An experiment in a wind tunnel generates cyclic waves. When the experiment starts (at time the wind is moving 13 feet per second (the slowest speed recorded). The speed maxes out at 71 feet per second and returns to 13 feet per second after 44 seconds. Let V represent the wind speed (velocity) in feet per second and let t represent the time in seconds. Write a sine equation that describes the wave.
Answer:
The sine equation for the wave is;
y = 29·sin[(π/22)·(x - 11)] + 42
Step-by-step explanation:
The given wind parameters in the wind tunnel are;
The slowest speed of the wind in the wind tunnel, v₁ = 13 feet per second
The maximum speed of the wind, v₂ = 71 feet per second
The time it takes the wind to complete one cycle = 44 seconds
Therefore, we have;
The general form of the sine equation is given as follows;
[tex]y = A \cdot sin \left [B(x - C)\right ] + D[/tex]
The period, T = 44 seconds = 2·π/B
∴ B = 2·π/44 = π/22
Given that the wave starts at the slowest speed, the horizontal shift
The amplitude, A = (v₂ - v₁)/2
∴ A = (71 ft./s - 13 ft./s)/2 = 29 ft./s
The vertical shift, D = v₁ + a = 13 ft./s + 29 ft./s = 42 ft./s
D = 42 ft./s
When x = 0, sin(B·C) = -1
∴ -B × C = -π/2
∴ C = π/2 ÷ B = π/2 ÷ (π/22) = π/2 × 22/π = 11
Therefore, the sine equation for the wave is;
the sine equation for the wave is;
y = 29·sin[(π/22)·(x - 11)] + 42
Simplify.
(2 x 108) + (4 * 103)
Give the answer in scientific notation
Answer:
628
Step-by-step explanation:
216+412 = 628
First you get rid of the brackets by solving what's in them. Then you just add up the numbers and BOOM. The equation is solved. :-)
Find a formula for a_n (for the geometric sequence), then find the 8th term. Solve for both or one of these questions, thank you so much!
Answer:
2a. aₙ = 12 * -2ⁿ⁻¹; a₈ = -1536
2b. aₙ = 4 * 3ⁿ⁻¹; a₈ = 8748
Step-by-step explanation:
The geometric sequence formula is aₙ = a₁ * rⁿ⁻¹.
2a:
a₈ = 12 * -2⁸⁻¹ {Subtract 1 from 8 to get 7}
a₈ = 12 * -2⁷ {2⁷ is 128. Since the exponent is odd, this will be negative.}
a₈ = 12 * (-128) {Multiply 12 by -128 to get -1536.
a₈ = -1536
2b:
a₈ = 4 * 3⁸⁻¹ {Subtract 1 from 8 to get 7)
a₈ = 4 * 3⁷ {7 is the 3rd number after 4 (a multiple of 4). As a result, this will end in a 7. 3⁷ is 2187.}
a₈ = 4 * 2187 {Multiply 4 by 2187 to get 8748}
a₈ = 8748
The volume, V, of any cube with side length, s, can be determined using the formula V = s3 . What is the volume, in cubic centimeters, of a cube with a side length of 0.2 centimeters?
A
3.2
B
0.6
C
0.006
D
0.008
Evaluate f(x) = 2|x – 5| for f(–5) and f(0).
f(–5) = –20, f(0) = –2
f(–5) = 10, f(0) = 0
f(–5) = 20, f(0) = 10
f(–5) = 12, f(0) = 5
Answer:
f(–5) = 20, f(0) = 10
Step-by-step explanation:
f(-5):
f(-5) = 2|-5 -5|
f(-5) = 2|-10|
f(-5) = 2(10)
f(-5) = 20
f(0):
f(0) = 2|0 - 5|
f(0) = 2|-5|
f(0) = 2(5)
f(0) = 10
Maria makes money by commission rates. She gets 15% of everything she sells. If Maria sold $23000 worth of items this month, what is her salary for the month?
Answer:
3450$ :)
Step-by-step explanation:
A NO PASSING ZONE road sign has the shape of an
isosceles triangle with angle measures shown. Write
and solve an equation to determine the value of x.
