Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 97 degrees during the day and the average daily temperature first occurs at 10 AM. How many hours after midnight, to two decimal places, does the temperature first reach 82 degrees?
Answers
Answer: After about 9.03 hours the temperature first reach 82 degrees.
Step-by-step explanation:
The sinusoidal function is given by :
\(y=A\sin[\omega(x-\alpha)]+C\)
where, A = amplitude; \(\omega=\dfrac{2\pi}{period}\) , α= phase shift on the Y-axis and C = midline.
As per given,
Average daily temperature= \(C=\dfrac{73+97}{2}=85\) [midline is average of upper and lower limit.]
A= 97-85 = 12
Phase shift: \(\alpha=10\)
Period = 24 hours;
\(\omega=\dfrac{2\pi}{24}=\dfrac{\pi}{12}\)
Substitute all values in sinusoidal function, we get
\(y=12\sin[\dfrac{\pi}{12}(x-10)]+85\)
Put y= 82, we get
\(82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03\)
Hence, After about 9.03 hours the temperature first reach 82 degrees.
Related Questions
what is the slope of -3 up to positive 3
Answers
The line or points has a slope value of -1
How to determine the slope of the point?From the question, we have the following statement that can be used in our computation:
The slope of -3 up to positive 3
For a start, we represent the above parameters using an ordered pair
The ordered pair is represented as
(x, y) = (-3, 3)
The slope of the point is then calculated using the following slope formula
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-3, 3) and (0, 0)
The coordinate (0, 0) represents the origin
Substitute the known values in the above equation
So, we have the following equation
Slope = (3 - 0)/(-3 - 0)
Evaluate the difference
So, we have the following equation
Slope = (3)/(-3)
Evaluate the quotient
So, we have the following equation
Slope = -1
Hence, the slope is -1
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Based on the graph of the function shown, identify the statement below that is FALSE. The straight line part of the graph is a ray. Recall that a ray has a fixed endpoint and extends Infinitely in one direction
Answers
Answer:
As even if we extend the line it will not meet another line
1. Consider the following quadratic function y=4-5x+3x². a) b) c) Generate the table of values of the function for all x ranging from to Use the table to plot the graph of the function y = f(x) for all scale 4or the y-axis and 2cm to I unit along the x-axis. Using the graph: Solve for the root of the equation 4-5x+3x²=0. Solve the equation 3x² -5x=2. (iii) Determine the range of values of x for which 35x
Answers
Answer: \(35x < 4-5x+3x^2\) is \(x < \frac{1}{3}\) or \(x > \frac{4}{3}\)
Step-by-step explanation:
A) To generate the table of values, we can substitute different values of x into the equation and solve for y.
x y
-2 26
-1 12
0 4
1 2
2 10
To plot the graph of the function, we can use the table of values and plot the corresponding points on a graph with a scale of 4 for the y-axis and 2cm to 1 unit along the x-axis. The graph should look like a parabola opening upwards.
c) To solve for the root of the equation 4-5x+3x^2=0, we can use the graph and find the x-coordinate of the point where the graph intersects the x-axis. This point is also known as the x-intercept or the root of the equation. From the graph, we can see that the root is approximately x=0.83.
To solve the equation 3x^2 -5x=2, we can rearrange it to the form 3x^2 -5x-2=0 and factor it as (3x+1)(x-2)=0. This gives us two solutions: x=-1/3 and x=2.
To determine the range of values of x for which 35x<4-5x+3x^2, we can rearrange the inequality to the form 3x^2-40x+4>0 and factor it as (3x-1)(x-4/3)>0. This means that either (3x-1) and (x-4/3) are both positive or both negative.
When (3x-1)>0 and (x-4/3)>0, we get x>1/3 and x>4/3, which means x>4/3.
When (3x-1)<0 and (x-4/3)<0, we get x<1/3 and x<4/3, which means x<1/3.
