In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled approximately by a trigonometric function. The lowest temperature is usually around 3^\circ C3 ∘ C3, degrees, C, and the highest temperature is around 18^\circ C18 ∘ C18, degrees, C. The temperature is typically halfway between the daily high and daily low at both 10\text{ a.M.}10 a.M.10, start text, space, a, point, m, point, end text and 10\text{ p.M.}10 p.M.10, start text, space, p, point, m, point, end text, and the highest temperatures are in the afternoon.
Answers
Answer:
The answer is "[tex]\bold{T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5}[/tex]"
Step-by-step explanation:
Given value:
Temp-maximum=[tex]18^{\circ}[/tex]
Temp. minimum = [tex]3^{\circ}[/tex]
It is halfway between 10 am and 10 pm to 4 am.
The sinus and cosine roles could be used throughout the year to predict fluctuations in climate models. Its type of formula that can be used to model such information is:
[tex]T = A \cos B(t-C) + D,[/tex] where parameters are A, B , C, D, T is the ° C temperature and t is the time (1-24)
[tex]A = amplitude = \frac{(T_{max} - T_{min})}{2}\\\\[/tex]
[tex]= \frac{(3 - 18)}{2}\\\\= - \frac{15}{2}\\\\ = -7.5[/tex]
[tex]B = \frac{2 \pi}{24}\\\\[/tex]
[tex]= \frac{\pi}{12}[/tex]
[tex]C = \text{ units translated to the right}= 4[/tex]
[tex]D = y_{min} + amplitude = units \ translated \ up\\\\[/tex]
D = 7.5 + 3 = 10.5
Its trigonometric function equation that model temperature T hours after midnight in Johannesburg t.
[tex]T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5[/tex]
Answer:
Hope this helps.
Step-by-step explanation:
Related Questions
Help Asap ! Find The Measure Of Angle A In The Triangle.
Answers
Answer: m<A = 35
Step-by-step explanation: The sum of the measures
of the interior angles of a triangle is 180°.
So we can setup the equation 3x + 5 + 8x + 65 = 180.
Combining our numbers and variables on the left, we have 11x + 70 = 180.
Now subtract 70 from both sides to get 11x = 110.
Dividing both sides by 11, we find that x = 10.
In the diagram, the m<A is represented as 3x + 5.
Plugging a 10 in for x, we have 3(10) + 5 or 30 + 5 which is 35.
So the m<A = 35.
the set of types of matter
well difined or not
Answers
Answer:
It is not well defined.
Step-by-step explanation:
Because set is a collection of well defined objet. And matter contains of solid, liquid and gas
Find the equation of the line from the following graph in slope-intercept form:
A) y = 3/2x + 2
B) y = -3/2x + 2
C) y = -2/3x + 2
D) y = 2/3x + 2
Answers
Answer: the slope is -3/2x and B is the only one that SLOPE
Step-by-step explanation:
RISE/RUN
IT WENT UP 3 AND WENT 2 TO THE LEFT
BTW: TO THE LEFT IS NEG AND POS IT TO THE RIGHT
so the slope is a neg be it is going toe the up towards left
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-1, -6), B(-1,7), C(1, 7), and D(1, -6). Given these coordinates, what is the length of side AB of this rectangle?
Answers
Answer:
13
A(-1, -6), B(-1,7)
7-(-6)=13
Answer:
13
Step-by-step explanation:
Lena says that and are like terms. Is she correct? Why or why not? A. No, because the same variables are not raised to the same powers. B. Yes, because both terms have a variable with a power of 3 and a power of 1. C. Yes, because both terms have an x and a y. D. No, because the two terms do not have the same coefficients.
Answers
Answer:
D because of the question
No, because the same variables are not raised to the same powers. which is the correct answer would be an option (A).
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Lena says that 4xy³ and -5x³y are like terms
⇒ 4xy³ and -5x³y
Here both polynomials are not like terms, because the same variables are not raised to the same powers.
Therefore, the correct answer would be an option (A).
Learn more about the polynomial here:
brainly.com/question/11536910
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The question seems to be incomplete the correct question would be
Lena says that 4xy³ and -5x³y are like terms. Is she correct? Why or why not?
A ball held 2.0 meters above the floor has 59 joules of potential energy. The ball’s mass
the answer3
Answers
Answer:
Step-by-step explanation:
potential energy=mgh
59=m×9.8×2
19.6 m=59m=59/19.6≈3.01 gram
The local library has a children’s section with picture books and chapter books. The ratio is 2:3. If there are a total of 500 books in the children’s section, then how many chapter books are in the section?
Answers
Answer:
300, I think.
Answer:
there are 300 chapter books in the children's section
Step-by-step explanation:
the way you'd solve these kinds of problems is to turn it into an equation.
the ratio of 2:3 with a total of 500
becomes
2x + 3x = 500
2x + 3x = 500
combine like terms
5x = 500
divide both sides of the equation by 5
5x/5 = 500/5
x = 100
now, substitute x in the original equation.
2x + 3x = 500
200 + 300 = 500
There are 300 chapter books
Sally has seventy dollars to spend on eight books. After buying them she had thirteen dollars. How much did each book cost?
