Answer:
θ = 0° , 60°
Step-by-step explanation:
[tex]\cos^2\theta + \sqrt{3}\sin \theta \cos \theta = 1[/tex]
Substract both the sides from 1.[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 1 - 1[/tex]
[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 0[/tex]
Rearrange the terms in L.H.S.[tex]=> (\cos^2 \theta - 1 )+ \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Replace the terms in brackets with '-sin²θ' by using the identity (sin²θ + cos²θ = 1).[tex]=> -\sin^2 \theta + \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Take 'sinθ' common from the whole expression in L.H.S.[tex]=> \sin \theta(- \sin \theta + \sqrt{3}\cos \theta) = 0[/tex]
Now solve each part separately :-
1) [tex]\sin \theta = 0[/tex]
[tex]=> \theta = \sin^{-1}0 = 0[/tex]
2) [tex]-\sin \theta + \sqrt{3} \cos \theta = 0[/tex]
Divide both the sides by 'cosθ'.[tex]=> \frac{-\sin \theta + \sqrt{3}\cos \theta }{\cos \theta} = \frac{0}{\cos \theta}[/tex]
[tex]=> \frac{-sin \theta}{\cos \theta} + \frac{\sqrt{3} \cos \theta}{\cos \theta} = 0[/tex]
[tex]=> -\tan \theta + \sqrt{3} = 0[/tex]
Add both the sides with 'tanθ'.[tex]=> -\tan \theta + \sqrt{3} + \tan \theta = 0 + \tan \theta[/tex]
[tex]=> \tan \theta = \sqrt{3}[/tex]
[tex]=> \theta = \tan^{-1}\sqrt{3} = 60[/tex]
∴ θ = 0° , 60°
Answer:
Solution given:
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
[tex] 1-sin^{2} \theta+\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] 1-1 +sin^{2}\theta=\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] Sin\theta(sin\theta -\sqrt{3}cos\theta)[/tex]
Either
[tex] sin\theta=\sqrt{3} cos \theta [/tex]
[tex] \sqrt{sin\theta}{cos \theta}=\sqrt{3} [/tex]
[tex] Tan \theta =\sqrt{3}[/tex]
[tex] Tan \theta =Tan 60,Tan(180+60),Tan (360+60)[/tex]
[tex] \theta =60°,240°,420°[/tex]
in terms of π is
[tex] \theta =⅓π,\frac{4}{3}π,[/tex]
Or
[tex] Sin\theta=1[/tex]
[tex]Sin\theta=Sin0° ,Sin180°[/tex]
In terms of π is
[tex]\theta=0π,π[/tex]
so
[tex]\theta=0π,⅓π,π,\frac{4}{3}π,[/tex]
What is the next number in the pattern below? 6, 13, 21, 30, ____
Answer:
40
Step-by-step explanation:
6+7=13
13+8=21
21+9=30
30+10=40
Answer by 11:59 today!!!
Answer:
x = 30
Step-by-step explanation:
These angles are all supplementary (they all add up to 180) so:
x + 3x + 2x = 180
6x = 180
x = 30
convert 8m 32 cm into centimeters
Answer:
832 cm one meter us equal to 100 cm so 8 multiply 100 plus 32 is equal to 832
if you know how to do this pls help thankyou!
Answer : 49
I hope you understand sorry for the ugly writing
Cora charges $20 for each lawn she mows. However, she has to pay her father $12
each day she uses his lawn mower. How much does she earn if she mows 3 lawns in
one day?
Answer:
$48
Step-by-step explanation:
Cora earns $20 for each lawn
She gives her father $12 EACH DAY for his lawn mower
In a day, she mows 3 lawns which is worth= 20*3= $60
but since it is in a day, she gives her father $12 for the day from the $60
Therefore, her final earning is, $60-$12= $48
Find the volume of the given cylinder
Answer:
The answer is 32 I just know it
Item 3
A rectangle is 29 feet long and 7 feet long.
What is the area of this rectangle?
203 ft²
143 ft²
107 ft²
72 ft²
Answer: 203
Step-by-step explanation:
to find the area, you have to multiply the length of the sides together. 29x7 = 203
4x + 8y = 20 and -4x + 2y = -30
Step-by-step explanation:
Given :-
4x + 8y = 20 -4x + 2y = -30Adding the equations :-
[tex]: \implies[/tex] 10y = -10
[tex]: \implies[/tex] y = -1
Put it (i) :-
[tex]: \implies[/tex] 4x - 8 = 20
[tex]: \implies[/tex] 4x = 20 + 8
[tex]: \implies[/tex] 4x = 28
[tex]: \implies[/tex] x = 28/4
[tex]: \implies[/tex] x = 7
What is the area of a circle with a radius of 3? Give your answer in terms of π.
Answer:
9π
Step-by-step explanation:
the area of a circle =
π×r² = π×3² = 9π
radius=r=3
Area
πr²π(3)²9π units ²
5. How many 1/2 cups can be filled with 500 milliliters of liquid?
Answer:
1/2 = 120ml
Step-by-step explanation:
500/120 = 4.16666666667 round to whole number equal 4 time
I NEED HELPPPPPP ¶×¶ ¶×¶
Find the RATIO and the EXACT VALUE of the given Sec A.
Answer:
Step-by-step explanation:
take angle A as reference angle
using sec rule
sec A=hypotenuse/adjacent
sec A=13/5
sec A=2.6
A=68 degree
for ratio,
sec A=13/5
Which of these best describes the circumference?
A The square root of the area of a circle
B. The ratio of the radius of a circle to its diameter
C. The radius of a circle times 3.14
D. The diameter of a circle times 3.14
Answer:
D
Step-by-step explanation:
Since the formula of circumference is 2πr
Dose anyone know how to solve this?
Answer:
Domain = [-5, -2) U (1, 3)
Range = (-3, 4]
Step-by-step explanation:
Domain is the x values
Domain = [-5, -2) U (1, 3)
Range is the y values
Range = (-3, 4]
f , what is the truncation error for S3?
0.016
0.031
0.219
0.234
Answer: it’s B, 0.031
Step-by-step explanation: edge 2021
what does the following expression mean?
7!
A. 7+6+5+4+3+2+1
B. 7·6·5·4·3·2·1
Answer: B
Step-by-step explanation:
A factorial is multiplying the integer and all of the integers below it together.
The product of a whole number 'n' with every whole number until 1 is called the factorial. The correct option is B.
What is a factorial?The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.
The expression 7! means 7 factorial which is expanded as,
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
Hence, the correct option is B.
Learn more about Factorial:
https://brainly.com/question/16674303
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A box of Pop-tarts costs $3.00 for 8. How much per pop-tart?
How do I find the angles
Answer:
if there smaller than 90 degrees then it's acute if the angle is bigger then 90 degrees it's obtuse
Step-by-step explanation:
I need help I’ll give brainlist answer.
Answer:
All beside D
Step-by-step explanation:
The transportation department predicts that about 800,000 cars will be registered in a certain state by year 2012. Their license plates are made using and two letters followed by and three digits from 0 to 9. Will there be enough possible arrangements?
Answer:
There won't be enough arrangement
Step-by-step explanation:
Given
[tex]Letters = 2[/tex]
[tex]Digits= 3[/tex]
[tex]Cars = 800000[/tex]
Required
Determine if the possible arrangement will be enough
The 2 letters can be selected from any of the 26 alphabets without restriction.
So, the selection of letters is:
[tex]Letters = 26 * 26[/tex]
The 3 digits can be selected from any of the 10 digits without restriction.
