how do i do this problem?
Answer:
Step-by-step explanation:
Prove that:
Question 1 :
[tex]\sqrt{\frac{1-sin\theta }{1+sin\theta} } =sec\theta -tan\theta[/tex]
Question 2 :
[tex]\sqrt{\frac{1+cos \theta}{1-cos\theta} } +\sqrt{\frac{1-cos\theta}{1+cos \theta} } =2cos \:ec\theta[/tex]
Answer:
Identities used:
1/cosθ = secθ1/sinθ = cosecθsinθ/cosθ = tanθcosθ/sinθ = cotθsin²θ + cos²θ = 1Question 1 (1 - sinθ)/(1 + sinθ) = (1 - sinθ)(1 - sinθ) / (1 - sinθ)(1 + sinθ) = (1 - sinθ)² / (1 - sin²θ) = (1 - sinθ)² / cos²θSquare root of it is:
(1 - sinθ)/ cosθ = 1/cosθ - sinθ / cosθ = secθ - tanθQuestion 2The first part without root:
(1 + cosθ) / (1 - cosθ) = (1 + cosθ)(1 + cosθ) / (1 - cosθ)(1 + cosθ) (1 + cosθ)² / (1 - cos²θ) = (1 + cosθ)² / sin²θIts square root is:
(1 + cosθ) / sinθ =1/sinθ + cosθ/sinθ =cosecθ + cotθThe second part without root:
(1 - cosθ) / (1 + cosθ) = (1 - cosθ)²/ (1 + cosθ)(1 - cosθ) = (1 - cosθ)²/ (1 - cos²θ) =(1 - cosθ)²/sin²θIts square root is:
(1 - cosθ) / sinθ = 1/sinθ - cosθ / sinθ =cosecθ - cotθSum of the results:
cosecθ + cotθ + cosecθ - cotθ = 2cosecθStep-by-step explanation:
Question 1:
Consider the left-hand side
[tex] \sqrt{ \frac{ 1 - \sin\theta }{1 + \sin\theta} } = \sqrt{ \frac{ 1 - \sin\theta }{1 + \sin\theta} \times \frac{1 - \sin\theta }{1 - \sin\theta } }[/tex]
[tex] = \sqrt{ \frac{ {(1 - \sin\theta )}^{2} }{(1 - { \sin}^{2}\theta) } } = \frac{1 - \sin\theta }{ \cos\theta} [/tex]
[tex] = \frac{1}{ \cos\theta} - \frac{ \sin\theta}{\cos\theta } [/tex]
[tex] = \sec\theta \: - \tan\theta[/tex]
Question 2:
The left-hand side can be rewritten as
[tex] \sqrt{\frac{1+ \cos \theta}{1- \cos\theta} \times \frac{1+ \cos \theta}{1+ \cos \theta} } \: +\sqrt{\frac{1- \cos\theta}{1+ \cos \theta} \times \frac{1 - \cos \theta}{1 - \cos \theta} }[/tex]
[tex] = \frac{1 + \cos\theta}{ \sin\theta} + \frac{1 - \cos\theta}{ \sin\theta}[/tex]
[tex] = \frac{2}{ \sin\theta } = 2 \csc\theta[/tex]
Analyzing
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Which statements correctly describe the properties of heat? Select all that apply.
A. Heat is an essential component of life on Earth.
B. Heat is energy that flows from one object to another.
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Prt Scna
Thus , Heat moves from a hotter object to a colder one, which accurately sums up the properties of the heat equation. Energy moves from one item to another in the form of heat.
What is equation?An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate
Here,
Heat's characteristics
The direction of this transmission is always determined by the temperature differential between the bodies.
To achieve an equilibrium temperature, heat is transferred from the hotter to the cooler body.
As a result of the fact that a body and its surrounds are at different temperatures, we can infer that heat is the energy that is transferred between them.
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Find the slope between (3,-2) (-4,1)
Answer:
- [tex]\frac{3}{7}[/tex]
Step-by-step explanation:
Change in y over the change in x.
(3,2)(-4,1)
The y values are 1 and 2.
The x values are -4 and 3.
You find the change by subtracting.
[tex]\frac{1--2}{-4-3}[/tex] = [tex]\frac{1+2}{-7}[/tex] = [tex]\frac{3}{-7}[/tex]
Can be written - [tex]\frac{3}{7}[/tex]
Liam Brought 5/8 Pound of cherries. Harrison Brought more cherries than Liam. Which could be the amountOf cherries that Harrison brought ?
The amount of cherries bought by the Harrison is 62.5 pounds.
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
The amount of cherries bought by the Harrison should be more than the cherries bought by the Liam which is 5/8. Thus, The amount of cherries bought by the Harrison is more than the 5/8 or 62.5 pounds of cherries percent.
