Seems like there is a correction in the first question (RHS is tanx.tany)
(i) For convenience: let tanx = a ; tany = b
Thus, tanx + tany = a + b
Moreover, cotx = 1/tanx = 1/a ; coty = 1/b
Thus,
cotx + coty = 1/a + 1/b = (a + b)/ab
Hence,
=> (tanx + tany)/(cotx + coty)
=> (a + b) / { (a + b)/ab }
=> ab(a + b)/(a + b)
=> ab => tanx.tany , proved.
(ii) For convenience: let sinx = a ; cosx = b
As we know, sin²x + cos²x = 1 => a²+b²=1
=> (a³ + b³)/(a + b)
=> (a + b)(a² + b² - ab) / (a + b)
=> (a² + b² - ab)
=> 1 - ab => 1 - sinx.cosx , proved
(iii): let x/2 = A
=> tan(x/2) + cosx.tan(x/2)
=> tanA + cos2A.tanA
=> tanA [1 + cos2A]
=> tanA (2cos²A) {1+cos2A = 2cos²A}
=> (sinA/cosA) (2cos²A)
=> sinA (2cosA)
=> 2sinAcosA
=> sin2A
=> sin2(x/2)
=> sinx proved
Letting x/2 = A is not mandatory. I did it to decease words*(in a line).
Indentities used:
• sin²A + cos²A = 1
• (a³ + b³) = (a + b)(a² + b² - 1)
• 1 + cosA = 2 cos²(A/2)
• tanA = sinA/cosA.
• 2sinAcosA = sin2A
what is it ???????????? pls help aspa
Answer:
This is curve sketching which is used in math
Step-by-step explanation:
we can see a graph plotting with the equation...of all sides
Write the decimal in simplest fractional form: -1.375
55" TV: $669 with a 23% markup
Answer:
what is the question?
Step-by-step explanation:
Price of one CD after February discount $
Price of one CD after March markdown $
After both discounts were taken separately
60% off the regular price?
Explain why the application of two separ
discount of 60%
Answer:
vssguudgebseisiehjejsieheusssushsbddjdhfbbfjfjfnfnfnfnfnnfjfngjfjfjfjfjfjfjfjf
Ben hires some buses to take 768 people to a football match. Each bus can take 56 people.
Ben hires the least number of buses needed to take all 768 people. Then 19 of the people decide not to go to the football match. Does Ben still need all the buses he has hired? You must show how you get your answer.
Answer:
yes, he still needs all the buses he hired
Step-by-step explanation:
768 people/56 people per bus = 13.71, so 14 buses
768 - 19 = 749 people going
749people/56 people per bus = 13.37, so still need 14 buses
Bethany is a biologist who has been measuring and recording the rabbit population at a park over the last several years. She has noticed that a trigonometric function can model the population, which reaches a maximum population, m, each summer and a minimum population, n, each winter. If she uses to represent the rabbit population t years from the start of her study, what is the domain of function p?
Answer:
[0,∞)
Step-by-step explanation:
Answer:
[0,∞)
Step-by-step explanation:
Correct on Plato!
What are some tips for the SAT math section?
Answer:
You should study hard and look through the test first to answer the ones you do know and then go back to the ones you don't know. Also if you use any methods or anything related to help with math try to use those through. Therefore try your best and just prepare for it, and always have supplies.
NEED HELP!!!
Find the value of X and Y
Answer:
x = 2
y = 152°
Step-by-step explanation:
✔️9x + 10 = 15x - 2 (corresponding angles theorem)
Collect like terms
9x - 15x = -10 - 2
-6x = -12
Divide both sides by -6
x = -12/-6
x = 2
✔️y + (15x - 2) = 180° (same-side interior angle theorem)
Plug in the value of x
y + (15*2 - 2) = 180
y + 28 = 180
y = 180 - 28
y = 152
Enrique collects miniature cars. He has one large case that holds 20 cars and 3 same-size, smaller cases to hold his cars.
Let n be the number of cars in each smaller case. Write an algebraic expression to represent how many total cars Enrique can fit in his cases.
Answer:
C = 3n + 20Step-by-step explanation:
There is one large case with 20 cars and 3 small cases with n cars in each.
Possible number of cars C is:
C = 3n + 20PLEASE HEELP IM GIVING BRAINLIEST TO THE FIRST CORRECT ANSWER!!!
