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:
https://brainly.com/question/19388300
determine the equation for the quadratic relationship graphed below.
Answer:
[tex]\large \boxed{\sf \bf \ \ y=3x^2-6x-1 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We can read from the graph that the vertex is (1,-4) , it means that the equation is, a being a real number.
[tex]y=a(x-1)^2-4[/tex]
And the point (0,-1) is on the graph so we can write.
[tex]a\cdot 1^2-4=-1 \\\\a-4+4=-1+4\\\\a = 3[/tex]
So the equation is.
[tex]y=3(x-1)^2-4\\\\=3(x^2-2x+1)-4\\\\=3x^2-6x+3-4\\\\=3x^2-6x-1\\\\=\boxed{3}x^2\boxed{-6}x\boxed{-1}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
[tex]y=3x^{2} -6x-1[/tex]
Step-by-step explanation:
lf y 1/4 · when x=5, find y when x=7. given that y varies directly with x.
y=
Answer:
y= 0.35
Step-by-step explanation:
y 1/4
when x=5,
find y=? when x=7.
given that y varies directly with x.
y = kx
Where k is the constant of proportionality
k= y/x
k= (1/4)÷ 5
k= 0.05
y= kx
y= (0.05)(7)
y= 0.35
I Hope this will helpful...
5 x 1/4
how can you use addition to show that your answer is correct?
Answer:
Step-by-step explanation:
[tex]5*\dfrac{1}{4}=\dfrac{5}{4}\\[/tex]
Using addition,
Add (1/4) , five times
[tex]\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{1+1+1+1+1}{4}\\\\=\dfrac{5}{4}[/tex]
Answer:
5/4
Step-by-step explanation:
Add 1/4 together 5 times:
1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/4
Square root & simplifying radicals
√30
Answer:
√30 =
5.4772255751
It can be simplified as this only, not more
simplify the following
Answer:
1) 11[tex]\sqrt{3}[/tex]
2) 2[tex]\sqrt{2}[/tex]
3) [tex]20\sqrt{3} + 15\sqrt{2}[/tex]
4) [tex]53 + 12\sqrt{10}[/tex]
5) -2
6) [tex]7\sqrt{2} - 5\sqrt{3}[/tex]
Step-by-step explanation:
1) 2[tex]\sqrt{12}[/tex] + 3[tex]\sqrt{48}[/tex] - [tex]\sqrt{75}[/tex]
=(2 × 2[tex]\sqrt{3}[/tex] )+ (3 × 4[tex]\sqrt{3}[/tex]) - 5[tex]\sqrt{3}[/tex]
= 4[tex]\sqrt{3}[/tex] + 12[tex]\sqrt{3}[/tex] - 5[tex]\sqrt{3}[/tex]
= 11[tex]\sqrt{3}[/tex]
2) 4[tex]\sqrt{8}[/tex] -2[tex]\sqrt{98}[/tex] + [tex]\sqrt{128}[/tex]
= (4 × 2[tex]\sqrt{2}[/tex]) - (2 × 7[tex]\sqrt{2}[/tex]) + 8[tex]\sqrt{2}[/tex]
= 8[tex]\sqrt{2}[/tex] - 14[tex]\sqrt{2}[/tex] +8[tex]\sqrt{2}[/tex]
= 2[tex]\sqrt{2}[/tex]
3) 5[tex]\sqrt{12\\}[/tex] - 3[tex]\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}[/tex]
= 5× [tex]2\sqrt{3}[/tex] - 3×[tex]3\sqrt{2}[/tex] + 4×[tex]6\sqrt{2}[/tex] + 2×[tex]5\sqrt{3}[/tex]
= [tex]10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}[/tex]
= [tex]20\sqrt{3} + 15\sqrt{2}[/tex]
4) [tex](2\sqrt{2} + 3\sqrt{5} )^{2}[/tex]
= [tex]8 + 12\sqrt{10} + 45[/tex]
= [tex]53 + 12\sqrt{10}[/tex]
5) [tex](1+\sqrt{3} ) (1-\sqrt{3} )[/tex]
= [tex]1 - 3[/tex]
= -2
6) [tex](2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )[/tex]
= [tex]2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}[/tex]
= 2×[tex]3\sqrt{2}[/tex] - 2×[tex]2\sqrt{3}[/tex] - [tex]\sqrt{3} + \sqrt{2}[/tex]
= [tex]6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}[/tex]
= [tex]7\sqrt{2} - 5\sqrt{3}[/tex]
Hope the working out is clear and will help you. :)
Step-by-step explanation:
please I solved the question in the diagram above
Mr. A runs 500 meters in 1 minute, Mr. R runs 450 meters in 50 seconds, Mr. M runs 600 meters in 70 seconds and Mr. K runs 400 meters in 45 seconds. Based on these times, which runner would win a 100 meter race?