The cherries bought by the Liam is 5/8 pounds
The cherries bought by the Harrison is more than the Liam.
As in the problem the number of cherries bought Harrison (let) should be more than the cherries bought by the Liam (let ). Therefore,
H > L
As we know that the number of cherries bought by the Liam is 5/8 pounds. Keep the value of in the above equation, we get,
H > 5/8
This equation can be rewritten in the percentile form as,
h > (5/8) * 100 %
h > (5/2) * 25 %
h > 62.5 %
Hence, The amount of cherries bought by the Harrison is more than 5/8 pounds or 62.5 pounds of cherries percent.
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Simon wants to drive 450 miles in 12 hours. He knows that stopping for breaks will take a total of 3 hours. What should be his average speed in miles per hour?
50
30
45
38
Answer:
it's 50 g
Step-by-step explanation:12-3=9 so u divide 450 by 9 and u get 50[][][][][][]brainliest?
URGENT PLEASE HELP SERIOUS ANSWERS ONLY verify 2 csc (2x)=1+ tan^2 x / tan x
Answer:
Use the Pythagorean identity
tan2x+1=sec2x
to start the simplification on the left side.
Step-by-step explanation:
・ᗜ・
Fine the measure of the arc or angle indicated
Answer:
Step-by-step explanation:
? = 1/2( big ∠ - small ∠)
? = 1/2(184 - 84)
? = 1/2(100)
? = 50 °
Peyton joins a video game club for a
one-time lee of $12. Each video game
that is rented is $2 Which equation
represents the relationship between the
number of video games that Peyton
rents and the total cost c?
answer:
2x + 12 = c
step-by-step explanation:
one time fee = $12each game = $2let x be the number of gamesc = total cost2x + 12 = c
HELP I HAVE 25 POINTS AND I WILL MARK U AS BRAINLIST A granola recipe calls for 3 cups of oats, 1 cup of almends. 1 cup of pecans, and 1 cup of dried fruit. What is the ratio of fruit to eats? Yolanda says that for every 2 cups of nuts, there are 2 cups of fruit. Explain why her answer is incorrect and give the correct ratio of nuts to fruit. Explain your answer.
Answer:
Yolanda's answer is incorrect because the recipe calls for 1 cup of almonds, 1 cup of pecans, and 1 cup of dried fruit, which totals 3 cups of nuts. The correct ratio of nuts to fruit in this recipe is 3:1. This means that for every 3 cups of nuts, there is 1 cup of fruit.
I need help, I don’t know what comes next I’m confused???
Answer:
x^2-9
Step-by-step explanation:
-3 + 3 = 0 so the x terms cancel out. This leaves you with only x^2-9
PLEASE HELPPP !!
Given the diagram below, which statement is true?
Answer:
C. ∠1 and ∠3 are vertical angles and congruent.
Mr. Cooper's garden is 28 feet long and 4 feet wide.
What is the area of his garden?
Answer:
112 feet squared
Step-by-step explanation:
Just multiply the length and the width then you get the area which is 112 ft squared.
Pleasssee helppp and thankkkss!!!
GIVING BRAINLIEST AND 50 POINTS
Answer:
2x + 2
Step-by-step explanation:
Combine all the like terms:
-5x + 7x -12 + 14 = 2x + 2
Answer:
2x + 2
Step-by-step explanation:
(- 5x - 12) + (14 + 7x) ← remove parenthesis
= - 5x - 12 + 14 + 7x ← collect like terms
= (- 5x + 7x) + (- 12 + 14)
= 2x + 2
Write an equation of the line passing through the point (1,8) and parallel to y=−3x+10
The equation of the line is 3x + y - 11 = 0.
The slope-intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
First we find the slope of the line y=-3x+10 by placing it into slope-intercept form:
y = -3 x + 10
Therefore, the slope of the line is m= -3
Now since the equation of the line with slope m passing through a point
(x₁ ,y₁) is y-y₁ = m(x-x₁)
Here the point is (1,8) and slope is m= -3, therefore, the equation of the line is:
y - 8 = -3(x - 1)
y - 8 = -3x +3
3x + y - 11 = 0
Hence, the equation of the line is 3x + y - 11 = 0.
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42minutes:5hours in ratio form
Answer:
31:150
Step-by-step explanation:
First of all we convert the hours into minutes:
5×60=300
which gets us 42:300, which we can simplify to:
31:150
and is 31 is prime and 150 can't be divided into it without a remainder, it is in it's simplest form and it is the answer.
Answer:
7:50
Step-by-step explanation:
The ratio:
42 min
-------------- can be rewritten in the equivalent
5 hours
42 min
--------------- = 42/300 = 7/50 or 7:50
300 min
Can someone answer the division questions?