What is an equation of the line that passes through the point (3.-1) and has a slope of 2?
y = 2x + 5
y = 2x -1
y = 2x-4
y= 2x -7
Answer:
y = 2x - 1
Step-by-step explanation:
-1 is the y-intersect of the slope
The average price for a gallon of gasoline in Germany is $5.57 and in France it is $5.54. Assume these averages are population averages in two countries, and that the probability distributions are normally distributed with the standard deviation of $.35 in Germany and standard deviation of $.25 in France. What is the probability that a randomly selected gas station in France charges more than $5.30 per gallon?
Answer:
0.8315 = 83.15% probability that a randomly selected gas station in France charges more than $5.30 per gallon
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The average price for a gallon of gasoline in France is $5.54. The standard deviation is $.25.
This means that [tex]\mu = 5.54, \sigma = 0.25[/tex]
What is the probability that a randomly selected gas station in France charges more than $5.30 per gallon?
This is 1 subtracted by the pvalue of Z when X = 5.30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.3 - 5.54}{0.25}[/tex]
[tex]Z = -0.96[/tex]
[tex]Z = -0.96[/tex] has a pvalue of 0.1685
1 - 0.1685 = 0.8315
0.8315 = 83.15% probability that a randomly selected gas station in France charges more than $5.30 per gallon
How many moles are in 9.03 x 1023 Li atoms?
please help me
Answer:
1.5 moles
Step-by-step explanation:
number of moles = no. of particles / Avagadro number
therefore, number of moles. = 9.033 * 10^23 / 6.022 * 10^23
therefore, no. of moles = 1.5
There are 1.5 moles in 9.033 * 10^23 Lithium atoms.
5. Alfredo made a container shaped like a triangular prism, as shown in the diagram
11 in.
What is the volume of the container in cubic inches?
Record your answer in the boxes. Be sure to use the correct place value.
I uploaded the answer to a file hosting. Here's link:
tinyurl.com/wpazsebu
if anyone could help me would be much appreciated, i provided the question in a picture!!
Part A:
8t + 5h = 220
t + 5h = 112
Part B:
T-shirt cost $13.50
Hat cost $22.40
HELP IM LITERALLY IN CLASS AND IM TAKING A TEST
Given the points (4,-3) and (0, -1), which other point lies on the line?
Find the x and y for numbers 2 and. 3 thank you
Answer:
(0, 4 ) and (2, - 4 )
Step-by-step explanation:
(2)
3x + 4y = 16 → (1)
- 3x + 2y = 8 → (2)
Adding (1) and (2) term by term will eliminate the x- term
0 + 6y = 24
6y = 24 ( divide both sides by 6 )
y = 4
Substitute y = 4 into either of the 2 equations and solve for x
Substituting into (1)
3x + 4(4) = 16
3x + 16 = 16 ( subtract 16 from both sides )
3x = 0 , then
x = 0
solution is (0, 4 )
(3)
2x - 4y = 20 → (1)
5x + 4y = - 6 → (2)
Adding (1) and (2) term by term will eliminate the y- term
7x + 0 = 14
7x = 14 ( divide both sides by 7 )
x = 2
Substitute x = 2 into either of the 2 equations and solve for y
Substituting into (2)
5(2) + 4y = - 6
10 + 4y = - 6 ( subtract 10 from both sides )
4y = - 16 ( divide both sides by 4 )
y = - 4
solution is (2, - 4 )
5/8 plus 1/16 simplified
Which function is graphed?
Answer:
B
Step-by-step explanation:
You can use Desmos to help with questions like these :)
if y varies inversely with the square of x, and y=6 when x=4, find y when x=0.1
Answer:
9600
Step-by-step explanation:
y varies inversely with the square of x
y=k/(x^2)
for some non-zero constant k
y=6 when x=4
6=k/(4^2)
k=96
y=96/(x^2)
x=0.1
y=96/(0.1^2)
y=9600
Which of the following shows the prime factorization of 200 using exponential notation?
Answer:
The prime factorization of 200 using exponential notation is [tex]2^{3}\times 5^{2}[/tex].
Step-by-step explanation:
First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.
