In January, the average temperature t hours after midnight in Mumbai, India, is given by:
T(t)=24.5-5.5sin((2pi(t+1))/24)
What is the coldest time of day in Mumbai? give an exact answer

Answers

Answer 1

The coldest time of day in Mumbai is 5 hours after midnight.

Since the average temperature t hours after midnight in Mumbai, India, is given by:

T(t)=24.5-5.5sin((2pi(t+1))/24)

We have that

T(t) = 24.5 - 5.5sin((2π(t+1))/24)

The coldest time of day is when T(t) is minimum.

T(t)  is minimum when 5.5sin((2π(t+1))/24) is minimum where t is the coldest time of day at minimum temperature, T(t).

Since for a sine function, -1 ≤ sinФ ≤ 1, the minimum value of sinФ = -1.

So, T(t) = 24.5 - 5.5sin((2π(t+1))/24) is minimum when

5.5sin((2π(t+1))/24) is minimum.

Also, -5.5sin((2π(t+1))/24) = 5.5 × -1 at minimum temperature T(t)

So, 5.5 × -1 = 5.5 × -sin((2π(t+1))/24)

So, -sin((2π(t+1))/24) = -1

sin((2π(t+1))/24) = 1

Taking inverse sine of both sides, we have

sin⁻¹sin((2π(t+1))/24) = sin⁻¹(1)

((2π(t+1))/24) = π/2

Multiplying both sides by 24, we have

(2π(t+1))/24 × 24 = π/2 × 24

(2π(t+1)) = 12π

Dividing both sides by 2π, we have

2π(t+1)/2π = 12π/2π

t + 1 = 6

t = 6 - 1

t = 5 hours

So, the coldest time of day in Mumbai is 5 hours after midnight.

Learn more about average temperature here:

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Related Questions

Can anyone help me with this?

Answers

I thing it lies on the negativity side of the number line between -2,24

Taehyung was sitting on the ground flying a kite. He had 22 feet of line let out to fly his kite, and the kite was 14 feet in front of him. How high was the kite?

Answers

30^∘ Another boy is standing on the roof of a 10 second string be x mIn Δ ABC sin 30^∘ = AC/AB 1/2 = AC/100 AC =

Answer: hope this helps ♡

The kite was 16.9 feet high.

Step-by-step explanation:

Pythagorean theorem

b = [tex]\sqrt{c^{2} - a^{2} }[/tex]

b = [tex]\sqrt{22^{2} - 14^{2} }[/tex]

b = [tex]\sqrt{484 - 196}[/tex]

b = [tex]\sqrt{288}[/tex]

b = 16.9

Gabriella has a smart phone data plan that costs $25 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Gabriella have to pay in a month where she used 5 GB over the limit? How much would Gabriella have to pay in a month where she used went over by x x GB?

Answers

I believe the answer would be 75+25= so $100

Determine el radio vector del punto medio del segmento que se forma al unir los puntos (-8, 7) y (6, 3).
Es para hoy

Answers

Answer:

The radius vector is (-8, 7) and (-1 , 5).

Step-by-step explanation:

Determine the radius vector of the midpoint of the segment that is formed by joining the points (-8, 7) and (6, 3).

The end points are (- 8, 7) and (6, 3) .

The mid point is given by

[tex]x = \frac{x' + x''}{2}\\\\y = \frac{y' +y''}{2}\\\\x =\frac{- 8 + 6}{2}=-1\\\\y = \frac{7+3}{2} = 5[/tex]

So, the radius vector is (-8, 7) and (-1 , 5).  

Someone help plsssss

Answers

Its either (top to bottom) 1 or 4

2. If you move 50 meters in 10 seconds, what is your speed?

Answers

Answer:

5 meters per second

Step-by-step explanation:

Find your speed by dividing the number of meters traveled by the number of seconds it took:

50/10

= 5

Your speed is 5 meters per second.

Answer:

5 m/sec

Step-by-step explanation:

The speed would be calculated as follows, as a unit rate:

 50 m

----------- = 5 m/sec

10 sec

REALICE LOS SIGUIENTES PROBLEMAS DE ECUACIÓN DE LA RECTA CORRECTAMENTe

1.- Encuentre la ecuación vectorial de la recta si tenemos A(4, -2) y el vector V=(2, 5) paralelo a la recta y que pasa por A


2.- Encuentre la ecuación general de una recta conociendo un punto P(-2 ; 4) y su pendiente m= - 5 y grafique la recta.