Round to the nearest tenth.
(3.25x)"
NO
PASSING
ZONE
*50*
X=
Answer:
15.38
Step-by-step explanation:
two angles are equal
3.25x=50
x= 15.38461538461
What is (4×-5)^2 in polynomial form
Answer:
[tex]4x^2-20x+25[/tex]
Step-by-step explanation:
We start with this expression.
[tex](4x - 5)^2[/tex]
When an expression inside parentheses are squared, we have to take two of the expression and multiply them together. To do this, we need to multiply each part of one expression and multiply it with every part in the other expression.
This means that [tex](4x - 5) (4x - 5)[/tex] would become...
[tex](4x)(4x) = 4x^2\\(-5)(4x) = -20x\\(-5) (-5) = 25[/tex]
Now, we simply need to put all of the terms into one expression.
[tex]4x^2-20x+25[/tex]
the cost of a school banquet is $95 plus $15 for each person attending. Write an equation that gives total cost as a function of the number of people attending. What is the cost for 77 people?
Answer:
equation: y=15x+95
it would cost $1250
Answer:
f(x) = 95 + 15x
Cost for 77 people = $1250
Step-by-step explanation:
15 x 77 = 1155
1155 + 95 = 1250
If the acceleration is 600m/s/s and the mass is 300kg, calculate the force? *
Answer:
600 m/s2 ×300 kg = 180000 kg.m/s2
Answer:
180000Kgm/s2
Step-by-step explanation:
Force is the product of mass and acceleration. So F=MA
F=600 x 300
F=180000
Can someone please solve this for me
Two parallel lines have same slopes so we need to find the slope of the line which passes through the given points.
Suppose : A = ( - 2 , 7 ) & B = ( 4 , 4 )
Slope = y ( B ) - y ( A ) / x ( B ) - x ( A )
Slope = 4 - 7 / 4 - ( - 2 )
Slope = - 3 / 4 + 2
Slope = - 3 / 6
Slope = - 1 / 2
------------------------------------------------------------
As you know The coefficient of x is the slope of the line in slope-intercept form.
Thus we have to find the option which x has - 1 / 2 as the coefficient .
Look we have that in D so the correct answer is D .
Jason is looking up at the light at the top of the lighthouse. The angle of elevation from Jason to the light is 34°. The height of the lighthouse is 217 feet. a) Draw the right triangle. Label the given information on the triangle. b) Label the sides OPP, ADJ, and HYP. PUT A BOX AROUND EACH LABEL. c) Determine the distance from Jason to the light. d) Round your answer to the nearest tenth. Show all work.
Answer:
6ix9ine
Step-by-step explanation:
I don’t know how to do that
Answer:
16
Step-by-step explanation:
Divide 64 by 8 to get 8. this is 1/8 of the books.
3/8 were non fiction, or 24
1/4 (2/8) were picture books, or 16
5/8 were non fiction or picture books, so ’the rest‘ of the chapter books is 3/8.
3/8 were chapter books, or 24.
add the amount of picture books and chapter books since they are the fictional texts.
16+24=40
subtract the amount of non fictional books from the amount of fictional books to get the sum.
40-24=16
A 9-foot (ft) ladder and a 4-foot ladder are leaning against a house. The two ladders create angles of the
same measure with the ground. The 4-foot ladder has a height of 3.8 feet against the house.
Help please!!
Answer:
The 9-foot ladder would have a height of 8.55 ft against the house
Step-by-step explanation:
The angles made by the 9-foot ladder and 4-foot ladder that are leaning against the house is 71.8 degrees.
The situation forms a right angle triangle.
What is a right angle triangle?A right angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonpometric ratios.
Therefore, the 9 foot and the 4 foot ladder forms the same angle.
The 4 foot ladder forms a 3.8 ft height against the wall.
Hence,
sin ∅ = opposite/ hypotenuse
sin ∅ = 3.8 / 4
∅= sin⁻¹ 0.95
∅ = 71.8051276612
∅ = 71.8°
Therefore, the angles made by the 9-foot ladder and 4-foot ladder that are leaning against the house is 71.8 degrees.
learn more on right triangle here: https://brainly.com/question/22894739
Look at the picture to see question please help
7a +42 +8 < -10 + 9a -6 + 4a
Answer:
a > 11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
7a + 42 + 8 < -10 + 9a - 6 + 4a
Step 2: Solve for a
Combine like terms (a): 7a + 42 + 8 < -10 + 13a - 6Combine like terms: 7a + 50 < 13a - 16[Subtraction Property of Equality] Subtract 7a on both sides: 50 < 6a - 16[Addition Property of Equality] Add 16 on both sides: 66 < 6a[Division Property of Equality] Divide 6 on both sides: 11 < aRewrite: a > 11Here we see that any value a greater than 11 would work as a solution to the inequality.
Simon bought a 10-pound bag of cat food. He gives his cat 0.3 pound of food per day. Which equation with two variables to describe how the amount of cat food in the bag changes over time.
Answer:
y = 10 - 0.3t
Step-by-step explanation:
Amount of cat food purchased= 10 pounds
Daily pounds fed to dog = 0.3 pounds
How the amount of cat food in bag changes over time ;
Let y = amount of cat food left in bag
t = number of days since cat food was purchased
Amount of cat food left in bag = amount of cat food purchased - (daily pounds fed to dog * Number of days since cat food was purchased)
y = 10 - 0.3t
Find the area of the figure to the nearest tenth.
165 7 in
Answer:
141.1 in
Step-by-step explanation:
r^2*theta
7^2*165pi/180
141.1
Answer:
Step-by-step explanation:
Which of the following examples has a unit rate of 25 feet per second? Select all that apply. A) 100 feet in 4 seconds B) 150 feet in 10 seconds C) 225 feet in 9 seconds D) 275 feet in 11 seconds E) 100 feet in 5 seconds
Answer:
A) C) D)
Step-by-step explanation:
We can simply divide them to find out the answer.
A) 100/4=25
B)150/10=15
C)225/9=25
D)275/11=25
E)100/5=20
Help me find the value of W
Answer:
what grade is this?
Step-by-step explanation:
amelia machine changes one red token into three white tokens and one white token into two red tokens. amelia has three red tokens and one white token. she uses the machine three times what is the smallest number of tokens she can end up with?
WHOEVER ANSWERS FIRST GETS BRAINLIEST BUT IT MUST BE CORRECT'
If anyone is really good at math please hmu ASAP.
Answer:
Same I'll help you all if you guys try to help me with my recent question.
Step-by-step explanation:
what is 500 times 10
Answer:
500*10=5,000
hope this helps
Answer:
5,000
Step-by-step explanation:
please correct me if im wrong
$17.40 is 120% of what price?
True or false
If two figures are similar and one is bigger than the other, the scale factor of bigger to smaller will be the same as the scale factor of smaller to bigger.
Will give brainly
Answer:
False
Step-by-step explanation:
if you are comparing two figures that are similar the scale factor will flip because you are altering the shape from the first shape
27 please I’ll try to give you brainliest
Answer:
Hexogen
Step-by-step explanation:
Meredith went to an aquarium with some of her friends. The tickets cost $12.95 each, and they spent $38 on souvenirs. The total amount spent was $115.70. Which equation can be used to determine how many tickets, t, were purchased?
Answer:
12.95t+38=115.70
Step-by-step explanation:
Which measures describe the variation on a data set? a. Mean b. Median c. Mode d. MAD e. Interquartile range f. Range
Answer:
e, f
Step-by-step explanation:
A measurement of variability is an overview of the amount of dispersion in a dataset. The measures that can describe the variation on a data set are Range, Interquartile Range, Variance, and Standard Deviation.
So ,The among the given options the e. Interquartile range f. Range
Range of dataset is the difference between the larges and smallest elements in the dataset .
The middle of the data between the upper and lower quartiles are called the inter-quartile range. That means that 50 percent of data points between Q1 and Q3 are included within the interquartile range.
Please help me, will mark brainliest
Answer:
EThir 83 or 180
Step-by-step explanation:
Find the value of x please and fast!!
Answer:
B) 5
Step-by-step explanation: