Answer:
π/2Step-by-step explanation:
Given the expression;
secθ − tan θ = cosθ
We are to find the solution in the interval [0, 2π).This is as shown;
From trigonometry identity;
secθ = 1/cosθ
tanθ = sinθ/cosθ
Substitute into the formula;
secθ − tan θ = cosθ
1/cosθ-sinθ/cosθ = cosθ
Multiply through by cosθ
1 - sinθ = cos²θ
1-sinθ = (1-sin²θ)
1-sin²θ-1+sinθ =0
-sin²θ+sinθ = 0
sin²θ = sinθ
sinθ = 1
θ = arcsin 1
θ = 90
θ = π/2
Hence the solution is π/2
The equation is an illustration of trigonometry ratios and identities
The solution in the interval [0, 2π) is [tex]\mathbf{\theta = \frac{\pi}{2}}[/tex]
The equation is given as:
[tex]\mathbf{sec\theta - tan \theta = cos\theta}[/tex]
In trigonometry identity, we have:
[tex]\mathbf{sec\theta = \frac{1}{cos\theta}}[/tex]
and
[tex]\mathbf{tan\theta = \frac{sin\theta}{cosθ}}[/tex]
So the equation becomes
[tex]\mathbf{\frac{1}{cos\theta} -\frac{sin\theta}{cos\theta} = cos\theta}[/tex]
Multiply through by cosθ
[tex]\mathbf{1 - sin\theta = cos\²\theta}[/tex]
In trigonometry,
[tex]\mathbf{cos\²\theta = 1 - sin^2\theta }[/tex]
So, we have:
[tex]\mathbf{1-sin\theta = 1-sin\²\theta}[/tex]
Subtract 1 from both sides
[tex]\mathbf{sin\theta = sin\²\theta}[/tex]
Divide both sides by [tex]\mathbf{sin\theta}[/tex]
[tex]\mathbf{1 = sin\theta}[/tex]
Rewrite as:
[tex]\mathbf{sin\theta = 1}[/tex]
Take arc sin of both sides
[tex]\mathbf{\theta = sin^{-1}(1)}[/tex]
This gives
[tex]\mathbf{\theta = \frac{\pi}{2}}[/tex]
Read more about trigonometry ratios at:
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Which of the following lists does not include all the factors of the number?
4: 1, 2,4
10: 1, 2, 5, 10
5: 1,5
21: 1, 21
4. The polynomial m is a function ofx. The graph of m has two zeros at -7 and 2. Which expression below
could be a possible expression of m?
a. (x + 7)(x - 2)
b. (x-7)(x+2)
c. - (x – 7)(x+2)
dr2 - 7x + 2
what’s the answer?
Answer: A foreshore
Step-by-step explanation:
Solve for c. a (c – b) = d. d + ab OC= a OC = d - ab 6 d - ab O c = a ab - d о с — a
Answer:
Solving the equation [tex]a (c -b) = d[/tex] for c we get [tex]\mathbf{c=\frac{d+ba}{a} }[/tex]
Step-by-step explanation:
We need to solve the equation [tex]a (c -b) = d[/tex] for c
Solving the given equation:
[tex]a (c -b) = d[/tex]
Divide both sides by a
[tex]\frac{a(c-b)}{a}=\frac{d}{a}\\c-b=\frac{d}{a}[/tex]
Adding b on both sides
[tex]c-b+b=\frac{d}{a}+b\\c=\frac{d}{a}+b\\c=\frac{d+ba}{a}[/tex]
So, solving the equation [tex]a (c -b) = d[/tex] for c we get [tex]\mathbf{c=\frac{d+ba}{a} }[/tex]
helppp please I will give brainliest
write an equation
Answer:
Step-by-step explanation:
c=100g+50
then plug in g to get c values
I dont get this
find the value of x
If P is the incenter of triangle JKL find each measure
Answer:
Check explanation section (check the attached file for the diagram to the question).
Step-by-step explanation:
Without mincing words let's dive straight into the solution to the question/ problem above.
From the question above, we have that the point p = the point at which the bisecting angle of the triangles meets, that is the term known as incenter.