Answers

Answer:

1. La ecuación vectorial de la línea es [tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]

2. La ecuación de la recta es, y = -5·x - 6

Step-by-step explanation:

 1. El punto dado en la línea es A (4, -2), el vector paralelo a la línea es (2, 5)

Por tanto, la ecuación vectorial de la línea es;

[tex]\begin{bmatrix} & x & \\ & y & \end{bmatrix} =\begin{bmatrix} & 4 & \\ & -2 & \end{bmatrix} + t \times \begin{bmatrix} & 2 & \\ & 5 & \end{bmatrix}[/tex]

Donde;

t = Cualquier número

2. El punto por el que pasa la recta es P (-2; 4)

La pendiente de la recta, m = -5

Por lo tanto, la ecuación de la línea en forma de punto y pendiente se presenta de la siguiente manera;

y - 4 = (-5) · (x - (-2)) = -5 · x - 10

∴ y - 4 = -5 · x - 10 + 4 = -5 · x - 6

La ecuación de la recta es, y = -5·x - 6

Find the area of the shaded region.

Answers

Answer:

pi × 18cm^2

Or approximately,

56.52cm^2 (using 3.14 for pi)

or

56.5487cm^2 (using pi button on calculator)

Step-by-step explanation:

Area of a circle is pi times [radius squared].

All circles are 360°.

Problem can be solved by finding area of whole circle, and then using ratios.

Whole Circle: area = pi × (9cm)^2 = pi × 81cm^2

80° / 360° = Area[shaded] / (pi × 81cm^2)

pi × 18cm^2 = Area[shaded]

((If you read my answer before the edit, I am sorry. I made a calculator error.))

Help! ASAP. The question is in the attachment below

Answers

Answer:

Step-by-step explanation:

The most obvious answer is the line y = 1.

Someone please explain this to me like you would a child
thank you

Answers

Answer:

12 degrees

Step-by-step explanation:

Answer:

15 degrees

Step-by-step explanation:

okay haha

so basically the cosine of an angle is the side adjacent to it, divided by the hypotenuse. the sine is the side opposite to that angle divided by the hypotenuse, and the tangent is the side opposite to that angle divided by the side adjacent to it.

in this case we are given the angle and the side opposite to it which is 10, and we are also given the hypotenuse of 39.

what trig function deals with opposite and hypotenuse?

the answer is sine

so we would find the sine of that angle which equals to opposite over hypotenuse:

sin(angle) = 10/39

but, they are asking for the inverse trig function. the inverse of sine is arcsin.

so :

arcsin(10/39) = angle

in a calculator, this would be equal to about 14.857 which is closest to 15.

A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that:
She plans to drive 400 miles.
She has at most $210 to spend.

Use the drop-down menu below to write an inequality representing dd, the total number of days Claire can rent the car while staying within her budget.

Answers

0.09x - 28y greater than or equal to 210

The required inequality that expresses the given condition is 36 + 29x ≤ 210.

Given that,
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that she plans to drive 400 miles. she has at most $210 to spend.

What is inequality?

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the number of days be x,
Total cost to drive 400 miles = 400(0.09) = $36.
According to the question,
36 + 29x ≤ 210

Thus, the required inequality that expresses the given condition is 36 + 29x ≤ 210.

Learn more about inequality here:

brainly.com/question/14098842

#SPJ5

Which Venn Diagram is NOT correct?

Answers

i need ur help to escape the police men because the only reason i stole his pickles was because i was going through this thing where all i wanted to do was eat PICKLES and my mom wouldn’t buy any. ANSWER IS LETTER B

Does 8in to 1ft reduce it or enlarge it

Answers

Answer:

enlarge it

Step-by-step explanation:

I ft = 12 inches

Thus 8 in → 12 in makes the transformation larger.

Thus going from 8 in to 12 in is an enlargement

What is the slope of a trend line that passes through the points (1, 3) and (10, 25)?
Negative StartFraction 15 Over 2 EndFraction
Negative one-half
StartFraction 22 Over 9 EndFraction
StartFraction 24 Over 7 EndFraction

Answers

Answer:

[tex]\displaystyle m = \frac{22}{9}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 3)

Point (10, 25)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]:                                                              [tex]\displaystyle m = \frac{25 - 3}{10 - 1}[/tex]Subtract:                                                                                                             [tex]\displaystyle m = \frac{22}{9}[/tex]

Answer:

c

Step-by-step explanation:

Write 128 as a product of its prime factors

Answers

Answer:

The prime factorization of 128 is 2 x 2 x 2 x 2 x 2 x 2 x 2.

