Answers
Answer:
[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]2\sin ^2 \theta + 3\sin \theta + 1 = 0[/tex]
In the interval [0, 2π).
Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:
[tex]\displaystyle 2u^2 + 3u + 1 = 0[/tex]
Factor:
[tex]\displaystyle (2u+1)(u+1) = 0[/tex]
By the Zero Product Property:
[tex]\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0[/tex]
Solve for each case:
[tex]\displaystyle u = -\frac{1}{2} \text{ or } u = -1[/tex]
Back-substitute:
[tex]\displaystyle \sin \theta = -\frac{1}{2} \text{ or } \sin \theta =-1[/tex]
Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:
[tex]\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}[/tex]
Related Questions
rovers,United and City are football teams
rovers scored x goals
United scored 8 goals more than rovers
City scored 3 goals less than twice the number of goals scored by rovers
the three teams scored a total of 117 goals
solve to find the value of x
Answers
Based on the information given, the value of x is 28 which means that Rovers scored 28 goals.
Number of goals scored by Rovers = x
United scored 8 goals more than rovers. This will be = x + 8
City scored 3 goals less than twice the number of goals scored by rovers. This will be: = 2[x} - 3 = 2x - 3
Since the three teams scored a total of 117 goals, this will be:
x + x + 8 + 2x - 3 = 117
Collect like terms
4x = 117 - 8 + 3
4x = 112
x = 112/4
x = 28
The value of x is 28
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What is the product of 180 and 170? HELP
Answers
Answer:
30600
Step-by-step explanation:
product is the answer to a multiplication problem
180 x 170= 30600
Question 10: If the product of all the numbers from 1 to 100 is divisible by 2^n, then what is the maximum possible value for n: A. 128; B. 87; C. 64; D. 97; E. 70.
Answers
Answer: D
Step-by-step explanation:
100!=2*3*4*...*100
Counting which numbers are divisible by 2:
2,4,6,8,10,12,14,...,96,98,100 : 50 numbers (100/2=50)
Counting which numbers are divisible by 4=2²:
4,8,12,16,20,...96,100: 25 numbers (100/4=25)
Counting which numbers are divisible by 8=2³:
8,16,24,32,40,...,96: 12 numbers (100/8=12.5 ==> 12)
Counting which numbers are divisible by 16=2⁴:
16,32,48,...,96: 6 numbers (100/16=6.25 ==> 6)
Counting which numbers are divisible by 32=2⁵:
32,64,96 : 3 numbers(100/32=3.125 ==>3)
Counting which numbers are divisible by 64=2⁶:
64 : 1 number (100/64=1.5625 ==>1)
Sum of those numbers= 50+25+12+6+3+1=97
100! is divisible by 2⁹⁷.
Answer D
There are 25 multiples of 4
There are 12 multiples of 8
There are 6 multiples of 16
There are 3 multiples of 32
There is one multiple of 64
Each of these is also counted in the line above
So the unique multiples are (1 x 64) x (2 x 32) x (3 x 16) x (6 x 8) x (13 x 4) x (25 x 2)
= (1 x 2^6) x (2 x 2^5) x (3 x 2^4) x (6 x 2^3) x (13 x 2^2) x (25 x 2^1)
So n = 6 + 10 + 12 + 18 + 26 + 25 = 97
The slow (but easier way) to see this is to write down all the even numbers in factors of 2 and count the number of 2S
Eg 2, 2x2, 2x3, 2x2x2, 2x5, 2x2x3, 2x7, 2x2x2x2, 2x9, 2x2x5, 2x11, 2x2x2x3, 2x13, 2x2x7, 2x15 etc
(This only got to 30 but you should get the idea - there are 26 twos up to there)
This is a tough question to explain simply
If 5x + 3 = 23 , what does 12x - 10 equal ?
Answers
Answer:
38
Step-by-step explanation:
5x+3 = 23
5x = 23-3
x = 20/5
x = 4
12x-10 = ?
12 (4) -10
48 -10
38
The value of the expression 12x - 10 will be 38.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 5x + 3 = 23. To calculate the value of 12x -10 first calculate the value of x.
5x+3 = 23
5x = 23-3
x = 20/5
x = 4
Calculate the value of 12x - 10.
12x-10 = ?