So, we have that; 7x - 6 = 5x + 4. Hence;
2x = 10; x = 5°.
Thus, the angle 5x + 4 = which is the angle KJP = 5x + 4. Recall from above that x = 5°.
Hence; 5x + 4 = 5(5) + 4 = 25 - 4 = 29°.
Also, the angle 7x - 6 = which is the angle KJP = 7x - 6. Recall from above that x = 5°.
Therefore, 7x - 6 = 7(5) - 6 = 35 - 6 = 29°.
The angle KJP + the angle LJP= the angle KJL.
Therefore, the angle KJL = 29° + 29° = 58°.
Angle KJL = 130 - ( angle KJL) - (angle KJL).
The angle KJL = 130° - ( 58°) - (52° ) = 70°
Cost of Freon Automobiles built before 1993 use Freon in their air
conditioners. The federal government now prohibits the manufacture of
Freon. Because the supply of Freon is decreasing, the price per pound is
increasing exponentially. Current estimates put the formula for the price per
pound of Freon at p(t) = 17.6(1.25)', where t is the number of years since
2000. Find the price of Freon in 2000 and 2010. How much will Freon cost in
the
year 2025?
9514 1404 393
Answer:
2000: 17.60 per pound2010: 163.91 per pound2025: 4,658.68 per poundStep-by-step explanation:
We assume your formula is intended to be ...
p(t) = 17.6(1.25^t)
__
For t=0, ...
p(0) = 17.6
For t=10, ...
p(10) = 17.6·1.25^10 ≈ 163.91
For t=25, ...
p(25) = 17.6·1.25^25 ≈ 4,658.68
!PLEASE HELP!
Find the value of x when the perimeter of a rectangle is 24 meters , the length = x + 3 meters and the width = 2x meters.?
how many real solutions does x²+8x+20=0 have?
Answer:
No real solutions
Step-by-step explanation:
Use the discriminant formula, D = b² - 4ac
D = b² - 4ac
Plug in b, a, and c:
D = b² - 4ac
D = (8)² - 4(1)(20)
D = 64 - 80
D = -16
Since the discriminant is negative, there are no real solutions
Since the solution is a complex value, hence the equation has no real solutions
Givne the quadratic expression x²+8x+20 = 0
Factorizing the function
x²+8x+20 = 0
x = -8±√8²-4(20)/2
x = -8±√64-80/2
x = -8±√-16/2
x = -8±4i/2
x = -4±2i
Since the solution is a complex value, hence the equation has no real solutions
Learn more on quadratic equations here:https://brainly.com/question/1214333
Find the radius of circle
Answer:
40 ft in think
Step-by-step explanation:
Answer: 20 feet
Step-by-step explanation:
radius of a Circe is half of the diameter
40 divided by 2 = 20 feet
if every red space i land on is -50 points, and i have -450 points, whats the minimum amount of spaces i could have landed on
Answer:I think 9 spaces
Step-by-step explanation:
Answer:
i think its 9
Step-by-step explanation: im not sure
Jaine has saved 7times as much as jared has saved. Jaine has saved $378.how much money has jared saved?
Answer:
54
Step-by-step explanation:
378 divided by 7 is how much Jared saved
Please help ASAP Due in a week! Marking Brainliest!
Answer:
what's due in a week?
Step-by-step explanation:
I will help btw.. ;)
Answer:
There is nothing here it is blank????
What do you need help with?
Step-by-step explanation:
Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
Answer:
(a). y = 3x - 11 ; (b). y = [tex]-\frac{1}{3}[/tex] x - 1
Step-by-step explanation:
Parallel lines have the same slopes
Slopes of perpendicular lines are opposite reciprocals.
