Answers
tan²(θ) - sin²(θ) = sin²(θ)/cos²(θ) - sin²(θ)
-- because tan(θ) = sin(θ)/cos(θ) by definition of tangent --
… = sin²(θ) (1/cos²(θ) - 1)
-- we pull out the common factor of sin²(θ) from both terms --
… = sin²(θ) (1/cos²(θ) - cos²(θ)/cos²(θ))
-- because x/x = 1 (so long as x ≠ 0) --
… = sin²(θ) ((1 - cos²(θ))/cos²(θ))
-- we simply combine the fractions, which we can do because of the common denominator of cos²(θ) --
… = sin²(θ) (sin²(θ)/cos²(θ))
-- due to the Pythagorean identity, sin²(θ) + cos²(θ) = 1 --
… = sin²(θ) tan²(θ)
-- again, by definition of tan(θ) --
Related Questions
Hai vòi nước cùng chảy vào một bể. Vòi thứ nhất chảy trong 8 giờ thì đầy bể, vòi thứ hai chảy trong vòng 10 giờ thì đầy bể. Hỏi:
a, cả hai vòi cùng chảy thì sau bao lâu sẽ đầy bể
b, Nếu có một một vòi thứ ba Thảo nước ra trong 16 giờ thì sẽ cạn hết bể đầy nước thì khi mở cả 3 vòi cùng một lúc sau bao nhiêu lâu sẽ đầy bể(lúc đầu bể đầy nước)
Answers
Answer:
Please say in English
Step-by-step explanation:
I don't understand, Sorry
A species of animal is discovered on an island. Suppose that the population size of the species can be modeled by the following function, where time t is measured in years. P(t) = 520/1 + 8e-0.3t Find the initial population size of the species and the population size after years.
Answers
Answer:
The initial population size is of 58.
The population size of the specie after t years is given by:
[tex]P(t) = \frac{520}{1 + 8e^{-0.3t}[/tex]
Step-by-step explanation:
Population size of the specie:
The population size of the specie after t years is given by:
[tex]P(t) = \frac{520}{1 + 8e^{-0.3t}[/tex]
Initial population size
This is P when [tex]t = 0[/tex], that is, [tex]P(0)[/tex]. So
[tex]P(0) = \frac{520}{1 + 8e^{-0.3*0} = \frac{520}{1+8} = \frac{520}{9} = 57.7[/tex]
Rounding to the nearest number, 58
The initial population size is of 58.
Solve this math problem 20 points
Answers
Answer:
46
Step-by-step explanation:
Diagonals of square are equal, Therefore,
KM=161
JL=4x-23
4x-23=161
4x=161+23
4x=184
x=184/4
x=46
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answers
Answer:
Step-by-step explanation:
Wage = rate / hr * the number of hours worked.
Wage = ?
rate = 15.45
time = 29.25 hours
Wage = 15.45 * 29.25
Wage = 451.91
A rectangle has vertices (−5, 6), (−1, 6), (−1, 3), and (−5, 3). It is first dilated by the rule (x, y)→(7x, 7y) and then translated 10 units down. What are the coordinates of the image?
A(−35, 32), (−7, 32), (−7, 11), (−35, 11)
B(−45, 42), (−17, 42), (−17, 21), (−45, 21)
C(−105, 42), (−77, 42), (−77, 21), (−105, 21)
D(−35,−28), (−7,−28), (−7,−49), (−35,−49)
Answers
What is the probability of rolling a number greater than 0 on a six-sided die? Someone pls help it’s urgent!!
Answers
Answer:
6/6=1
Step-by-step explanation:
There are six sides on a die and you have six total outcomes. Hope this helps! :)
Prove that if a and b are positive integers,then there exists a unique integers q and r such that a=bq+r where 0≤r<b
Answers
Step-by-step explanation:
Correct option is
C
0≤r<b
If r must satisfy0≤r<b
Proof,
..,a−3b,a−2b,a−b,a,a+b,a+2b,a+3b,..
clearly it is an arithmetic progression with common difference b and it extends infinitely in both directions.
Let r be the smallest non-negative term of this arithmetic progression.Then,there exists a non-negative integer q such that,
a−bq=r
=>a=bq+r
As,r is the smallest non-negative integer satisfying the result.Therefore, 0≤r≤b
Thus, we have
a=bq1+r1, 0≤r1≤b
PLEASE HELP!! will give brainliest!!
Suppose cos(x) = 1/sqrt5 and sin(x) > 0. What is the value of tan(2x)?
Answers
-4/3
For your question: Suppose cos(x) =1/(sqrt(5)) and sin(x) >0. What is the value of tan(2x)?
The value of tan(2x) is equal to -4/3
Which is correct?????????????
Answers
Answer:
It discusses the role of the God in influencing our decisions
Answer:
I believe it is choice D
Step-by-step explanation:
in the excerpt it talks about how sight gives us the ability to observe and experience. it also states "we prefer sight to almost everything else." hope I'm right! ☺️
Will mark brainlest!!!
Answers
Step-by-step explanation:
We have,
[tex]g(x)=x^3+x^2-x-2[/tex]
To find g(-1), put -1 in place of x i.e.
[tex]g(-1)=(-1)^3+(-1)^2-(-1)-2\\\\=-1[/tex]
To find g(1), put 1 in place of x i.e.
[tex]g(1)=1^3+1^2-1-2\\\\=-1[/tex]
To find g(2), put 2 in place of x i.e.
[tex]g(2)=2^3+2^2-2-2\\\\=8[/tex]
g(2) + g(1) = 8+(-1)
= 7
Hence, this is the required solution.
Answer:7
Step-by-step explanation: mark brainliest pls lol
In the expression 5x6 + 3xy − 7yz2 + , which of the following choices is the exponent in the term 5x6?
Answers
Answer:
The exponent is 6.
Basically, the term 5x^6 is asking you to raise 'x' to the 6th power (the exponent) and then multiply it by 5.
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
I NEED HELP PLEASE!!!
Answers
Answer:
Step-by-step explanation:
1.
[tex]-\frac{5 \pi }{6} +2\pi =\frac{-5\pi +12 \pi }{6} =\frac{7\pi }{6}[/tex]
2.
405-360=45°
An electrician needs 4 7/10 rolls of electrical wire to wire each room in a house. How many rooms can he wire with 9 2/5 rolls of wire?
Answers
Answer:
2 rooms
Step-by-step explanation:
Let; 4 7/10 = 47/10
9 2/5=47/5
So; if each room(1) = 47/10
47/5 should be x rooms
Equation form47/10 = 1
47/5 = x
cross multiplying
47/10x = 47/5
L.C.M = 10
10×47/10x = 10× 47/5
47x = 47 × 2
x = 47 × 2/47
x = 2
Therefore x being 9 2/5 rolls of wire will wire 2 rooms
Please anybody? Line intergal
Answers
Parameterize the path by
r (x) = (x, x + 2)
with 0 ≤ x ≤ 2. Then
r' (x) = (1, 1) ==> ||r' (x)|| = √(1² + 1²) = √2
and the line integral is
[tex]\displaystyle\int_Lxy\,\mathrm ds=\sqrt2\int_0^2x(x+2)\,\mathrm dx=\boxed{\frac{20\sqrt2}3}[/tex]
There are four points on a line: A, B, C and D, so that AB=1,BC=2,CD=4. Find the length of segment AD. Consider all possibilities and draw a picture for each one of them.
All possible answers for the length of AD are, _, _, _, _, _.
Answers
Answer:
7
Step-by-step explanation:
Since it's on a line, we add up all of the numbers. So 1 + 2 + 4 = 7.
Answer:
7, 1, 5, and 3
Step-by-step explanation:
Because you have to consider all possibilities, you will have multiple different-looking number lines. Using the ratios given in the problem, just by playing around with the letters' placements on the number line you can easily find the length of AD.
I need help help help
Answers
Answer:
use app Gauthmath its will give you the answer
What are the zeros of the quadratic function f(x)
128² - 10x - 3?
Answers
Answer:
When 2x^2 - 10x - 3 is plugged into the quadratic equation, the resulting zeroes are x = (5 + sqrt(31))/2 and (5 - sqrt(31))/2. Hope this helps!
Step-by-step explanation:
If my answer is incorrect, please correct me! If you like my answer and explanation, mark me as brainliest!
giving brainliest to whomever answers correctly!
Answers
Answer:
B: A systematic random sample
Step-by-step explanation:
Systematic sampling is a type of probability sampling in which members of a larger population are chosen at random from a larger population but at a fixed, periodic interval. This interval, also known as the sampling interval, is calculated by dividing the population size by the sample size desired. Despite the fact that the sample population is chosen in advance, systematic sampling is still considered random if the periodic interval is set in advance and the starting point is chosen at random.
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
pila ka adlaw ang 288 ka oras
Answers
Answer:
anu po yan salamat po sa point
What is the y-intercept of a line that has a slope of 3 and passes through point (–1, –7)?
Answers
Answer:
the y intercept is -4 (as a point it is (0,-4))
Step-by-step explanation:
Hi there!
We are given a slope (m) of 3 and the point (-1,-7).
We need to find the y intercept of the line that has the slope of 3 and passes through (-1,-7)
One way to find the y intercept is to write the equation of the line in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept).
Since we are given the slope, we can immediately substitute it into the equation
Here it is so far:
y=3x+b
now we need to find b (the y intercept)
since the line passes through the point (-1,-7), we can use it to solve for b
substitute -1 as x and -7 as y into the equation
-7=3(-1)+b
multiply
-7=-3+b
add 3 to both sides
-4=b
so the y intercept is -4 . If you need it as a point, its (0,-4) as the y intercept is the point where the equation passes through the y axis, so the value of x is 0.
Hope this helps! :)
if the bookstore pays $60 to the publisher what will be the selling price?