Step-by-step explanation:
1minute=60seconds
500 meters=60
100 meters=x
cross multiply
500×x=100×60
500x=6000
x=12
Mr. A will use 12seconds
450meters=70
100=a
cross multiply
450×a=100×70
450a=7000
divide both sides by 450
400=45
100=n
cross multiply
400×n=100×45
400n=4500
divide both sides by 400
divide and get your answer
Find the slope of (3,-20), (5,8)
Answer:
14
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= ( 8 - -20)/(5 -3)
= (8+20)/ (2)
28/2
14
Answer:
14!!!
Step-by-step explanation:
Plug the numbers into the slope formula to find the output.
y2-y1/x2-x1
find the distance between the pair of points (2, -5) and (3, -7)
Step-by-step explanation:
Using distance formula:
√(- 7 - (-5))² + (3 - 2)²
√(- 7 + 5)³ + 1²
√(-2)² + 1
√4+1
√5
Ten tiles numbered 1 through 10 are turned face down. One tile is turned up at random, and a die is rolled and the number is square. What is the probability, written as a percent, that the product of the numbers on the tile and the die will be a perfect cube?
Answer:
18.33333333%. Please mark as brainliest if I’m Correct. :)
Step-by-step explanation:
Please help explanation if possible
Answer:
y=-4x+16
Step-by-step explanation:
Okay, so a perpendicular line has an opposite reciprocal slope.
The slope for the first line is x/4, but I like to write it as 1/4x, since it's easier to look at.
The opposite reciprocal for 1/4x is -4x
So far, we have y=-4x+ [ ]
To find the remaining b value, we can use the given point intersection.
plug in the x and y values given (4, -1) and solve for b.
The equation for the perpendicular line is y=-4x+16
Can u guys answer question 2 pls
Answer:
"2.93BAR
LET X=2.93BAR
10X=29.393BAR
100X=293.93BAR
NOW WE WILL SUBTRACT THE FIRST EQUATION FROM THIRD EQUATION
100X=293.93BAR
X= 2.93BAR
99X=291.00BAR
IT CAN ALSO BE WRITTEN LIKE
X=291/99"
This was an answer from the same question someone else asked.
This answer was given by grvbundela008p3f6id
Step-by-step explanation:
If the angles a°&b° are complements of each other, then a°+b°= 90° 180° 270° 360°
Answer:
a + b = 90°
Step-by-step explanation:
If sum of two angles are 90°, then the two angles are complementary
Angles that are complements form corners. I've bolded the "co" letters to help remember that complementary angles form a 90 degree corner. Whereas supplementary angles form a straight line (both "supplementary" and "straight" start with "S"). So that's one way to remember the two terms.
Anyways, if a and b are complements of each other, then a+b = 90.
а
The marked price of a mobile is 25% above its cost price, When it is sold at a gain of
10%, the profit amounts to Rs 725. Find the marked price of the mobile.
Answer:
The marked price is Rs 823.86
Step-by-step explanation:
Let the cost price be Rs x. The marked price of the mobile is 25% above its cost price. Therefore:
The marked price = x + 25%(x) = 1 + 0.25x = 1.25x
When the mobile phone is sold at a gain of 10%. the profit is Rs 725, to find the cost price we use:
x + 10%(x) = 725
x + 0.1(x) = 725
1.1x = 725
x = 725/1.1 = 659.09
The cost price is Rs 659.09. Therefore the marked price is given as:
Marked price = 1.25x = 1.25(659.09) = 823.86
The marked price is Rs 823.86
how many are 5 raised to 4 ???