Answers
Answer:
7.13 each
Step-by-step explanation:
70 - 13 = 57. Divide 57/8 and get your answer
(7.125 rounded is 7.13)
how do you write 2/11 as a decimal using long division
Answers
Answer:
0.18
Step-by-step explanation: Converting the fraction 2/11 into a decimal is very easy. To get 2/11 converted to decimal, you simply divide 2 by 11.
Answer:
About 0.18
Step-by-step explanation:
Divide 2 by 11
what is the midpoint of (-9, -4) and (-6, -3) ?
A (-3, -2)
B (3, 2)
C (-3, 12)
D (-12, -5)
Answers
Answer: c hope this helps
11.0453610171873
Midpoint
(−6.5,3.5)
Slope
11
x intercept
−6.82
y intercept
75.00
Step-by-step explanation:
Question
1 pts
I bought a new bike! It was originally $600 but I had a 25% coupon. What
was the discount?
O $25
O $150
O $450
$1000
Question 3
1 pts
I NEED THIS DONE ASAP
Answers
Answer:
b or 150
Step-by-step explanation:
Need some help please...
Answers
Answer:
C: Starting at 1103 you gain 91 feet each additional hour of climing.
Step-by-step explanation:
The classroom has 10 desks with boys and
girls. Show one combination of boys and
girls
Answers
Answer:
one combination could be 6 girls and 4 boys
6 fall between what two intergers
Answers
Answer:
5 and 7
Step-by-step explanation:
5 and 7 are the nearest integers, and 6 is right in between them
Answer:
5 and 7.
Step-by-step explanation:
Integers are whole numbers, therefore numbers such as 5 or 6 would be an integer, but something like 3.5 or a fraction would not be an integer. Hope this helps!
What is x if f(x)=-2
Answers
f(x) = -2
f(x) is the same thing as x
f(x) is the same thing as -2
Now think about it. If f(x) and -2 are the same thing, what is x?
this problem makes me wanna cry
Answers
Answer:
k=45
Step-by-step explanation:
its an isosceles triangle, so k=45
to check it, 45+45+90=180
Tien Chou's tax return for last year shows a total tax of $8,278. Tien's employer withheld $8,450 from her wages during the year. What refund should Tien receive
Answers
Answer: 16,728
Step-by-step explanation:
please help need asap
Answers
Answer:
b and e.
Step-by-step explanation:
You will find this by solving each equation for 15b (get 15b by itself)
A tree initially measured 38 1/2 feet tall. Over the next 5 1/2 years, it grew to a final height of 49 1/2 feet. During those 512 years, what was the average yearly growth rate of the height of the tree? (I NEED THE ANSWER ASAP IF YOU CANT ANSWER IT its fine:)
Answers
Answer:
2 feet per year
Step-by-step explanation:
A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation y = –3.64x + 96.5, where x represents the number of procrastination days and y is the predicted grade. What is the predicted grade of a student who procrastinated for 2 days?
25.96
85.58
89.22
103.78
Answers
Answer:
89.22
Step-by-step explanation:
just plug in 2 to the x in a calc like so: -3.64(2)+96.5 and it will give you 89.22 . got it right on my quiz like 5 min ago sooo yeah hope this helps people in the future.
Answer:
The person above me is correct.
The answer to this is C, 89.22
If you're looking for a question that is one week instead of two days, the answer is 71.02 (B). (This is a similar question that asks for 7 days instead of two)
ED2021
Question 6(Multiple Choice Worth 1 points) (02.05 MC) Choose the table that represents g(x) = 4⋅f(x) when f(x) = x − 5. x g(x) 1 −4 2 −3 3 −2 x g(x) 1 −16 2 −12 3 −8 x g(x) 1 −20 2 −18 3 −16 x g(x) 1 −1 2 −2 3 −3
Answers
Answer: (b)
x g(x)
1 -16
2 -12
3 -8
If g(x) is 4*f(x), then we can find g(x) by multiplying 4 by x-5
g(x) = 4(x-5)
= 4x-20
Now we can plug in 1,2, and 3 for x to see which table makes sense.
g(1) = 4(1) - 20
= -16
g(2) = 4(2) - 20
= -12
g(3) = 4(3) - 20
= -8
hope this helps
Answer:
x g(x)
1 -16
2 -12
3 -8
Step-by-step explanation:
A drink is mixed in the ratio
lemonade : orange : cranberry = 6 : 3 : ?
If the fraction for cranberry juice is 3/12, what would be the missing number in the ratio?
Answers
Answer:
3
Step-by-step explanation:
Drink mix ratio:
Lemonade : Orange : Cranberry
6 : 3 : C
Fraction of Cranberry juice = [tex]\frac{3}{12}[/tex]
Sum of the ratio = 6 + 3 + C = 9 + C
Fraction of Cranberry;
[tex]\frac{C}{9 + C}[/tex] = [tex]\frac{3}{12}[/tex]
3(9 + C) = 12C
27 + 3C = 12C
27 = 12C - 3C
9C = 27
C = 3
The missing number will be 3
4. For a function that models a real-world situation, the dependent variable
y represents a person's height. What is a reasonable range? Explain.
HURRY!!!! ASAP!!!!
Answers
Answer:
Age
Step-by-step explanation:
Typically the older you get, the taller you grow
can someone please help me
Answers
Answer:
18=2x+7, The internship pays $5.50 an hour.
Step-by-step explanation:
The box on the far left is the amount the student is paid at their job, which is $18 an hour in this case. Solve 18-7 to get 11, then divide 11 by 2 to get the pay for the internship. To check your work, plug 5.50 into the equation.
18=2(5.50)+7
18=11+7
18=18
Answer:
The equation would be:
18 = 2x + 7
The internship pays $5.5 an hour
Step-by-step explanation:
18 - 7 = 2x
(Since we moved the 7 to the other side, in order to combine like terms)
11 = 2x
(Divide both sides by 2)
5.5 = x
(x = 5.5)
x would be the pay the internship pays an hour.
(Sorry if this is wrong, notify me if it is, and I'll delete this post Xc)
PLEASE HELP ME I DONT UNDERSTAND THIS MATH PROBLEM
Answers
Answer:
Infinite amount of solutions
Step-by-step explanation:
Step 1: Write equation
5(x + 2) = 5x + 10
Step 2: Solve for x
Distribute 5x + 10 = 5x + 10Subtract 10 on both sides: 5x = 5xDivide both sides by 5: x = xWe see here that x is infinite amount of solutions. We can plug in any value x and it would render the equation true.
Answer:
Step-by-step explanation:
When you are solving this problem is there is there always a equal answer say like u get 5=5 that would be a solution
How to solve (x-10)(x + 10)
Answers
Answer:
x² - 100
Step-by-step explanation:
Use the FOIL method. The FOIL method is the way in which you multiply the terms:
FOIL stands for First, Outside, Inside, Last. Multiply:
First:
x * x = x²
Outside:
x * 10 = 10x
Inside:
-10 * x = -10x
Last:
-10 * 10 = -100
Combine like terms:
x² + 10x - 10x - 100
x² + (10x - 10x) - 100
x² - 100
x² - 100 is your answer.
~
Answer:
x^2-100
Step-by-step explanation:
Use the F.O.I.L method
x^2+100x-100x-100
What distribution of clothing should Nancy have for German males and females? Should she produce more small or large sizes, or should she have an even distribution of all sizes?
Answers
Answer: I sacrificed my answer for yours here u go love
Step-by-step explanation:
Nancy should produce more large sizes of the male clothing for German men since the data is skewed left, meaning there are more data values that lie on the right side, representing taller males. For women, she can have a roughly even distribution of sizes since the data set is symmetric.
Nancy should produce more large sizes of the male clothing for German men and for women, she can have a roughly even distribution of sizes since the data set is symmetric.
What is skewness in histogram?Skewness is the tendency for the values to be more frequent around the high or low ends of the x-axis.Skewness is the measure of the asymmetry of a histogram (frequency distribution). A histogram with normal distribution is symmetrical.Given is to find what distribution of clothing should Nancy have for German males and females.
The shape of the data for German male adult heights is skewed left, but the shape of the data for female adult heights is close to symmetric. So, the distribution of the data is not the same. Each data set has the same minimum height of 145 centimeters. However, the maximum male adult height is 220 centimeters and the maximum female height is 185 centimeters. So, the range of values is not the same. The data for male adult heights has an outlier, but the data for female adult heights doesn't have any outliers.Nancy should produce more large sizes of the male clothing for German men since the data is skewed left, meaning there are more data values that lie on the right side, representing taller males. For women, she can have a roughly even distribution of sizes since the data set is symmetric.
Therefore, Nancy should produce more large sizes of the male clothing for German men and for women, she can have a roughly even distribution of sizes since the data set is symmetric.
To solve more questions on skewness, visit the link below -
https://brainly.com/question/3907939
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Solving systems by substitution
Answers
Tank 2: v = 236 + 6m
109 minutes, less than two hours, since two hours is 120 minutes (60 minutes in one hour, times 2)
Set them equal to each other to find out when they will have the same number of gallons: 1540 - 6m = 236 + 6m
1304 = 12m
108.667 rounded to the nearest minute is 109 minutes, which is the answer.
30 pts! Will make brainliest
Ben tracked the attendance in his class over a period of time and recorded the data in a frequency table.
Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots
Answers
The data recorded by Ben shows the attendance log of his classmates over a given period of time.
What is a Dot Plot?This refers to a simple chart that resembles a histogram that is used to represent small data.
Hence, we can see that because Ben tracked the attendance of the class over a given time period with the frequency on a frequency table, a sample of a dot plot has been provided below,
Read more about dot plots here:
https://brainly.com/question/25957672
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Answer: took the
Step-by-step explanation:
6
Directions - Determine the correlation for the situation. Choose Positive/ Negative/ or No correlation for each.
The outside temperature in the summer and the cost of the electric bill (for air conditioning).
A) Positive correlation
B Negative correlation
No Correlation
Answers
Probably No correlation because they don't relate to each other
A is correct - they both increase and decrease together