(3, - 2)
The slope of given line is 3
(a). Equation of ║ line is
y + 2 = 3(x - 3)
y = 3x - 11
(b). Slope of perpendicular line is [tex]-\frac{1}{3}[/tex]
y + 2 = [tex]-\frac{1}{3}[/tex] (x - 3)
y = [tex]-\frac{1}{3}[/tex] x - 1
The required equation of a line parallel to the line will be y = 3x - 7
The required equation of the perpendicular line is y = -1/3 - 7
Using the coordinate points to get the equation of the line (1, -4) and (2, -1)
The standard form of the equation is expressed as y = mx + b
m is the slope
b is the y-intercept
Get the slope:
m = y2-y1/x2-x1
m = -1+4/2-1
m = 3/1
m = 3
Get the y-intercept
-4 = 3(1) + b
b = -4-3
b = -7
The required equation of a line parallel to the line will be y = 3x - 7
For the equation of the line perpendicular, the slope of the line will be -1/3
The required equation of the perpendicular line is y = -1/3 - 7
Learn more here: https://brainly.com/question/17003809
Express in slope form
3/4 divided by 1/5 in its best form
Answer:
it's 15\4 ur answer dear.
Just multiply 1\3 by reciprocal of 1\5.
Hope u Got it .
Mark it As Brainliest please.
what does "x'' equal if 16=x-12
Answer:
x=28
Step-by-step explanation:
16 + 12 = 28
x=28
this is ez
Answer:
28
Step-by-step explanation:
Find the value of y in the given square. Only write the number value of y. *
1 point
Answer: y would =4 because the other answers if you plug in 9 with the X you will get 13 and when you plug 4 where the Y is you get 13
Step-by-step explanation:
Rachel runs 3.2 miles each weekday and 1.5 miles each day of the weekend. How many miles will she have run in 6 weeks?
You are most likely to encounter an irrational number when you are
Answer:
dealing with circles (using pi for circumference, area, arc angle, etc)
Answer:
Well, you can finding the area of a circle
Step-by-step explanation:
what is |13| 16 is it = > < ?
Answer:
<
General Formulas and Concepts:
Math
Reading a number lineAlgebra I
|Absolute Value| makes all numbers positiveStep-by-step explanation:
Step 1: Define
|13| = 13
16
Step 2: Compare
16 is greater than 13.
Therefore, |13| < 16.
Answer:
<
Step-by-step explanation:
because the absolute value of |13| is 13 so 13 is less than 16
Complete parts (a) and (b) below.
The number of dogs per household in a small town
Dogs
0
1
2.
3
Probability 0.650 0.216 0.087
0.026
4
5
0.014
0.009
(a) Find the mean, variance, and standard deviation of the probability distribution
Find the mean of the probability distribution
(Round to one decimal place as needed.)
Answer:
a) The mean of the probability distribution = 0.6
b) The variance of the probability distribution = 0.3
c) The standard deviation of the probability distribution = 0.5
Step-by-step explanation:
a) Data and Calculations:
number of dogs per household in a small town
Dogs Probability Expected Mean Diff Mean Diff.
Value Squared
0 0.650 0 -0.569 0.32376
1 0.216 0.216 -0.353 0.12461
2 0.087 0.174 -0.395 0.15603
3 0.026 0.078 -0.491 0.24108
4 0.014 0.056 -0.513 0.26317
5 0.009 0.045 -0.524 0.27458
The mean = 0.569 (Sum of expected value)
Variance = mean of squared differences = 0.27665 (1.38323/5)
Standard deviation = square root of variance = 0.526 = 0.5
The mean, variance and standard deviation of the considered probability distribution are evaluated to be:
Mean of the distribution = 0.569Variance of the distribution = 0.923 approxStandard deviation of the distribution = 0.96 approxHow to find the mean (expectation) and variance of a random variable?Supposing that the considered random variable is discrete, we get:
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i\\\\Variance = Var(X) = (\sum_{\forall x_i} f(x_i)x^2_i) - (E(X))^2\\[/tex]
As standard deviation is positive root of variance, thus,
[tex]\sigma = \sqrt {Var(X)}[/tex]
where [tex]x_i; \: \: i = 1,2, ... ,n[/tex] is its n data values
and [tex]f(x_i)[/tex] is the probability of [tex]X = x_i[/tex]
For this case, let we suppose that:
X = number of dogs per household in the considered town.