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Since, the prime factors of 120 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

Select the reason why these triangles are
similar. If they are not, select "Not similar."
1
88°
3
2
88
6
A. AA
B. SAS
C. SSS
D. Not similar

Answers

Answer:

B. SAS

Step-by-step explanation:

Ratio of sides equal:

• 4/2= 6/3

So the 2 sides are congruent and also share same angle between.

• B. SAS is the similarity reason

Have fun all !!! This is my trash account. You all can have my points.

Answers

Answer:

Step-by-step explanation:

OK

Answer:

rshjgdlf

FGshjfgsfds

Step-by-step explanation:

GIMME'

Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial
function.
f(x) = 2^(5x-6)
h(x) = 3x^5 - 2x^3 - 4x + 7
x=4
x=7
x = 6
x=5

Answers

Answer: ¿Hablas español porque no entiendo esto? Si lo haces, ¿puedes decirme en español?

Step-by-step explanation:

Hello hello hello hello hello hello hello hello hello hi bye-bye I am so sorry I cannot help you I don’t know math I just need points bye-byeGirls know to bye what no

Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589. You must show all of your work to receive credit.

PLSSS SHOW WORK <3

Answers

Answer:

x = 18

Step-by-step explanation:

First, let's find the ratios between the two triangles

We'll use AV and AC

372 ÷ 589 = 12/19

All of the sides of the smaller triangle are 12/19 of the bigger triangle

Now let's find x

We know that AU + UB = AB

So it's 20x + 108 + 273 = AB

12/19 of a bigger triangle side equals a small triangle side

(12/19)AB = AU

For this equation multiply both sides by 19/12 to isolate AB

(12/19)AB x 19/12 = AU x 19/12

AB = (19/12)AU

Now we have this

20x + 108 + 273 = (19/12)(20x + 108)

20x + 381 = (19/12)(20x + 108)

Distribute the 19/12

20x + 381 = 95/3x + 171

Move all like terms to one side

20x + 381 = 95/3x + 171

       - 171                 - 171

20x + 210 = 95/3x

- 20x           - 20x

Don't forget about common denominators

210 = 95/3x - 60/3x

210 = 35/3x

Multiply both sides by 3

210 x 3 = 35/3x x 3

630 = 35x

Divide both sides by 35

630/35 = 35x/35

x = 18

Answer:

Step-by-step explanation:

[tex]\frac{20x+108}{20x+381}[/tex] = [tex]\frac{372}{589}[/tex]

589( 20x + 108 ) = 372( 20x + 381 )

11780x + 63612 = 7440x + 141732

4340x = 78120

x = 18

Help pls ?? I really don’t know what to do

Answers

Answer:

The answer is "C" f(x)= x+ 4 and g(x)= x^3 - 1

Step-by-step explanation:

all you have to do is replace the x in "G" with the "F" function

Answer:  Choice C

F(x) = x+4  and  G(x) = x^3-1

===========================================================

Explanation:

Let's try choice A to see if it works or not

G(x) = (x+4)^3

G( F(x) ) = ( F(x)+4 ) ^3 .... replace every x with F(x)

G( F(x) ) = ( x-1+4 ) ^3 .... plug in F(x) = x-1

G( F(x) ) = (x+3)^3

This isn't the same as (x+4)^3 - 1. You can confirm this with a graph or a table of values. We cross choice A off the list.

------------

Let's try choice B

G(x) = x+4

G( F(x) ) = F(x)+4

G( F(x) ) = x^3-1 + 4

G( F(x) ) = x^3 + 3

Similar to choice A, this isn't the same as (x+4)^3-1. We can cross this off the list as well.

--------------

Now choice C

G(x) = x^3 - 1

G( F(x) ) = ( F(x) )^3 - 1

G( F(x) ) = (x+4)^3 - 1

We found the final answer.

what is the answer for 7 to the negitive second power.