Answers
Answer:
This means that, when the price of a book from a publisher is $60, the bookstore will sell it for $88 to the students.
can someone give me the anwser please?
Answers
Answer:
5/6 + 11/6 = 16/ 6
Step-by-step explanation:
Distance between any Teo labeled tick marks =
(1 - 2/3) / 2 = 1/3 ÷ 2 = 1/3 * 1/2 = 1/6
From the left :
2/3 + 1/6 = 5/6
5/3 + 1/6 = 11/6
5/6 + 11/6 = (5 + 11) / 6 = 16/6
5/6 + 11/6 = 16/ 6
Given the triangle below, what is the length of the third side, rounded to the
nearest whole number?
B
18
A
12
620
Triangle not drawn to scale
A. 18
B. 14
C. 16
D. 20
Answers
Answer:
Option C
Step-by-step explanation:
In this question measure of two sides and and the angle between these sides of a triangle is given.
We have to calculate the measure of third side.
By applying cosine rule in the given triangle.
BC² = AB² + AC² - 2(AB)(AC)cos(A)
BC² = (18)² + (12)² - 2(18)(12)cos(62°)
BC² = 324 + 144 - 202.81
BC² = 265.19
BC = 16.28
BC ≈ 16 units
Therefore, Option C will be the correct option.
What side is the shortest in the picture?
A. GF
B. DG
C. EF
D. GE
F. DE
Answers
Answer:
A. GF
Step-by-step explanation:
The shortest side in a triangle is opposite the smallest angle
<d = 180 -52 -61 =67
The smallest angle is 52 so the smallest side is DG
<f = 180 - 48-85 =50
The smallest angle is 48 so the smallest side is FG
The smallest angle is 48 so the smallest side overall is FG (GF)
What is the length of the hypotenuse of the triangle?
Answers
Answer:
[tex]\sqrt{58}[/tex]
Step-by-step explanation:
To find the hypotenuse, we need to use the pythagorean theorem which is [tex]a^2+b^2=c^2[/tex]
[tex]3^2+7^2=c^2[/tex]
[tex]9+49=c^2[/tex]
[tex]58=c^2[/tex]
[tex]\sqrt{58} =c^2[/tex]
Hope this helps
Answer:
Step-by-step explanation:
√58
Clara, Dean and Elaine were candidate in an election in which 1000 people voted.elaine won the election receiving 95 more votes than Dean,and 186 more than Clara. how many votes did dean receive?
Answers
Answer:
E = 427 votes
Step-by-step explanation:
Let Elaine's vote be ELet Dean's vote be DLet Clara's vote be C.Translating the word problem into an algebraic expression, we have;
E = D + 95
E = C + 186
Equating the two equations, we have;
D + 95 = C + 186
D = C + 186 - 95
D = C + 91
Also, the sum of all the votes is equal to 1000.
E + D + C = 1000
Substituting the value of "D" we have;
E + (C + 91) + C = 1000
E + C + 91 + C = 1000
E + 2C + 91 = 1000
E + 2C = 1000 - 91
E + 2C = 909
But, E = C + 186
Substituting the value of "E" we have;
(C + 186) + 2C = 909
C + 186 + 2C = 909
3C + 186 = 909
3C = 909 - 186
3C = 723
C = 723/3
C = 241 votes
Next, we would find Elaine's vote;
E = C + 186
E = 241 + 186
E = 427 votes
Lastly, we would find Dean's vote;
E = D + 95
427 = D + 95
D = 427 - 95
D = 332 votes
Check:
E + D + C = 1000
427 + 332 + 241 = 1000
1000 = 1000
What is the value of x?
O x = 32
O x = 36
O x = 37
O x = 40
Answers
Answer:
x=40
Step-by-step explanation:
I went through each answer one by one and the only one that satisfies the question is 40.
The line equals 180°, so x + (4x-20) must equal 180.
x+(4x-20)
40+(4(40)-20)
40+(160-20)
40+140=180
x=40
Answer:
x= 40
Step-by-step explanation:
sum of angle on a straight line= 180;
To find X,
sum of angles = 180
x+(4x-20)= 180
: x= 180- [x+(4x-20)]
opening the brackets,
= 180-x-4x+20= 0
taking like terms:
= -x-4x+180+20= 0
= -5x+200=0
= -5x= -200
= x= 200/5
x= 40°
Find the range of the function represented by the list of ordered pairs below.
{(5,-8),(-1, -9),(0, -11), (9,1)}
Answers
What is the other number to this math equation?
Answers
Answer:
You need to ask yourself what times 20 gives you 600. Then ask yourself what times 20 gives you 160. Then that will give you your answer.
Step-by-step explanation:
I NEED HELP! You throw a ball from an initial height of 6 feet and with an initial velocity of 46 feet per second. Write an equation that gives the height of the ball (in feet) as a function of the time (in seconds) since it left your hand, then find the time it takes for the ball to hit the ground.
Answers
Answer:
t = 0.77930
t = 1.2832
Step-by-step explanation: