The function f(t) = 5*cos ((pi/4)*t) + 11 represents the tide in Dark Sea. It has a maximum of 16 feet when time (t) is 0 and a minimum of 6 feet. The sea repeats this cycle every 8 hours. After six hours, how high is the tide?
A. 11 feet
B. 6 feet
C. 8.5 feet
D. 10.5 feet
After six hours, the tide is 11 feet high.
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."For given question,
We have been given a function [tex]f(t)=5\times cos((\frac{\pi}{4} )t)+11[/tex]
which represents the tide in Dark Sea and t represents the time in hours.
We need to find the height of the tide after 6 hours.
For t = 6, we need to find the value of function f(t)
[tex]\Rightarrow f(6)=5\times cos((\frac{\pi}{4} )6)+11\\\\\Rightarrow f(6)=5\times cos((\frac{3\pi}{2} ))+11\\\\\Rightarrow f(6)=0+11\\\\\Rightarrow f(6)=11[/tex]
Therefore, after six hours, the tide is 11 feet high.
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Isaiah’s family drove 348.2 miles per day on their vacation across county. How many miles did Isaiah’s family travel in 2.5 days?
multiply miles per day by number of days
348.2 * 2.5 = 870.5 miles
Find 0.001 more than 18.852.
How do you solve this using the elimination method of systems of equations?
25x - 5y= 30
- 25x + 10y=15
------------------
-5y-(+10y)=30-15
-5y-10y =15
-15y= 15
divide both sides by -15
y= -1
finding the value of x by subs. y=-1
into equation 1
5x-(-1)=6
5x +1=6
5x=6-1
5x=5
divide both sides by 5
x= 1
an elevator traveled from the 10th floor to the 2nd floor in 6 seconds. what was the rate of the elevator in floors per second
The elevator travels 4/3 levels per second, or floors per second.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, an elevator traveled from the 10th floor to the 2nd floor in 6 seconds.
Elevator cover total distance = 10 -2 = 8 floors
since it took elevator 6 seconds
thus
elevator travels in 6 seconds = 8 floor
elevator travels in 1 seconds = 8/6 =4/3 floor
Therefore, the rate of the elevator in floors per second is 4/3 floor per seconds
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Grandma Jean is preparing the turkey for Thanksgiving dinner.The turkey weighs 12 lbs and there will be a total of 18 people at sinner.If each person eats the same amount of turkey,how much turkey will each person get
n - (-24) =12 find the value
at the animal shelter 5/8 are cats. Of the cats, 2/3 are kittens. What fraction of animals at the shelter are kittens?
How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters
125 three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters.
What is Combination?A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.
We need to find three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters.
The given letters are FGHIJ.
As we need to find three letter words.
This can be done by using 5³ as the repetitions are allowed.
Five power cube number of three words can be formed.
5×5×5
One hundred twenty five.
125
Hence, 125 three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters.
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Each row in a window display of compact disk cartons contains two more boxes than the row above. The first row has one box. How many rows will make to where there is 144 boxes
Do you think a bar model would be a good model for converting miles to feet
A dripping faucet wastes a cup of water if it drips for three minutes. The amount of water wasted varies directly with the amount of time the faucet drips. What is the constant of variation?
A. 1/3
B. 2
C. 1/2
D. 3
Answer:
A. 1/3
Step-by-step explanation:
Suppose x represents the amount of the water ( in cups ) wasted in t minutes,
∵ The amount of water wasted varies directly with the amount of time the faucet drips,
⇒ x ∝ t
⇒ x = kt
Where,
k = constant of variation,
If x = 1, t = 3,
[tex]\implies 1 = k(3)\implies k = \frac{1}{3}[/tex]
Hence, the constant of variation is [tex]\frac{1}{3}[/tex]
OPTION A is correct.
The ratio of the ages of three children is 2:4:5. The sum of their ages is 33. What is the age of each child?
Step-by-step explanation:
let the given ages be 2x , 4x and 5x.
Here,
2x + 4x +5x =33
or,x = 33/ 11
or,x =3
Hence,
2x =2 (3)=6years
4x=4(3)=12years
5x=5(3)=15years
Answer:
6,12,15
Step-by-step explanation:
Let the ages be 2x,4x,5x
Given
2x+4x+5x=33
11x=33
x=3.
2x=2×3=6
4x=4×3=12
5x=5×3=15
You have two fractions, 2/5 and 3/10, and you want to rewrite them so that they have the same denominator (and whole number numerators). What number(s) could you use for the denominator?
Choose the 2 answers that apply:
A. 15
B.5
C.20
D.10
HELP PLS I WILL GIVE BRAINLIEST AND TWENTY POINTS PLS HELP
Simplify: (13x + 10y) - (6x - 7y) +5x
the are of a rectangular tablecloth is 4 1/6 square meters. the width of the tablecloth is 1 1/4 meters. what is the length of the table cloth?
The length of the rectangular table cloth is [tex]\mathbf{ 3\dfrac{1}{3} m}[/tex]
What is a rectangle?A rectangle is a plane figure that has an equal size of the opposite side. These sides are called the length and the width.