Answer:
The answer for the first one is 5 2/5
The answer for the second one is 3 1/7
The last answer is 3
Step-by-step explanation:
An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A
The equation of the magnitude of the force applied at the back of otter is F is (P+P0)A F is ( P + P 0 ) A .
What does the term magnitude of the force mean?The amount that encapsulates the force's power is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude may be thought of as simply the "value" or "amount" of any physical quantity.
The surface area of the otter's back is A = 0.55 m2.
The fluid pressure at the depth of the otter is P = 11500 Pa.
Thus, the equation of the magnitude of the force applied at the back of otter is F=(P+P0)A F = ( P + P 0 ) A .
The complete question is
An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A = 0.55 m2. The fluid pressure at the depth of the otter is P = 11500 Pa.
Write an equation for the magnitude of the force F on the back of the otter in terms of the pressure P and the atmospheric pressure P0.
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Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
A) -2 - i√3 , -2 + i√3
Step-by-step explanation:
Solve using quadratic formula
x² + 4x + 7 = 0
The Almighty Formula
= -b ± √b² - 4ac/2a
Where ax + bx² + c = 0
From the above question
a = 1, b = 4, c= 7
Hence,
-4 ± √4² - 4 × 1 × 7/2 × 1
-4 ± √16 - 28/2
=( -4 ± √-12)/2
Since
b² - 4ac < 0
We have two complex roots
Simplifying
( -4 ± √-12)/2
= -4/2 ± √-12/2
= -2 ± 2√3i/2
= -2 ± √3i
Therefore,
-2 - √3i , -2 + √3i
or
-2 - i√3 , -2 + i√3
Option A , is the correct answer
The planet Mercury travels 180,600 miles in its orbit during the 7 hours that make
up a typical school day. Find the unit rate.
Answer:25800 for 1 hour
Step-by-step explanation:
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It's Lila's turn to host movie night, and she's picking movies to rent. Flick City Digital Movies is having a sale, so Lila rents 5 movies for a total of $24.75. Each movie costs the same amount.
Find the area of the following color regions?
Answer:
Step-by-step explanation:
Identify the root of f(x)=-2(x+9)(x-1)
Answer:
(-9,0) and (1,0)
Step-by-step explanation:
6 is 20% of what number
I don’t really need the answer but I have to do a lot of these so I need like instructions on how to figure out the answer
If f(x) = x5 - 1, g(x) = 5x², and h(x) = 2x, which expression is equivalent to [go fo h](9)?
O2(5(95-1)²)
O2((5-92)5-1)
O5((2-9)5-1)²
O(5(2-9)2)5-1
The response to the given domain range questions is [go f oh]. (9) = 5(18^2 - 1 )
What are the domain and range?Domain and range. A function's authorised range of values is known as its domain. The x values in a function like f make up this set (x). A function's range is the collection of values that it can take as input. When we enter an x value, the function outputs this set of values.
According to the given information:f(x) = x^5 – 1, g(x) = 5x^2, and h(x) = 2x
[g o f o h](9)=g(f(h(9))
Let's find h(9) first
h(x)= 2x
h(9)= 2(9) =18
Now plug in 18 for h(9)
[g o f o h](9)=g(f(h(9)) = g(f(18))
now we find f(18)
f(x) = x^5 – 1, f(18)= 18^5 -1
Now we plug in 18^5 -1 for f(18)
[g o f o h](9)=g(f(h(9)) = g(18^5 -1)
Plug it in g(x)
g(x)= 5x^2
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Select the correct answer.
Which statement about this system of equations is true?
A. The system has no solution.
B. The system has a unique solution at (0,6).
C. The system has a unique solution at (0,-4).
D. The system has infinitely many solutions.
The statement that is true on the system of equations is that A. The system has no solution.
Why is there no solution ?There is no solution in the given system of equations because the lines formed by the equations are parallel to each other. This means that they will never intersect with each other.
A solution is only derived at the points where the systems of equations intersect with each other. As there is no point where these equations intersect, it means there is no solution for these system of equations.
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Ellis purchased $74.62 worth of
party supplies. He paid with at
$100 bill. How much change
does he receive?
Answer:25.38
Step-by-step explanation:
Estimate 91 +94 by first rounding each number to the nearest ten.
Answer:
about 180
Step-by-step explanation:
(when rounding, numbers 0-4 "stay" meaning you'd round down. If the numbers are 5-9, you round up)
91 rounded to the nearest ten would be 90
94 rounded to the nearest ten would be 90 as well
So, 90 + 90 = 180
Technically though, 91+94 = 185. So rounding this to the nearest ten would be 190.
Do what you will :)
can someone anyone help me with my hegaty maths work
I'll post the answers on here you just answers them
Answer:
sure
Step-by-step explanation:
Answer:
okey I'm not sure but
I can try to help u...