The given expression is
[tex]\sqrt[3]{5xy^2}[/tex]
We need to find the expression in rational exponent form.
It can be written as
[tex](5xy^2)^{\frac{1}{3}}[/tex] [tex][\because \sqrt[n]{x}=x^{\frac{1}{n}}][/tex]
[tex]=(5)^{\frac{1}{3}}(x)^{\frac{1}{3}}(y^2)^{\frac{1}{3}}[/tex] [tex][\because (ab)^m=a^mb^m][/tex]
[tex]=5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
Therefore, the required expression is [tex]5^{\frac{1}{3}}x^{\frac{1}{3}}y^{\frac{2}{3}}[/tex].
To work out the area in m² of material required for a pair of curtains, a seamstress squares the height of the window in m and adds 0.5.
a) What area of material is required for a window of height 1.2meters?
b) What area of material is required for a window of height p meters?
c) if the area of material required is 2.75m²,what is the height of the window?
Answer:
a. Area = 1.94m²
b. Area = (p² + 0.5)m²
c. Height = 1.5m
Step-by-step explanation:
Given
Let H represents Height and A represents Area
From the first and second statements, we have that:
[tex]A = H^2 + 0.5[/tex]
a. Calculating Area When Height = 1.2
[tex]A = H^2 + 0.5[/tex]
Substitute 1.2 for H
[tex]A = 1.2^2 + 0.5[/tex]
[tex]A = 1.44 + 0.5[/tex]
[tex]A = 1.94[/tex]
Hence, the area is 1.94m²
b. Calculating Area When Height = p
[tex]A = H^2 + 0.5[/tex]
Substitute p for H
[tex]A = p^2 + 0.5[/tex]
Hence, the area is (p² + 0.5)m²
c. Calculating Height When Area = 2.75m²
[tex]A = H^2 + 0.5[/tex]
Substitute 2.75 for A
[tex]2.75 = H^2 + 0.5[/tex]
Subtract 0.5 from both sides
[tex]2.75 - 0.5 = H^2 + 0.5 - 0.5[/tex]
[tex]2.75 - 0.5 = H^2[/tex]
[tex]2.25 = H^2[/tex]
Take Square Root of both sides
[tex]\sqrt{2.25} = \sqrt{H^2}[/tex]
[tex]\sqrt{2.25} = H[/tex]
[tex]1.5 = H[/tex]
[tex]H = 1.5[/tex]
Hence, the height is 1.5m
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Suppose you deposit $5,000 in a savings account where the interest earned is compounded continuously
at a rate of 12.5%. How many years will it take the balance in the account to triple (round your answer to
the nearest year)?
0 9 years
O 8 years
Answer:
9 years i think
Step-by-step explanation:
Waves with an amplitude of 2 feet pass a dock every 30 seconds. Write an equation for a cosine function to model the height of a water particle above and below the mean water line. Explain your steps.
Answer:
The cosine function to model the height of a water particle above and below the mean water line is h = 2·cos((π/30)·t)
Step-by-step explanation:
The cosine function equation is given as follows h = d + a·cos(b(x - c))
Where:
[tex]\left | a \right |[/tex] = Amplitude
2·π/b = The period
c = The phase shift
d = The vertical shift
h = Height of the function
x = The time duration of motion of the wave, t
The given data are;
The amplitude [tex]\left | a \right |[/tex] = 2 feet
Time for the wave to pass the dock
The number of times the wave passes a point in each cycle = 2 times
Therefore;
The time for each complete cycle = 2 × 30 seconds = 60 seconds
The time for each complete cycle = Period = 2·π/b = 60
b = π/30 =
Taking the phase shift as zero, (moving wave) and the vertical shift as zero (movement about the mean water line), we have
h = 0 + 2·cos(π/30(t - 0)) = 2·cos((π/30)·t)
The cosine function is h = 2·cos((π/30)·t).