Answer:
625
Step-by-step explanation:
5⁴ = 5x5x5x5 = 625
A class has 25 students in it. 4 students drop the class. What is a reasonable estimate for the percentage of students that dropped?
Answer:
16% drop
Step-by-step explanation:
4/25 drop
Multiply by 4/4
16/100
16% drop
Answer:
16%
Step-by-step explanation:
SInce 4 students left the class, and there are 25 students, let's make it a fraction.
4/25.
As it is asking for a percentage though we could simply convert our fraction to a percentage.
Simply divide the numerator (4) by the denominator (25).
This gives us 0.16.
Which is 16%.
11.Area of Triangle is 18 cm sq. and Sum of Base and Altitude is 12 cm. The Base and Altitude are:
(1 Point)
4 , 8 4 cm, 8 cm
8, 4 8cm, 4 cm
6 , 6 6 cm, 6 cm
10 , 2 10 cm, 2 cm
Answer:
base and altitude both are 6 cmand 6cm
Please Help Find the indicated side of the right triangle
Answer:
3 sqrt(3)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 60 = x/3
3 tan 60 = x
3 sqrt(3) = x
Answer:
x = 3[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{x}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
x = 3[tex]\sqrt{3}[/tex]
During the hours from 9:00 PM on Friday to 9:00 pm on Sunday, Kristin spent 1/3 of her time sleeping, 1/8 of her time raking leaves, 1/12 of her time reading a book, 1/16 of her time working on her science project, 1/24 of her time riding in the car, and 1/48 of her time watching television. How many hours in this time period remained for all other activities?
Answer:
16 hrs of Sleep
6 hrs of Raking Leaves
4 hrs reading
3 hrs science project
2 hrs riding car
1 hr watching tv
Step-by-step explanation:
Its division on all of them, 9:00 PM on Friday to 9:00 PM on Sunday, would be 2 days, there being 24 hrs on one day, and since its 2 days, its 48, then you divide 48 by the denominator, and there you should get your timed answer.
For example, for the 1/3, you'll divide the denominator (the bottom number, in this case 3) by 48, since that's the whole amount, and the 3 is the amount of time they spent out of that whole. The division is written 48 ÷ 3 = 16
Hope this helped a bit :)
which is the solution set of 18 - 3n + 2 = n + 20 - 4n Ф 0 all reals
Answer:
all reals
Step-by-step explanation:
Simplified, you have ...
20 -3n = 20 -3n
The equation is a tautology, true for all values of n.
The solution set is "all reals."
I need to know this fairly soon pleaseee
Answer:
m<PQT= 94°
Step-by-step explanation:
If line QS bisect <PQR
m<PQS = m < SQR
7x-6= 4x+15
7x-4x= 15+6
3x= 21
X= 21/3
X= 7
m<PQS= 7x-6
m<PQS= 7(7)-6
m<PQS= 49-6
m<PQS= 43°
m<PQS= m<SQR
<mSQR=43°
m<PQR= m<PQS + m < SQR
m<PQR=43+43
m<PQR= 86°
BUT
m<PQR= m<TQW
m<PQT= m<RQW
m<PQR+m<TQW +m<PQT+ m<RQW
= 360°
Let m<TQW= x
86+86+x+x= 360
2x+172= 360
2x= 188
X= 94°
m<PQT= 94°
Complete the conditional statement. If 2 > -a, then _____.
Well, in this case we can take a as the protagonist.
We can, for example, take the a in the first member of the disequation, the 2 in the second one, changing the signs
so
+ 2 > - a
a > - 2
In fact,
"If 2 > - a, then a > -2."
create a fraction using (-3,-2)(1,-6)
Convert to a simplified fraction.
(-3,-2)
3/2
(1,-6)
-1/6
Together they just equal -9, so hopefully, your teacher wants those fractions instead.