Answers

Answer:

the negative just tell you you put a one over the number. Once that's done, the power will be positive, and you can square like normal

Are you asking about  [tex]7^{-2}[/tex]  ?

If so:

A negative in the exponent tells us that we must take the reciprocal of the number, in this case, 7, and then use the exponent like normal:

[tex]7^{-2}[/tex] =

[tex](\frac{1}{7})^{2}[/tex] =

[tex]\frac{1}{49}[/tex],

So our answer is 1/49.

I need help ASAP!! Please explain how to solve the problem

Answers

Answer:

B=.5*8*6=.5*48=24

h = 8

P=10+6+8=24

Surface area =2*24+24*8=48+192=240

Step-by-step explanation:

The base is a triangle, and the area of a triangle is 1/2 base (or width) times height (or length). In this case, base is 8 and height is 6, so the area can be found either by multiplying .5*8*6 or by dividing 8*6 by 2, either of which will give you the same answer of B=24.

Height is given, h=8.

Perimeter is simply the sum of the sides, which are given, so the perimeter is 8+6+10=24.

The formula for surface area is given, so all you need to do is plug in your previous answers and you've got it!

An angle measures 2 more than the measure of its complementary angle

Answers

Answer:

let x be the complementary angle

then x + 2 is the angle

x+2 +x =90

2x = 88

x = 44°

x + 2° = 46°

Refer to picture
Need help on Q.8

Answers

Answer:

Rajan = 436.36 rupees and Kamal = 363.63 rupees

Step-by-step explanation:

Total ratio = 11/30

Amount to be shared = 800

Rajan = Individual ratio / Total ratio x the total amount to be shared

1/5 ÷11/30 × 800 = 436.36

Kamal = 1/6 ÷ 11/30 × 800 = 363.63

100÷50000 it's has to be step by step aka show work ​

Answers

100÷50000 can be written as 100/50000, then cancel out 2 of the zeroes, and you will get 1/500 or 0.002 as your final answer.

Determining the Domain and Range from a Graph
Determine the domain and range of the given function.
The domain is
ty
4
The range is
2
-4
-2
4
Into

Answers

Answer:

Domain is all real numbers, and range is all numbers greater than or equal to -2.  If thee was anything you didn't understand let me know.  

Step-by-step explanation:

The domain is what x values work, or it may be better to say the horizontal axis.  is there any number you cannot use?  if you cannot tell, this is a parabola, like x^2.  Is there any number you cannot plug into x^2.  The answer is no, the domain for all parabolic functions is all real numbers.

The range you really want to look at visually here.  Range is y values you can get, or values on the vertical axis.  I would also compare it to x^2 again.  You should know you can make it as high as you want, here is the same.  but at -2, there is no point below that.  so the range is -2 and up

The other options are just specific numbers.  you can disprove those by choosing a number not on their lists.  For the domain literally any other number.  For range any number not on the list greater than -2

1. The position of a particle moving along a coordinate axis is given by: s(t) = t^2 - 5t + 1. a) Find the speed of the particle b) Find the acceleration of the particle c) Find the velocity of the particle

Answers

Answer: [tex]\left | 2t-5\right |,\ 2,\ 2t-5[/tex]

Step-by-step explanation:

Given

Position of the particle moving along the coordinate axis is given by

[tex]s(t)=t^2-5t+1[/tex]

Speed of the particle is given by

[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=\left | 2t-5\right |[/tex]

Acceleration of the particle is

[tex]\Rightarrow a=\dfrac{dv}{dt}\\\\\Rightarrow a=2[/tex]

velocity can be negative, but speed cannot

[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=2t-5[/tex]

1. Three products from renewable resources are​

Answers

Animals, wood, plants

Answer:

biomass energy (such as ethanol), hydropower, geothermal power, wind energy, and solar energy.

the table of values below represents a liner function and show the amount of money in the savings account since she began her part-time job what is her monthly rate of savings​

Answers

Answer:

she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)

What is the area for the circle?

Answers

Answer:

108 squared centimeters

Step-by-step explanation:

Let's exchange π for 3:

area = πr^2

        = 3r^2

Now, as you can see, the radius of this circle is 6. Let's plug in the value of r:

area = 3r^2

        = 3 · 6^2

Simplify 6^2:

area = 3 · 6^2

        = 3 · 36

Multiply 3 by 36:

area = 3 · 36

area = 108

108 squared centimeters

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