Therefore, the range of values of x for which 35x<4-5x+3x^2 is x<1/3 or x>4/3.
what equation equivalent to 4x - 6y = 12
Answers
Answer:
12+6y=4x
Step-by-step explanation:
Answer:
y=2/3x−2
Step-by-step explanation:
Can anyone help me, please? Thanks
Answers
**** keep in mind (dy/dx) becomes like a letter itself
5.
x⁴+y⁴=2
Taking the derivative of both sides with respect to x:
4x³ + 4y³ (dy/dx) = 0
4y³ (dy/dx) = -4x³
(dy/dx) = -4x³/4y³
4's cancel out
(dy/dx) = -x³/y³
At (1,-1), we have
(dy/dx) = -x³/y³
(dy/dx) = -(1)³/(-1)³
(dy/dx) = -1/-1
(dy/dx) = 1
7.
y² = 4x
Taking the derivative of both sides with respect to x:
2y (dy/dx) = 4
divide 2y on both sides
(dy/dx) = 4/2y
simplify
(dy/dx) = 2/y
At (1,2), we have
(dy/dx) = 2/y
(dy/dx) = 2/(2)
(dy/dx) = 1
9.
sin y=5x⁴-5
Taking the derivative of both sides with respect to x:
cos y (dy/dx) = 20x³
(dy/dx) = 20x³/cos y
At (1,π), we have (dy/dx) = 20/(-1) = -20.
11.
cos y=x
Taking the derivative of both sides with respect to x:
-sin y (dy/dx) = 1
(dy/dx) = -1/sin y
At (0,π/2), we have (dy/dx) = -1.
6.
x=e^y
Taking the derivative of both sides with respect to x:
1 = e^y (dy/dx)
(dy/dx) = 1/e^y
At (2,In 2), we have (dy/dx) = 1/e^(In 2) = 1/2.
8.
y²+3x= 8
Taking the derivative of both sides with respect to x:
2y (dy/dx) + 3 = 0
(dy/dx) = -3/(2y)
At (1,√5), we have (dy/dx) = -3/(2√5).
10.
√x-2√y = 0
Taking the derivative of both sides with respect to x:
1/(2√x) - 1/√y (dy/dx) = 0
(dy/dx) = √y/(2√x)
At (4,1), we have (dy/dx) = 1/4.
12.
tan xy=x+y
Taking the derivative of both sides with respect to x:
y sec² (xy) (dy/dx) = 1 + y
(dy/dx) = (1 + y)/[y sec² (xy)]
At (0,0), we have (dy/dx) = 1/0, which is undefined.
5-12. Implicit differentiation Carry out the following steps.
a. Use implicit differentiation to find (dy/dx)
b. Find the slope of the curve at the given point.
5. x⁴+y⁴=2 ; (1,-1)
6. y² = 4x ; (1,2)
7. sin y=5x⁴-5 ; (1,π)
8. cos y=x ; (0, (π/2))
9. x=e^y ; (2, In 2)
10. y²+3x= 8 ; (1, √5)
11. √x-2√y = 0 ; (4,1)
12. tan xy=x+y ; (0,0)
ChatGPT
Find the median the data. 55,44,40,55,48,44,58,67
Answers
Answer:
51.5
Step-by-step explanation:
Answer:
51.5---------------------------
To find the median of the given data set, we need to first arrange the data in numerical order:
40, 44, 44, 48, 55, 55, 58, 67There are a total of 8 numbers in this set, which is an even number, so to find the median we need to take the average of the two middle numbers:
Median = (55 + 48)/2 = 51.5Therefore, the median of the data set is 51.5.
Choose all of the transformations??
Answers
An auto mechanic earns $498.75 in 35 hours during the week. His pay is $2.50 more per hour on weekends. If he works 6 hours on the weekend in addition to 35 hours during the week, how much does he earn?
Answers
Answer:
$513.75
Step-by-step explanation:
An auto mechanic earns $498.75 in 35 hours during the week. His pay is $2.50 more per hour on weekends.
$498.75 + $2.50 × x
If he works 6 hours on the weekend in addition to the 35 hours during the week:
$498.75 + $2.50 × 6
= $498.75 + $15
= $513.75
For a single randomly selected steel rod, find the probability that the length is between 213.3-cm and 213.7-cm.
Answers
Answer: probably like 1.8%
Step-by-step explanation:
What is the distance between -60 and -10 on
a number line?
units
90-80 -70 -60 -50-40-30-20 - 10
0
10
Answers
Answer:
50
Step-by-step explanation:
60-10
Choose the equation that represents the line that passes through the point (-1, 6) and has a slope of -3.
y=-3x + 3
y=-3x - 6
y = 3x - 3
y = 3x - 1
Answers
Answer:
Equation of line is \(\mathbf{y=-3x+3}\)
Option A is correct.
Step-by-step explanation:
We need to write an equation that represents the line that passes through the point (-1, 6) and has a slope of -3.