Mathematically;
The area of the rectangle = Length × width
From the parameters given:
Area of a rectangle = 4 1/6 square meters.The width = 1 1/4 metersUsing the formula for the area of a rectangle, we have:
[tex]\mathbf{4 \dfrac{1}{6} m^2 =length \times 1 \dfrac{1}{4} \ m }[/tex]
[tex]\mathbf{ \dfrac{25}{6} m^2 =length \times \dfrac{5}{4} \ m }[/tex]
Multiply both sides by [tex]\mathbf{\dfrac{4}{5}\times \dfrac{1} {m}}[/tex]; we have:
[tex]\mathbf{ \dfrac{25}{6} m^2 \times \mathbf{\dfrac{4}{5}\times \dfrac{1} {m}} =length \times \dfrac{5}{4} \ m \times \mathbf{\dfrac{4}{5}\times \dfrac{1} {m}}}[/tex]
[tex]\mathbf{ length = \dfrac{25}{6} m \times \mathbf{\dfrac{4}{5}} }[/tex]
[tex]\mathbf{ length = \dfrac{5}{3} m \times \mathbf{\dfrac{2}{1}} }[/tex]
[tex]\mathbf{ length = \dfrac{10}{3} m}[/tex]
[tex]\mathbf{ length = 3\dfrac{1}{3} m}[/tex]
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The temperature was 29*F. By the end of the day, the temperature dropped TO -7*F. what was the total distance in the temperature change?
A school policy requires that there be at least one chaperone for every 8 students on a field trip. How many chaperones are required for a field trip with 67 students?
Solve the following equation: -3 = 1 3/5 + m
what is 20x34 equal.
maya tried to play a new video game.on her first 4 tries,she lost 14 points,lost 8 points,and finnaly gave up.write and find the value of an integer expression to show her final score
Write the slope-intercept form of the given line. Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Edwin walks for 2 1/2 hours. He walks 1 2/3 miles in the first hour, 1 3/4 miles in the second hour and 1/4 of the total distance in the last 1/2 hour.What is the total distance Edwin walks?
Answer:
The total distance is 41/9 = 4 5/9 miles
Step-by-step explanation:
Total time is 2 1/2 hours.
First hour, he walks 1 2/3 = 5/3 miles.
Second hour, he walks 1 3/4 = 7/4 miles.
The last half hour he walks 1/4 of total distance. If we call total distance x.
[tex]\frac{5}{3} + \frac{7}{4} +\frac{x}{4} = x[/tex]
Now, we can eliminate the denominator, multiplying by four and by three.
[tex]5*4 + 7*3 + 3*x = 4*3*x\\20 + 21 + 3x = 12 x\\41 +3x = 12x \\41 = 12x - 3x\\41 = 9x\\x = 41/9\\x = 4 \frac{5}{9}[/tex]
Total distance is 4 5/9 miles
What are the factors of the expression? 6/7cd
Answer:
The factors of the expression are 6/7, c and d.
Step-by-step explanation:
The given expression is
[tex]\frac{6}{7}cd[/tex]
We need to find the factors of the expression.
Factors: Numbers and variables multiplied to get an expression, then these numbers and variables are known as factors.
The factor form of given expression is
[tex]\frac{6}{7}cd=\frac{6}{7}\times c\times d[/tex]
Therefore, the factors of the expression are 6/7, c and d.
does each set of side lengths form a right triangle 10 m, 11 m, 15 m or 15 m, 8 m, 17 m,
10m, 11m, 15m is not a right triangle
15m, 8m, 17m is a right triangle
What is the product of −3 1/4 and −1 1/2 ? Enter your answer as a mixed number, in simplified form, in the box.
Answer:
Mixed number is [tex]4\frac{7}{8}[/tex] and the simplified form of this mixed number is [tex]\frac{39}{8}[/tex].
Step-by-step explanation:
The two mixed numbers are
[tex]-3\frac{1}{4}=-\frac{13}{4}[/tex]
and [tex]-1\frac{1}{2}[/tex]
= [tex]-\frac{3}{2}[/tex]
Now we will multiply these negative fractions.
[tex](-\frac{13}{4})(-\frac{3}{2})[/tex]
When two negative signs get multiplied they become positive.
= [tex]\frac{13}{4}\times \frac{3}{2}[/tex]
= [tex]\frac{39}{8}[/tex]
= [tex]4\frac{7}{8}[/tex]
Therefore, mixed number is [tex]4\frac{7}{8}[/tex] and the simplified form of this mixed number is [tex]\frac{39}{8}[/tex].
John made $195 for 13 hours of work. At the same rate, how much would he make for 17 hours of work?
Final answer:
John's hourly wage is calculated to be $15 per hour. For 17 hours of work at this rate, John would earn $255.
Explanation:
John made $195 for 13 hours of work, which means his hourly wage is the total amount earned divided by the total hours worked. To find John's hourly wage we calculate $195 ÷ 13 hours = $15 per hour. To determine how much he would make for 17 hours of work at this same rate, we multiply his hourly wage by 17 hours.
$15 per hour × 17 hours = $255
Therefore, at the same hourly rate, John would make $255 for 17 hours of work.
Mr. O’Brian is paid $7.30 per hour for 40 hours he works in a week. He is paid 1.5 times that rate for each hour after that
What is -6 over 0 equal to?
8/9, 85%, 0.92 least to greatest