Answer:
θ = [tex]\frac{\pi }{3}[/tex] (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = [tex]\frac{1}{2}[/tex] , so
θ = [tex]cos^{-1}[/tex] ([tex]\frac{1}{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex] ( or 60° )
Answer:
[tex] \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASlet's solve:[tex] \sf \: rewrite \: \sin ^{2} ( \theta) \: as \: 1 - \cos ^{2} ( \theta) : \\ \sf \implies \: \cos ^{2} ( \theta) - (1 - \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: remove \: parentheses \: and \: change \: its \: sign : \\ \sf \implies \: \cos ^{2} ( \theta) - 1 + \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: add : \\ \sf \implies \: 2\cos ^{2} ( \theta) - 1 = 2 - 5 \cos( \theta) [/tex][tex] \sf \: move \: left \: hand \: sides \: expression \: to \: right \: hand \: sides \: : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 5 \cos( \theta) - 1 -2 = 0[/tex][tex] \sf \: rewrite \: 5\cos( \theta) \: as \: 6 \cos( \theta) - \cos( \theta) : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 6 \cos( \theta) - \cos( \theta) - 3 = 0[/tex][tex] \sf \:factor \: out \: 2 \cos( \theta) \: and \: - 1 : \\ \sf \implies \: 2\cos ( \theta)( \cos( \theta) + 3 ) -1( \cos( \theta) + 3) = 0[/tex][tex] \sf \: group: \\ \sf \implies \: (2\cos( \theta) - 1) ( \cos( \theta) + 3 ) = 0[/tex][tex] \sf \: rewrite \: as \: two \: seperate \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) - 1 = 0\\ \cos( \theta) + 3 = 0 \end{cases} [/tex][tex]\sf add \: 1 \: to \: the\: first \: equation \: and \: substract \: 3 \: from \: the \: second \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) = 1\\ \cos( \theta) = - 3 \end{cases} [/tex][tex] \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation[/tex]
[tex] \sf substract \: both \: sides \: by \: 2 : \\ \implies\frac{ 2\cos( \theta) }{2} = \frac{1}{2} \\ \implies\cos( \theta) = \frac{1}{2} \\ \therefore \: \theta \: = {60}^{ \circ} [/tex]Please help me out. I will be picking the brainiest Answer!!!
Answer: I think the answer is 63.
Step-by-step explanation:
Im sorry if im wrong.
He wants to wrap the present. How much wrapping paper does he need if it’s 1:00 in the afternoon and he wants to give it to her at 5:00pm?
A trader bought 20 cups of rice at 5 cups for 100 naira and sold them at 4 cups for 100naira . what was his profit
Answer:
He is making 20 naira profit for every 4 cups that he sells for 100 naira
Therefore, if he selled all this cups for 100 naira per 4 cups he made a total profit of 100 naira
Please help me find the answer.
Answer:
I think 3/6
Step-by-step explanation:
because there is 6 cards and 3 of them are odd but im not postive
Solve for ppp. -5\left(p+\dfrac35\right) = -4−5(p+ 5 3 )=−4minus, 5, left parenthesis, p, plus, start fraction, 3, divided by, 5, end fraction, right parenthesis, equals, minus, 4
Answer:
p = 1
Step-by-step explanation:
4 - 5(p + 3/5) = -4
Find P
4 - 5(p + 3/5) = -4
4 - 5p -15/5 = -4
4 - 5p - 3 = -4
-5p + 1 = -4
-5p = -4 - 1
-5p = -5
p = -5/-5
p = 1
Check:
4 - 5(p + 3/5) = -4
4 - 5(1 + 3/5) = -4
4 - 5 - 15/5 = -4
4 - 5 - 3 = -4
4 - 8 = -4
-4 = -4
Answer:
ITS HELLA 1/5 NOT 1
Step-by-step explanation:
>:(
Which of these is a pair of adjacent angles?
Answer:
Answer A
as taught to us till now
Help me please thanks
Answer:
5/6
Step-by-step explanation:
(-6 - 4) / (3 * -4) [substitute a and b]
-10 / -12 [multiply the values in parenthesis]
5 / 6 [simplify by dividing by the common factor 2]
Answer:
[tex]\frac{5}{6}[/tex]
Step-by-step explanation:
[tex]\frac{b+a}{3a} \\\\\frac{-6-4}{3(-4)} \\\\\frac{-10}{-12} \\\\\frac{5}{6}[/tex]
HELP EASY PAGE OF REVIEW I NEED THIS DONE BY TONIGHT!!! PLEASE
Answer:
1) .0335
2) -30
3) -12
4) +1058
5) x 0 1 2 3 4 5
y 6 11 16 21 26 31
6) 5:25 or 1:5
7) 140
8) 256
9) 10
10) 16
11) 7
12) 18 nights
13) 1252
14) 18/25
15) 72%
16) .8
17) 80%
18) 9/10
19) .9
Step-by-step explanation:
55 x 32 / 32
HELPPP GIVING BRAINLIEST
Answer:
55
Step-by-step explanation:
Just multiply then divide:
55 x 32 = 1760
1760 ÷ 32 = 55
Or just easier like:
55 x 32 ÷ 32 = 55
Hopefully this helps :3 Sorry if wrong :( Plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
Pls Help!!!!! I will pick the brainiest answer as well. ;)
Answer:
49
Step-by-step explanation:
20+4=24 24+25=49
Can you guys pleas help me Find the answer to 523÷32 .
Answer:
16.34375
Step-by-step explanation:
Answer: 16.34 but if rounded16.30
Step-by-step explanation:
This histogram shows the number of shoppers in various age groups at a clothing store.
How many shoppers are at least 20 years old?
a. 7 shoppers
b. 12 shoppers
c. 13 shoppers
d. 18 shoppers
(IF ITS NOT CLEAR SWITCH PICRTURES)
(PLEASE HELP)
I’m sure it’s 7 sorry if I’m wrong
Answer:
sorry im late but 12
Step-by-step explanation:
m- 0.3 > 1.45
Answer?
Answer:
[tex]m > 1.75[/tex]
Step-by-step explanation:
1) Add 0.3 to both sides.
[tex]m > 1.45 + 0.3[/tex]
2) Simplify 1.45 + 0.3 to 1.75.
[tex]m > 1.75[/tex]
Therefor, the answer is m > 1.75.
pls help! right answer = gets brainiest
Answer:
2,4 because they are hitting each other at that point
Answer:
D
Step-by-step explanation:
The solution is where the the red and blue line intersect.
Jenny wants to buy an MP3 player that costs $30.98. Write an equation so find how much change (x) she receive if she gives the cashier $40. *
Answer:
40.00-30.98=x
A circular garden is 20 feet across; a gardener wants to cover it with sod. If each sod piece is two square feet, how much sod will be needed?
Answer:
750
Step-by-step explanation:
I NEEED HELP PLEASE ANYONE!! With step by step answer
Answer:
x = 2
Step-by-step explanation:
Let me know if you have questions
What is the mean of the data set?
Fifth Grade Jump Distance
2 0
3 2 4 6
4 0 2 4 8
5 5
6 5
2 0 = 20 inches
42
40
45
20
Answer:
42
Step-by-step explanation:
Add all the numbers 20+, 32, 34, 36, 40, 42, 44, 48, 55, 65=416
then divide by total number of digits
(Mean: The mean is the average. It is found by adding all the data values and then dividing by the number of data points.)
41.6 rounded to 42
last year ,david earned a salary of d dollars.This year ,he recieved a 1.5% raised.Which expression represents the salary david will earn this year? selet all that apply
A.0.015d
B.0.15d
C.1+0.015d
D.1+0.15d
E.1d+0.015d
F.1d+0.15d
G.1.015d
H.1.15d
Answer:
E. 1d+0.015d
G. 1.015d
Step-by-step explanation:
A is incorrect, as it only shows the 1.5% raise. B is incorrect, since that would be a 15% raise. C and D are incorrect because it's impossible to add a number with a variable to one without a variable. E is correct because it properly adds 100% (the amount he made without the raise) and 1.5% (the raise) together. F is incorrect because again, it adds 15%. G is correct because it is the total amount he makes, with the raise. H is incorrect because again, it adds 15%.
The line y = 2x +k is a tangent to the curve x² + 2xy + 20 = 0.
a Find the possible values of k.
b For each of these values of k, find the coordinates of the point of contact
of the tangent with the curve.
solve attached problem
Answer:
what is the dot for?
Step-by-step explanation:
How do i find surface area of a triangler prisim
Answer:
A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.
Hope it helps..
Have a great day : P
Answer:
A prism that has 3 rectangular faces and 2 parallel triangular bases, is a triangular prism (refer to the attached picture). This three-sided prism is a polyhedron that has a rectangular base, a translated copy and 3 faces joining sides.
This three-sided prism is a polyhedron that has a rectangular base, a translated copy and 3 faces joining sides.The surface area of a triangular prism is nothing but the amount of space on the outside.
This three-sided prism is a polyhedron that has a rectangular base, a translated copy and 3 faces joining sides.The surface area of a triangular prism is nothing but the amount of space on the outside.The Surface area of a triangular prism is given as:
[tex]ab \: + 3bh[/tex]
2 times what gives you 16
Answer:
8
Step-by-step explanation:
2x = 16
2x/2 = 16/2
x = 8
Answer:
2 time 4 gives you 16
plz check
A perfect square is the product of any positive whole number used as a factor exactly two times. [Example: 49 is a perfect square because 7 × 7 = 49] The positive whole number N, when multiplied by 150, is a perfect square. What is the least possible positive whole number value for the number N?
you rode a bicyde for 2 hours and travelled 43 km, calculate your average
speed.
Answer:
22.5km per hour
Step-by-step explanation:
NEED HELP!!!
WITH PROBLEM
Answer:
x=32 hope it helps, if it does can i get 5.0 or brainliest
Step-by-step explanation:
WILL GIVE BRAINLIEST IF GOTTEN RIGHT DONT ANSWER IF YOU DONT KNOW
Answer:
Option C: I and II
Step-by-step explanation:
When you look at the question, it says that BD and AE is correct. When looking at the options we have to find which ones include BD and AE.
A. "I only" This is incorrect because "I" is not the only answer with BD and AE.
B. "III only" This is also incorrect because "III" doesn't have AE.
C. "I and II" This is correct because both "I" and "II" have BD and AE.
D. "I and III" This is incorrect because it has only BD.
Please please help please please ASAP please I'm begging you please I have 10 minutes please y'all help please any ACE that can help please
Answer:
MN
Step-by-step explanation:
ML:RQ = MN:RS = LN:QS (corr side, similar triangles)
Write down two facts of advice that you can give to other learners who would
want to engage in a fundraising activity.
Please help me solve :(((
Answer:
θ ≈ 15°
Step-by-step explanation:
Using the sine rule in the triangle
note 7.56 × 10² = 756 and 2.4 × 10³ = 2400 , then
[tex]\frac{756}{sin0}[/tex] = [tex]\frac{2400}{sin125}[/tex] ( cross- multiply )
2400 × sinθ = 756 × sin125° ( divide both sides by 2400 )
sinθ = [tex]\frac{756sin125}{2400}[/tex] , then
θ = [tex]sin^{-1}[/tex] ( [tex]\frac{756sin125}{2400}[/tex] ) ≈ 15° ( to the nearest degree )