What are the solutions of x2 + 20 = 12x.
Answer:
x₁ = 2
x₂ = 10
Step-by-step explanation:
x² + 20 = 12x
x² - 12x + 20 = 0
(x-2)(x-10) = 0
then:
x₁ = 2
x₂ = 10
Check:
x₁
2² + 20 = 12*2
3 + 20 = 24
x₂
10² + 20 = 12*10
100 + 20 = 120
What is happening to this graph when the x-values are between - 1 and 1?
A. It is decreasing.
B. It is constant
C. It is increasing
Answer:
A. It’s decreasing
Step-by-step explanation:
Hey there!
Well on the graph at points -1 and 1 we can tell the line is going down,
meaning the line is decreasing.
Hope this helps :)
Answer:it is increasing
Step-by-step explanation:
Estimate the correlation coefficient that would best describe the data below.
0.4
-0.4
0.9
-0.9
Answer:
Step-by-step explanation:
Draw a line through the data points with about half of the points on one side of the line and the other half on the other side. You'll see that there is a slight positive rise in the graph as we move from left to right, but the correlation is weak. Thus, 0.4 is the correct correlation coefficient in this case.
The correlation coefficient that would best describe the data give in the table is 0.4 which is a weak positive correlation.
CorrelationWhat is correlation?The statistical concept of correlation describes how closely two variables move in tandem with one another.
Types of correlation:(1) Positive correlation:The two variables are considered to have a positive correlation if they move in the same direction.When there is a complete positive correlation, the correlation coefficient is 1.(2) Negative correlation:We say there is a negative correlation between the variables when the 'y' variable tends to decrease as the 'x' variable increases.(3) No correlation:We claim there is no correlation between the two variables when there is no obvious connection between them.Description for the graph:As the graph is scattered in such a way that,if we draw a line from the centre, we can observe that as 'x' increases 'y' also increases so the relation is positive correlation.
But it is seen in the graph that these points are scattered, so this relation is weak. For positive weak correlation the value should be less than 0.5.
Therefore, the given graph shows positive weak correlation with value 0.4.
To know more about statistics, here
https://brainly.com/question/23724696
#SPJ2
Points A, B, and C are collinear. Point B is between A and C. Solve for x. Find x if BC = 2x+10, AC = x+21, and AB = 11.
the answer choices:
*0 *-4 *-11 *-1
Answer:
x = 0
Step-by-step explanation:
Since the points are collinear , then
AB + BC = AC , that is
11 + 2x + 10 = x + 21
2x + 21 = x + 21 ( subtract x from both sides )
x + 21 = 21 ( subtract 21 from both sides )
x = 0
antara berikut yang manakah faktor perdana bagi 28 A.1 B.4 C.2 D.28
Answer:
C.2
Step-by-step explanation:
Faktor perdana adalah faktor numbor² bagi sesuatu nombor yang juga merupakan nombor perdana.
Faktor nombor 28 adalah 1 ,2, 4 , 7 ,14 dan 28.
Dalam list nombor perdana ini hanya 2 dan 7 merupakan nombor perdana. Maka , jawapan soalan ini adalah 2.
In ΔABC,if a=6cm,b=5cm and c=4cm.find the value of ∠A.PLZ solve it fast plz help me out of it it's urgent
Answer:
the value of angle A is 82.819°
PLS HELP ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST!!
Mary wants to get spray foam insulation in her attic space. Shown here is a diagram of her attic - is the spray foam costs $3.15 per cubic meter, how much will it cost Mary to get her whole attic done?
Answer:
v = (base x height x length)/2
(7 x 10 x 13)/2 = 455 x 3.15 = 1433.25$
hope that answers your question
The sum of first three terms of an arithmetic series is 21. If the sum of the first two terms is subtracted from the third term then it would be 9. find the three terms of the series
Answer:
The terms are - 1, 7 and 15.
Step-by-step explanation:
Let the terms be a-d, a and a+d
ATQ, a-d+a+a+d=21, a=7. a+d-(a+(a-d))=9. d=8. The terms are - 1, 7 and 15.