Then we have the probability distribution for values of X as:
Number of dogs Probability
0 0.650
1 0.216
2 0.087
3 0.026
4 0.014
5 0.009
Thus, we get:
Mean of X : E(X) = [tex]0 \times 0.650 + 1 \times 0.216 + 2 \times 0087 + 3 \times 0.026 + 4 \times 0.014 + 5 \times 0.009 = 0.569[/tex]
Variance of X:
Var(X) =
[tex](0^2 \times 0.650 + 1^2 \times 0.216 + 2^2 \times 0.087 + 3^2 \times 0.026 + 4^2 \times (0.014)\\ + 5^2 \times (0.009)) - (0.569)^2 \approx 0.923[/tex]
Standard deviation of X = [tex]\sigma = \sqrt {Var(X)} \approx \sqrt{0.923} \approx 0.96[/tex]
Thus, the mean, variance and standard deviation of the considered probability distribution are evaluated to be:
Mean of the distribution = 0.569Variance of the distribution = 0.923 approxStandard deviation of the distribution = 0.96 approxLearn more about expectation of a random variable here:
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Aly's science class was looking at bacteria through a microscope. Aly's teacher said some bacteria can be as small as 0.00365 cm long. What is the length of the bacteria written in scientific notation?
Answer:
The answer is 3.65 x 10^3 power.
Step-by-step explanation:
In scientific notation, you need only the one's place, so 36.5 would not work. I hope this helps, I know this is a day late and you probably figured it out, but just in case you didn't, here is the answer :)
Use the law of sines to find side b.
Answer:
83.3
Step-by-step explanation:
Completely factored form of t2 - 36
Answer:
( t + 6 ) ( t − 6 )
Step-by-step explanation:
t 2 − 36
since 36 is a square number, you'll have to unsquare it to get
t 2 − [tex]6^{2}[/tex]
Since both terms are perfect squares, factor using the difference of squares formula, a 2 − b 2 = ( a + b )( a − b ) where a = t and b = 6
You should get : ( t + 6 ) ( t − 6 ) !
Hope this helped :)))
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds
and each large box of paper weighs 75 pounds. A total of 24 boxes of paper were
shipped weighing 1410 pounds altogether. Write a system of equations that could be
used to determine the number of small boxes shipped and the number of large boxes
shipped. Define the variables that you use to write the system.
Michael spent $18 at a local farmers’ market. The apples he bought cost $2 per pound, and the peppers cost $3 per pound. How many pounds of apples and peppers did he buy?
This equation represents the scenario:
2a + 3p = 18
Choose the equations that are equivalent.
Check all that apply.
p = two-thirds a + 6
p = negative two-thirds a + 6
a = negative 1 and one-half p + 9
a = 1 and one-half p + 9
a = StartFraction negative 3 p + 18 Over 2 EndFraction
Answer:
p=-2/3a + 6
a=-1 1/2p + 9
a= -3p+18/2
Answer:
B C and E
Step-by-step explanation:
got it right on edge after clicking A instead of B
HURRY AND ANSWER ILL GIVE 50 POINTS AND BRAINLIST! HOW YOU WORKED OUT THE PROBLEM MUST BE INCLUDED
ALL FOUR NEED TO BE DONE!
Answer:
Question #12: a. ⅛ b. ³/₂₀
Question #4: 9 ÷ 3 = 3
Question #5: a. 80½ yards² b. $1288.00
Question #9: 1½ inches
Question #8: 16/20
Step-by-step explanation:
I hope this helped!
Find the value of 7u-5 given that 13u-6= 7.
Simplify your answer as much as possible.
please help asap if it’s not a real answer i will report but anyways ty if you answer
Answer:
Step-by-step explanation:
13u - 6= 7
13u = 7 + 6
13u= 13
u = 13/13 = 1
Putting value of u in the equation
7u - 5
7(1) - 5
= 7 - 5
= 2
Find the diameter of a circle which has an area of 2.7 cm?
Answer:
1.85
Step-by-step explanation:
please mark me brainliest
Answer:
5.94cm²
Step-by-step explanation:
d = 2.75
r = d/2 = 2.75/2 = 1.375
A= πr² = π(1.375)² = 5.94cm²
please mark brainliest