A small ball floats on the surface of the water in a wave pool. As a wave moves past the ball, the ball's
height above the bottom of the pool varies from 22 inches to 34 inches. The waves occur every
6 seconds. Which function models the distance from the bottom of the pool to the ball, as it moves
from wave crest to wave crest, as a function of t in seconds?
d(t) = 12 cos(3At) + 28
d (t) = 6 cos(3mt) + 28
34 in.
d(t) = 6 cos (+) +
+ 28
22 in
d(t) = 12 cos( 5 ) + 28
Answer:
The correct option is;
d(t) = 6·cos(π/3·t) + 28
Step-by-step explanation:
The general form of a cosine function is given as follows;
y = A·cos(B·x - C) + D
Where;
A = The amplitude = The distance from the peak to the midline = 1/2×(Maximum - minimum)
The amplitude = 1/2 × (34 - 22) = 6 inches
B = 2·π/P = 2·π/6 = π/3
P = The period = 6 seconds
C/B = The phase shift
D = The midline = Minimum + Amplitude = 22 + 6 = 28 inches
x = The independent variable
Therefore, to model the function of the wave can be given as follows;
d(t) = 6·cos(π/3·t) + 28
A function that models the distance from the bottom of the pool to the ball, as it moves from wave crest to wave crest, as a function of t in seconds is [tex]d(t)= 6cos(\frac{\pi}{3} t) + 28[/tex]
The standard wave equation is expressed as;
[tex]y=Acos(Bx-C)+D[/tex] where:
A is the amplitude
Get the amplitude:
[tex]A=\frac{1}{2}(34-22)\\A=\frac{1}{2}(12)\\A= 6\\[/tex]
If the wave occurs every 3 seconds, then:
[tex]B=\frac{2 \pi}{k} \\B=\frac{2\pi }{6}\\B=\frac{\pi}{3}[/tex]
Get the midline D
[tex]D=minimum + amplitude\\D=22+6\\D = 28[/tex]
Substitute the given parameters into the equation above to have;
[tex]y= 6cos(\frac{\pi}{3} t) + 28[/tex]
Hence a function that models the distance from the bottom of the pool to the ball, as it moves from wave crest to wave crest, as a function of t in seconds is [tex]d(t)= 6cos(\frac{\pi}{3} t) + 28[/tex]
Learn more here: https://brainly.com/question/25524388
find the range of the following functions.f(x)=2+5sin3x
Answer:
Range: [-3, 7]
Step-by-step explanation:
Range is all the y-values that are outputted.
When we graph the equation, we should see our minimum y-value and maximum y-value.
can someone help me? “Fond the measure of the missing angle” pleaseee
Answer:
It's Below.
Step-by-step explanation:
1) 180° - 124° = 56°
2) 90° - 58° = 32°
3) 90° - 34° = 56°
4) 180° - 107° = 73°
Don't forget to put the degrees symbol! :)
I need help determining the rang of this graph
The highest point is when y = 0 and the lowest point is when y = -5
We can see this if we draw horizontal lines through the highest and lowest points (see the diagram below). Note where the horizontal lines cross the y axis. For y = 0, we don't really need a horizontal line but I'll draw it anyway.
Since y ranges from y = -5 to y =0, the range is therefore [tex]-5 \le y \le 0[/tex]
Answer: y is a real number such that [tex]-5 \le y \le 0[/tex]Side note: to write this in interval notation, you would say [tex][-5, 0][/tex]. The square brackets say to include each endpoint as part of the range.
Travis is deciding how to study math tonight. He is choosing between studying graphs (G) patterns (P) or equations (E). He is also deciding whether he should use a textbook (T) or videos (V) to study. He will choose one topic and one method of learning. Which combo is tight
A. GT,GV,PT,PV
B. GT PT ET GV PV EV
C GT GV PT PV ET EV TV
D GP GE GT GV PE PT PV ET EV TV
Answer:
The correct option is;
B. GT PT ET GV PV EV
Step-by-step explanation:
The given information we have;
The number mathematics topics Travis has to chose from tonight = 3 topics
The number of ways he can chose to study each topic = 2 ways
Therefore the number of different combo Travis can chose from is given as follows;
The number of combos = The number of topics × The number of ways
∴ The number of combos = 3 × 2 = 6 combos
Therefore, the possible combos are;
B. GT PT ET GV PV and EV which is the same as GT, GV, PT, PV, ET, and EV.
The price of bananas can be determined by the equation p=0.45n where p is the price and n is the number of bananas. What is the constant of proportionality (unit rate)
Answer:
The constant of proportionality is 0.45.
Step-by-step explanation:
The constant of proportionality is the ration of two different quantities or is the unit value of a quantity.
The expression representing the price of bananas is:
[tex]p=0.45n[/tex]
To determine the unit rate of bananas divide the price by the number of bananas.
[tex]\text{Unit Rate}=\frac{p}{n}[/tex]
[tex]=\frac{0.45n}{n}\\\\=0.45[/tex]
Thus, the constant of proportionality is 0.45.
a) x² - y² - x + y Factorize
Answer:
(x - y) (x+y -1)
Step-by-step explanation:
See steps of factorization:
x² - y² - x + y =(x² - y²) - (x - y) = (x - y) (x + y) - (x- y) =(x - y) (x+y -1)Amira has a bag of cat food her cat eats 1/10 of a bag per week how many weeks will the food last ?.
Answer:
10 weeks
Step-by-step explanation:
6. Simplify: i) (a + b)(5a – 3b) + (a – 3b)(a – b) ii) (a – b) (a2 + b2 + ab) – (a + b) (a2 + b2 – ab) iii) (b2 – 49) (b + 7) + 343 okay, I know I posted this question before but, if you're giving your answers, please explain how you got it,
Answer:
Step-by-step explanation:
6. I will multiply then I respect the sign rules
- * - = +
- * + = -
I will atach the file immediately.
I multiplied the paranthesis and then I added the results
Answer:
i)6a^2-2ab-6b^2
ii)ab^2-1a^2b
iii)b^3-42b
Step-by-step explanation:
Use distributive property
Collect like terms
(a+b)(5a-3b)+(a-3b)(a-b)
(a+b)(5a-3b)---- Distributive property
5a^2-3ab+5ab-3b^2
5a^2+5ab-3ab-3b^2
5a^2+2ab-3b^2
(a-3b)(a-b)
a^2-ab-3ab-3b^2
a^2-4ab-3b^2
So,
5a^2+2ab-3b^2+a^2-4ab-3b^2---Collect like terms
5a^2+a^2+2ab-4ab-3b^2-3b^2
6a^2-2ab-6b^2
(a–b)(a^2+b^2 +ab)–(a + b)(a^2+b^2 –ab)
(a–b)(a^2+b^2 +ab)----Distributive property
a^3 since a^(1+2)=a^3
a^3+ab^2+a^2b-ba^2-b^3-ab^2
a^3+ab^2-ab^2+a^2b-ba^2-b^3
a^3+a^2b-a^2-b^3
a^3-b^3
(a+b)(a^2+b^2-ab)
a^3+ab^2-a^2b+ba^2+b^3-a^2b
a^3+ab^2+ba^2+b^3-a^2b-a^2b
a^3+ab^2+ba^2+b^3-2a^2b
So,
a^3-b^3-a^3+ab^2+ba^2+b^3-2a^2b--Collect like terms
a^3-a^3-b^3+b^3+ab^2-2a^2b+a^2b
ab^2-1a^2b
(b^2–49)(b + 7)+343---Distributive property
b^3+7b-49b-343+343---Collect like terms
b^3-49b+7b
b^3-42b
Hope this helps ;) ❤❤❤
which expression is equivalent to 1/2 x + (-7) -2 q/4 x - (-2) ?
Answer:
−1 /2 qx+ 1 /2 x-5
Step-by-step explanation:
Let's simplify step-by-step.