1) [tex]\frac{200}{2} = 100[/tex] (Even number)
2) [tex]\frac{100}{2} = 50[/tex] (Even number)
3) [tex]\frac{50}{2} = 25[/tex] (Even number)
4) [tex]\frac{25}{5} = 5[/tex] (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
5) [tex]\frac{5}{5} = 1[/tex] (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)
Now, we construct the prime factorization using exponential notation:
[tex]200 = 2^{3}\times 5^{2}[/tex]
The prime factorization of 200 using exponential notation is [tex]2^{3}\times 5^{2}[/tex].
Answer:
2 * 3 * 5
Step-by-step explanation:
made a 100 on the text trust!!!!!
Find the equation of the line
Use exact numbers
Thank you in advance!
Answer:
the answer is 3/6 cause you go up 3 and over 6
can some pals help me
Answer:
1/8th of a foot
Step-by-step explanation:
All you have to do is divide the 5 feet by how ever many sections there are in this case it's 8.
5 / 8 = 0.625 = 1/8
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
y=x+2
Step-by-step explanation:
what is the discounted price of a $15.50 with a 20% discount
Answer:
$12.40
Step-by-step explanation:
100% -20% discount = 80%
15.50 x 0.80 = 12.40
Help mmmmmmmmmmemmmemeeeee
Answer:
P-E-M-D-A-S
Step-by-step explanation:
Ok, so start with what i call "P-E-M-D-A-S"
P: parentheses | Also known as these: ( )
E: exponents | Its a small number by another number, like the 3 on your screen
M: Multiply | Also Known as x or a dot
D: Divide | i forgot how to make it
A: Add | also known as +
S: Subtract | also known as -
now go in order to solve it, it makes it much more easy!
Answer:
49 is your answer
Step-by-step explanation:
let's do b-pemdas
brackets
parentheses
e(I forgot the name for it but it's basically a small number next to the big number)
Multiply
Divide
Add
Subtract
you do the equation in that order
so
2+8•7-(3^2)
we focus on (3^2)
that's 3•3 which equals to 9
so now the equation is
2+8•7-9
Now we focus on 8•7 which equals to 56
the equation now looks like
2+56-9
you then add 56 to 2 which equals to 58 and then subtract 9 from it so it should look like this
2+56=58
58-9= 49
and 49 is your answer
hope this help!!!
if you would give me brainliest that would help a lot!!
Plzz help me I am timed!!
Answer:
B : 10 cm^3
Step-by-step explanation:
L x W x H = V
4cm x 2cm x 1 1/4 (1.25) = 10cm^3
1 1/4 = 4 x 1 = 4 + 1 = 5/4 = 1.25
Hope this helps!
I am pretty sure this is right.
An automobile dealer can sell 12 cars per day at a price of $17,000. He estimates that for each $300 price reduction he can
sell two more cars per day. If each car costs him $14,000, and fixed costs are $1000, what price should he charge to
maximize his profit? [Hint: Let x = the number of $300 price reductions.]
How many cars will he sell at this price?
Answer:
$ 1100
Step-by-step explanation:
Let p(x) be the price he charges for a car after x price reductions.
Since car costs him $10,000, and fixed costs are $1000
p(x) = 13000-10000-1000-300x = 2000 - 300x
Let q(x) = 12 + 2x the quantity of cars sold after x price reductions.
and the profit he can make are given by:
Profit = R(x) = (12+2x)(13,000 - 10,000 - 1,000 - 300x) dollars.
As you can see, maximizing profit , we have to check where P'(x) = 0
And P''(x)<0.
So we get x = 3.
Replacing the value we get we get 2000 - 300 X 3 = 2000 - 900
= $ 1100
]
Isaiah decided to build a fence around his property. He lives on a rectangular lot 70 feet long and 50 feet wide. How many feet of fence does he need to buy?
Answer:250 feet
Step-by-step explanation: a rectangle has four sides, now you have two numbers, 70 and 50. so you do 4÷2 = 2 now take 2 a multiply it 70(140) now do it with 50(100) now add em (250) it is how i do it
Which graph shows that y varies directly as x?
Answer:
Step-by-step explanation:
AB =
Round your answer to the nearest hundredth.
A
50°
B
2
с
Answer:
50.04
Step-by-step explanation:
Answer: 3.11
Step-by-step explanation:
khan academy hint.