So, the selection of digits is:
[tex]Digits = 10*10*10[/tex]
The total arrangement is:
[tex]Total = Letters * Digits[/tex]
[tex]Total = 26*26*10*10*10[/tex]
[tex]Total = 676000[/tex]
By comparison:
[tex]Total < Cars[/tex]
i.e.
[tex]676000 < 800000[/tex]
Hence, the arrangement will not be enough
can y’all help me i’m taking a test
Answer:
Over time, the function is DECREASING. Cho ran at a faster rate during segment K.
Step-by-step explanation:
If Jayna's shuffler is working properly and randomizing the playlist after each song, what is the probability of playing a slow song?
ANSWER IS 33.33%
Answer:
1 song is a slow song, 2 songs are not
Step-by-step explanation:
that would give you 1/3 probability = 33.3333333333333%
Help me find answers ASAP please
Solve the problem and enter your solution for the variable below. Do not include units in your answer. The scale below shows the weight, in grams, of two identical blocks. How many grams does one of the blocks weigh?
Answer:
1) 100+10+10 = 120
2) 120 : 2 = 60
1 block — 60
2x-y=10 y=-4x+2 substitution method
Answer:
the solution is (2, -6)
Step-by-step explanation:
Substitute the second equation into the first, replacing y in the first:
2x - (-4x+2) = 10
Simplifying, we get:
2x + 4x - 2 = 10, or:
6x = 12, which yields x = 2.
Substituting 2 for x in the second equation yields y = -4(2) + 2 = 0, or y = -6
Then the solution is (2, -6).
What does this mean and what is the answer?
-3(-7)
Answer:
-3 * -7 = 21
Step-by-step explanation:
-3(-7) = -3 * -7
Multiply
Remember: negative * negative = positive
So -3*-7 = 21
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Gulliver tossed a coin 100 times and got 43 heads. What percent of the tosses where tails?
Answer:
53 %
Step-by-step explanation:
you have the percentage of 43% for heads and you subtract 43 from one hundred and you get 57%
Answer: 57%
Dont ask how but it is 57%
Im just like dat
The ratio of the measurement of an angle to its complement is 1: 2. Find the measurement of the angle and it’s complement.
Answer:
1.x=90 degrees
2.smaller angles =30
3.larger angles =(30×2)=60
Step-by-step explanation:
Complement angle=90 degrees
90/3 (because need to separate into 3 parts) =30 degrees
1part =30 degrees
1:2
(1×30):(2×30)
30:60
How do I solve this?
Answer:
25
Step-by-step explanation:
C = √a^2+b^2
√7^2+24^2
√49+576
√625
C=25
help will give brainly
Answer:
Is it 72?
Step-by-step explanation:
Mr. Carr is hiring a plumber to repair his sink. The cost of Plumber T is shown in the table.
A table titled Plumber T Costs is shown. It has three columns and two rows. Row one is labeled Hours, h. Row two is labeled Cost, c. One hour, one hundred twenty-eight dollars. Two hours, two hundred fifteen dollars. Three hours, three hundred two dollars.
Part A. What is the initial cost and hourly rate of Plumber T?
Part B. Write an equation to represent the function shown in the table.
Part C. Plumber W charges $95 per hour and an additional $32 for the parts needed. What is the difference in cost between Plumber W and Plumber T if the repair Mr. Carr needs takes 5 hours?
Enter the correct answers in the boxes.
A. Initial cost: $
Rate per hour: $
B. Equation:
C. Difference in cost: $
The hourly rate of plumber T is $87 per hour and have an initial cost of $41.
Linear equationLinear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial amount.
From the table, using points (1, 128) and (2, 215):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-128=\frac{215-128}{2-1}(x-1)\\ \\y= 87x+41[/tex]
The hourly rate of plumber T is $87 per hour and have an initial cost of $41.
Find out more on Linear equation at: https://brainly.com/question/14323743
Answer:
Initial cost: $ 41
Rate per hour: $87
Equation: y=87x+41
Step-by-step explanation:
Sorry I do not know the difference in cost.