1 /2 x−7− 2q/ 4 x−(−2)
= 1 /2 x+−7+ (−1/2) qx+2
Combine Like Terms:
= 1 /2 x+−7+ (−1 /2 qx+2
=( −1 /2 qx)+( 1 /2 x)+(−7+2)
= −1 /2 qx+ 1 2x+−5
Answer:
= −1 /2 qx+ 1 /2 x-5
HOPE THIS HELPS!!!!!! :)
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Lin created a scaled copy of Triangle A with an area of 72 square units. How many times larger is the area of the scaled copy compared to that of Triangle A
Answer:
The question is not complete, here is a possible match to the complete question:
Here is Triangle A. Lin created a scaled copy of Triangle A with an area of 72 square units. What scale factor did Lin apply to the Triangle A to create the copy? Remember: A=1/2bh
a) 4
b) 8
c) 16
Answer:
Scale factor = 16
Step-by-step explanation:
From the diagram attached to this solution, the triangle was plotted on a graph sheet, and each grid on the graph represents 1 unit. hence the dimensions of Triangle A from the diagram is as follows:
Base = 3 units
Height = 3 units
Next, in order to determine the scale factor of the area of the triangle after scaling, let us calculate the area of the unscaled triangle.
Area of Triangle = 1/2 (base × height)
Area or Triangle = 0.5 × 3 × 3 = 4.5 square units
Therefore,
Area of unscaled triangle = 4.5 squared units
Area of scaled triangle = 72 squared units
since the area of the scaled triangle is larger than the unscaled triangle, the scale factor is simply the number of times by which the scaled triangle was enlarged, compared to the unscaled triangle. This can be calculated by dividing the scaled triangle by the unscaled triangle as follows:
Scale factor =(scaled triangle) ÷ (unscaled triangle)
Scale factor = 72 ÷ 4.5 = 16
A line passes through the point (4,-4) and has a slope of 5/4.
Write an equation in slope-intercept form for this line.
Answer:
y = 5/4x - 9
Step-by-step explanation:
y = mx + b
when you plot 4, -4 you have your first clue and point. then go up 5 and right 4 or down5 and left 4. When you go down you will reach the y intercept. On the number- 9. So -9 is your y intercept which goes in b.
Since 5/4 goes in the mx since it is slope the answer is y = 5/4 - 9
how would i simplify the expression?
Which figure is described below?
The locus of points 6 units from the
point (1, -2) on the coordinate plane.
Answer:
C; Circle
Step-by-step explanation:
In this question, we are interested in giving a term to the locus of points which are at a certain distance from a fixed point.
The correct answer to this is a circle.
From the question, we can picture a situation which we have the point (1,2) as the center of the circle. This point serve the starting point in which all other points which are exactly 6 units away are plotted.
Thus, from this center point, we can mark off several points around the center point. By tracing the marked points from these center, we can obtain a circular path which when traced completely will give us the identity of a circle, where these points represent the line bounding the circle which is referred to the circumference of the particular circle in question.
Further more, from the definition of the radius of a circle, it is the distance from the center of a circle to the circumference. While the point (1,2) represents the center of the circle in question, the distance 6 units stand for the radius of the circle.
Answer:
circle
Step-by-step explanation:
Which equation matches the graph of the absolute value function seen here?
A) y = -|x|
B) y = -
1
2
|x| - 1
C) y =
1
2
|x - 3| - 1
D) y = |
1
2
x - 2| - 1
Answer:
Step-by-step explanation:
A collection of nickels, dimes and pennies has an average value of 7 cents per coin. If a nickel were replaced by five pennies, the average would drop to 6 cents per coin. What is the number of dimes in the collection?
Answer: The number of dimes is:
Dimes = -(Nickels + Pennies) + 24.
Such that Nickels + Pennies < 24, and each quantity refers to the initial number of coins of the given type.
Step-by-step explanation:
Let's call N = number of nickels, D = number of dimes, and P = number of pennies.
The total number of coins is N + D + P
We know that the total value in nickels is:
N*$0.05
The total value in dimes is:
D*$0.10
And the total value on Pennies is:
P*$0.01
Then, the "mean" value of the coins will be equal to the total value of all the coins, divided the total number of coins.
$0.07 = (N*$0.05 + D*$0.10 + P*$0.01)/(N + D + P)
we can mutiply at both sides by the total number of coins, and we have:
$0.07*(N + D + P) = N*$0.05 + D*$0.10 + P*$0.01
Now, if we remove one nickel by five penies, we have:
$0.06 = ((N-1)*$0.05 + D*$0.10 + (P+5)*$0.01)/(N - 1 + D + P + 5)
Again, we multiply in both sides by the total number of coins and:
$0.06*(N - 1 + D + P + 5) = ((N-1)*$0.05 + D*$0.10 + (P+5)*$0.01)
Ok, now we have two equations:
$0.07*(N + D + P) = N*$0.05 + D*$0.10 + P*$0.01
$0.06*(N + D + P + 4) = ((N-1)*$0.05 + D*$0.10 + (P+5)*$0.01)
We can take the second equation and write the right side as:
$0.06*(N + D + P + 4) = ((N-1)*$0.05 + D*$0.10 + (P+5)*$0.01)
= N*$0.05 + D*$0.10 + P*$0.01 - 1*$0.05 + 5*$0.01
= N*$0.05 + D*$0.10 + P*$0.01
Now, the two equations are:
$0.07*(N + D + P) = N*$0.05 + D*$0.10 + P*$0.01
$0.06*(N + D + P + 4) = N*$0.05 + D*$0.10 + P*$0.01
Then we have that:
$0.07*(N + D + P) = $0.06*(N + D + P + 4)
D*($0.07 - $0.06) = ($0.06 - $0.07)*(N + P)) + 4*$0.06
D*$0.01 = -$0.01(N + P) + 4*$0.06
D = (-$0.01(D + P) + 4*$0.06)/$0.01 = -(N + P) + 24
So the number of Dimes is related to the number of pennies and nickels that we have at the begginig.
Such that in both cases the number of dimes is equal:
D = -(N + P) + 24
Notice that N + P can not be larger or equal than 24, so we have the rule:
N + P < 24.
D
Find the value of x. A. 3 B. 2 C. 5 D. 6
Answer:
[tex]\Huge \boxed{x=5}[/tex]
Step-by-step explanation:
Apply the intersecting chord theorem.
DK × BK = AK × CK
12(4x+1) = 14(3 + 3x)
Expand brackets.
48x + 12 = 42 + 42x
Subtract 42x and 12 from both sides.
6x = 30
Divide both sides by 6.
x = 5
Answer:
C
Step-by-step explanation:
Given 2 chords intersecting inside a circle, then
the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is
12(4x + 1) = 14(3 + 3x) ← distribute parenthesis on both sides
48x + 12 = 42 + 42x ( subtract 42x from both sides )
6x + 12 = 42 ( subtract12 from both sides )
6x = 30 ( divide both sides by 6 )
x = 5
Evaluate y5 + x(-7)
When x = 2, y = -5
Answer:
45
Step-by-step explanation:
OK, first we turn the variables into into the actual values:
The equation will look like this:
(2)5 + (-5)(-7)
Now its easier to solve! Lets solve (2)5!
2 * 5 = 10
The equation looks like:
10 + (-5)(-7)
We will also solve (-5)(-7). Remember that a negative number times a negative number is positive!
-5 * -7 = 35
Lets finish the rest:
10 + 35 = 45.
Hope this is correct and have a nice day!
Christine went shopping and bought each of her eight nephews a gift, either a video costing $14.95 or a CD costing $16.88. She spent $131.18 on the gifts. How many
videos and how many CDs did she buy?
Answer:
Step-by-step explanation:
Define number of videos purchased as "n" and number of CD's purchased as "c" then we can equation the total purchases and the costs by:
8 nephews:
n + c = 8
Spent $121.53
14.95*n + 16.88*c = 121.53
Substitute one variable as a function of the other. Preference the simpler equation (n + c = 8)
n = 8 - c
=>
14.95*(8-c) + 16.88c = 121.53
119.60 + 1.93c = 121.53
1.93c = 1.93
c = 1
=>
n = 7
*Check:
14.95*(7) + 16.88*(1) = 121.53
im so sorry if this is wrong :/
What is the y-intercept of the graph? Thank you!!
Answer: 4
Step-by-step explanation: The y-intercept is a point
where a line crosses the y-axis.
All y-intercepts have an x-coordinate of zero.
The equation shown here is in slope-intercept form or y = mx + b form.
In this form, the m represents the slope and the b is y-intercept.
So here, we can tell that the y-intercept is 4.
what is the expression of 2+32times5
Answer:
2+32×5
If you want the answer:
2+160
162
Step-by-step explanation:
Answer:
2+5^32
Step-by-step explanation:
A logarithm question: 3² +㏒₂5
Answer:11.322
Step-by-step explanation:
3^2 + log2 5 =9+(ln5/ln2)=9+2.322=11.322
Can someone help me
Answer:
4 is the answer
Step-by-step explanation:
8 + x + 2 = 4x -2
8 + 2+ 2 = 4x - x
12 = 3x
x =12/3 = 4
help me yall this for me aint it.
Answer:
20(4 + 5)
Step-by-step explanation:
GCF is just the biggest number each value can be divided by. Here, it's 20, so that goes outside of the parenthesis. Now, what can you multiply by 20 to get 80? 4, so that goes in the second box. What can you multiply by 20 to get 100? 5, so that goes in the last box. You can check your answer by doing 80 + 100 = 180; 20(9) = 180.
So you have to find the GCF (Greatest Common Factor) or 80 and 100, which is 20.
20(?+?)
20 times what gets you 80?
20 times 4 gets you 80.
20 times what gets you 100?
20 times 5 gets you 100.
20(4+5) = 80+100 = 180
♡ Hope this helped! ♡
❀ 0ranges ❀
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling? algebra
Answer:
50 miles per hour =73.33 feet per second (the conversion rate)
now if Morris is travelling 3 feet per second less than Aneesha so, the speed of Morris is 70.33 feet per second;
if we convert this to Miles per hour;
70.33 feet per second= 48 miles per hour (approximately)
so here the last last option is the right
48 miles per hour
Answer:
48 miles per hour
Step-by-step explanation:
What’s the area of this shape?
Answer:
212 m²
Step-by-step explanation:
Break it down into 3 rectangles.
10x8=80
4x13=52
16x5=80
80+52+80=212
Skate station charges a flat rate of $5.00 for skate rental plus $2.00 per hour of skating. If the number of hours is represented by "h," which algebraic expression represents the overall rate for "h" hours of skating?
Answer:
The answer is 5+2h because it is $2 per hour so 2h and $5 per day. it does not have a variable for $5 per day
What is 0.6 as a simplified fraction?
Answer
3/5
0.6 / 1 = 6 / 10 = 3/5
Answer:
3/5
Step-by-step explanation:
0.6=6/10
[dividing through by two]
=3/5
An irrational number is considered irrational if it meets one of two rules. What are the two rules?
Answer:
Step-by-step explanation:
A number that cannot be exactly expressed as a ratio of two integers.
An irrational number cannot be written as a simple fraction.
Pi is a famous irrational number.
Write the given number in the form a × 10 n , where a is a real number such that 1 ≤ |a| < 10 and n is an integer. 230,000,000,000 = 2.3 × 100,000,000,000 = 2.3 × 10 11
Answer:
2.3 x 10^11.
Step-by-step explanation:
There are 11 digits after the first digit (2).
The answer is 2.3 x 10^11.
This is called scientific notation.