The equation will be of slope-intercept form: \(y=mx+b\)
where m is slope and b is y-intercept
We are given slope m =-3, we need to find y-intercept b
Finding y-intercept
using slope m=-3 and point (-1, 6)
\(y=mx+b\\6=-3(-1)+b\\6=3+b\\b=6-3\\b=3\)
So, y-intercept b is 3
Now the equation of line having slope m= -3 and y-intercept b = 3 is
\(y=mx+b\\y=-3x+3\)
Equation of line is \(\mathbf{y=-3x+3}\)
Option A is correct.
Answer:
a or the first one
Step-by-step explanation:
y=-3x+3
please help asap math question
Answers
86.1 and 90.5 should be the answer
The fire department wants to send booklets on fire hazards to all teachers and homeowners in town. How many booklets
does it need, using the following statistics?
35000 homeowners
4000 teachers
1000 teachers who own their own homes
O 5000
O 38000
O 32000
O40000
Answers
The fire department wants to send booklets on fire hazards to all teachers and homeowners in town. 38000 booklets does it need. The correct answer is (B) 38000.
To determine the number of booklets the fire department needs, we need to consider the total number of homeowners and teachers separately. Additionally, since some teachers are also homeowners, we should avoid duplicating the booklets for those individuals.
Total number of homeowners = 35,000
Total number of teachers = 4,000
Number of teachers who own their own homes = 1,000
To calculate the number of booklets needed, we need to subtract the number of teachers who own their own homes from the total number of teachers. This is because they will receive both the teacher booklet and the homeowner booklet.
Number of booklets needed for homeowners = Total number of homeowners = 35,000
Number of booklets needed for teachers = Total number of teachers - Number of teachers who own their own homes = 4,000 - 1,000 = 3,000
Therefore, the total number of booklets needed is:
Number of booklets for homeowners + Number of booklets for teachers = 35,000 + 3,000 = 38,000
Therefore, the correct answer is (B) 38000.
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add 91, 129, and 16, and then divide by 24
help me iswtg ima die tn
Answers
Answer:
9.8333... or 59/6
Step-by-step explanation:
According to my calculator
Answer:
\(\dfrac{59}{6}\)
Step-by-step explanation:
Let x be the answer,
\(x = \dfrac{91 + 129 + 16}{24}\)
\(x = \dfrac{236}{24}\)
\(x = \dfrac{59}{6}\)
Relative intensity of 9 decibels is how many times higher than that of 8 decibels
Answers
Answer:
what do you mean by land ?
The intensity of sound is proportional to the square of its amplitude.
Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:
I9/I8 = (10^(9/10))/(10^(8/10))
I9/I8 = 10^(0.1)
I9/I8 = 1.2589
Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.
May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
When first observed an all steel covers 2 mi.² measurement shows that the area is tripleling every eight hours find the exponential model for the area a (in mi^2) of the oil spill as a function of time t(in hr) from the beginning of the spill
Answers
The initial area is 2 mi².
The area is trippling every eighth hour, therefore
The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
Answers
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
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Solve the inequality 3(x – 2) + 1 ≥ x + 2(x + 2).
Answers
Answer:
no solution
Step-by-step explanation:
3(x – 2) + 1 ≥ x + 2(x + 2).
Distribute
3x – 6 + 1 ≥ x + 2x + 4
Combine like terms
3x -5 ≥ 3x +4
Subtract 3x from each side
-5 ≥ 4
This is never true so there is no solution
By solving the given inequality "\(3(x – 2) + 1 \geq x + 2(x + 2)\)", we get "\(-5 \geq 4\)".
The given inequality is:
\(3(x - 2) + 1 \geq x + 2(x + 2)\)By solving the brackets, we get
→ \(3x-6+1 \geq x+2x+4\)
→ \(3x-5 \geq 3x+4\)
By subtracting "3x" from both sides, we get
→ \(3x-5-3x \geq 3x+4-3x\)
→ \(-5 \geq 4\)
Thus the above answer is right.
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can someone please find the slope for this?
Answers
As you take two points the line passes though, then use the rise/run equation to find the slope or gradient
Lucy collects data from a random sample of seventh-graders. Out of 140 respondents, 28 attend after-school programs. Of the 400 seventh-graders attending Lucy’s school, how many would be expected to attend afterschool programs?
Answers
A number of 80 student would be expected to attend after school programs.
What does respondents means?Respondents refers to an individuals who complete a survey or interview for the researcher, or who provide data to be analyzed for the research study.
Out of 140 respondents, 28 attend after school programs. This give us a fraction of 28/140 = 0.2. So, 20% of students attend after school programs.
Now, out of 400 seventh-graders, the number of student expected to attend after school programs is:
= 20% * 400
= 80. Therefore, 80 student would be expected to attend after school programs.
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What do 9 and 6 have a LCD?
Answers
Answer:
LCM = 18
Step-by-step explanation:
Multiples of 6: 6, 12, 18
Multiples of 9: 9, 18
4. Compare using <> or =
-5
O
-9
Answers
Answer:
-9 <-5 <0
Step-by-step explanation:
hope it helps
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josh makes $7.25 an hour working at the local grocery store. His paycheck shows that he worked 12.5 hours the past week. How much money did he make (giving branlist)
A. $19.00
B. $19.75
C. $84.00
D. $90.63
Answers
Answer:D
Step-by-step explanation:
money times hours
$7.25 times 12.5
90.63
Given the drawing as shown below and that pllq. Which of the following cannot be supported by the evidence shown? Worth 10 points
Answers
The relation that can not be supported by the evidence in the image is option B
What happens when a transversal cuts a parallel line?
Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.
Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.
Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.
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Tariq has earned $54 for cutting the grass of three houses.
Part A: If he continues to earn money at this rate, how much will he make after cutting all 11 lawns on his street?
Part B: How many lawns would he need to cut if he wanted to earn enough money to buy an Xbox One that costs $324?
Answers
Answer:
Part A: $198
Part B: 18 lawns
Step-by-step explanation:
Part A:
Find out how much he earns for cutting the grass of one house.
3 houses = 54
1 house = 54 ÷ 3 = 18
11 houses = 18 x 11 = 198
(Final answer)
Part B:
Since you know how much you earn for cutting the grass of one house, take the amount of money needed divided by how much you earn for cutting grass per house.
324 ÷ 18 = 18
(Final answer)
1 pts
Compute the total amount accumulated if you invested $850 for 4 years at 2.4% compounded
semiannually. Round your answer to the nearest cent and include '$' in your response.
Answers
9514 1404 393
Answer:
$935.11
Step-by-step explanation:
The amount is given by the formula ...
A = P(1 +r/n)^(nt) . . . P invested at rate r for t years compounded n per year
A = $850(1 +0.024/2)^(2·4) = $935.11
The amount accumulated will be $935.11 after 4 years.
Your teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each. Let x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators. Write an inequality that represents the number of each type of calculator she can buy.
Answers
The inequality that represents the number of each type of calculator she can buy will be 25x + 65y ≤ 800
Given that teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each.
Consider that x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators.
The inequality that represents the situation becomes as;
25x + 65y ≤ 800
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Bryon is making a garage for his toy car out of shoebox as shown below. Each toy is 5 cm wide. If all the toy cars are parked in one row, sided by side, what is the greatest number of toy cars Bryon can fit in the garage?
How did you get it
Answers
Bryon is making a garage for his toy car out of a shoebox as shown below. Each toy is 5 cm wide. the greatest number of toy cars Bryon can fit in the garage is 5.
What is the greatest number of toy cars Bryon can fit in the garage?Generally, To find the greatest number of toy cars Bryon can fit in the garage, we need to find the length of the garage in centimeters and divide it by the width of each toy car in centimeters.
The length of the garage is the width of the shoebox, which is shown as 25 cm. The width of each toy car is 5 cm, so the greatest number of toy cars Bryon can fit in the garage is 25 cm / 5 cm = 5 toy cars.
To check our answer, we can visualize the toy cars lined up in the garage. If we have 5 toy cars, the last one will fit completely inside the garage. If we try to fit a 6th toy car, it will not fit because it will extend beyond the width of the shoebox.
Therefore, the greatest number of toy cars Bryon can fit in the garage is 5.
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52.311 is greater than 52.31
Answers
52.311 is greater than 52.31 because look at 52.311 and 52.31
Answer: 52.311 is greater because 52.31 dosen't have an extra 1 to be equal
Step-by-step explanation:
whats the median of the set 22,37,49,15,82
Answers
Answer:
The median is 37
Step-by-step explanation:
The median is the middle number in the set when organizaed from low to high:
15, 22, 37, 49, 82
From this arrangement, we can see that 37 is the middle number making it the median.