12x-10 = 12 (4) -10
12x-10 = 48 -10
12x-10 = 38
Therefore, the value of the expression 12x - 10 will be 38.
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2. sale price $1,089
sales tax rate: 6.25%
Answers
Answer:
0.0625
Step-by-step explanation:
PLEASE HELP (GEO) Find X
Round to the nearest tenth.
20 ft
\22 ft
Y
X 18 ft
X= [?]
Law of Cosines: c2 = a2 + b2 - 2ab cos C
Answers
Answer:
70.5°
Step-by-step explanation:
cos x = (20²+18²-22²)/2(20)(18)
= (400+324-484)/720
= 240/720
= 1/3
so, X = arc cos ⅓ = 70.5°
plz help!! math isn’t my thing!! i’ll give brainliest!!
Answers
Answer:
3x + 5 + 6x -6 = 80
9x -1 = 80
9x = 81
x = 9
3(9) +5 = 32
< DBC = 32
6(9)-6 = 48
<ABC = 48
Please help-
I don't understand how to fiure this out-
Answers
Answer:
It's y< -3/2x -2
Step-by-step explanation:
put each answer choice into desmos and match the graphs.
Which expression is equivalent to 4x4y - 8x*y - 32x+y?
Answers
Answer:
Option D
Step-by-step explanation:
Hope it will help you.
Answer:
It is 4x²y(x - 4)(x + 2)
Step-by-step explanation:
[tex] {4x}^{4} y - {8x}^{3} y - {32x}^{2} y[/tex]
factorise out 4x²y :
[tex] = 4 {x}^{2} y( {x}^{2} - 2x - 8)[/tex]
find the factors of x² - 2x - 8:
[tex] = 4 {x}^{2} y \{(x - 4)(x + 2) \}[/tex]
Alexandra's family took a road trip to the Grand Canyon. Alexandra slept for the last 48 miles of the trip. If the total length of the trip was 800 miles, what percentage of the total trip had they travelled when Alexandra fell asleep
Answers
Answer:
She fell asleep for 6% of the trip.
Step-by-step explanation:
You take 48 and divide it by 800. That gives you 0.06.
0.06 equals 6%.
Answer:
6%
Step-by-step explanation:
Divide 48 and 800 together.
48/800 = 0.06
48 is the miles she's sleeping and 800 is the total miles.
So, she was asleep only 6% of the trip.
Hope this helped.
will mark brainliest if correct
Answers
Answer:
identity
commutative
associative
distributive
Step-by-step explanation:
Examine the graphs. Determine whether each function is discrete, continuous, or neither discrete nor continuous. Then state the domain and range of each function.
Answers
Hey there! I'm happy to help!
Discrete data are data that are usually counted and are represented by points that are not connected by a line.
Continuous data are data that are represented by a straight line.
Our graph has a continuous function because it is made of continuous.
In a function, the domain is all of the x-values and the range is all of the y-values.
With discrete data, the domain and range are usually more finite, and with continuous data, it is usually infinite.
What x-values on this graph include any possible number. If we follow the arrow on the bottom left side of our line, it will go down forever and go in the direction of infinitely many negative x-values. The same goes for the other direction with the other side of our arrow.
So, our domain is going to be -∞ ≤ x ≤ ∞.
If we look at our range, we have the same thing happening. We will have infinite negative y-values and infinitely positive as our arrow goes infinitely in both directions.
So, our range is going to be -∞ ≤ y ≤ ∞.
Have a wonderful day and keep on learning! :D
3x(2-x)+2x(x-1)=5x(x+3)
Answers
Step-by-step explanation:
6x - 3x^2 + 2x^2 -2x = 5x^2 + 15x
4x -x^2 = 5x^2 + 15x
-11x - 6x^2 = 0
-6x^2 - 11x = 0
use the quadratic formula
(-b±√(b²-4ac))/(2a)
X=- 11/6
Need help ASAP please
Answers
Answer:
Terms for 4a^2-5a-3: 4a^2, -5a, -3
Terms for Equation 2 is correct.
Constants for 4a^2-5a-3: -3
Constants for Equation 2 is correct.
Coefficients for 4a^2-5a-3: 4, -5
Coefficients for Equation 2: 7, -3
Step-by-step explanation:
Segment AB is a line segment on a number line. Endpoint A is at –18, and the midpoint is at -6.
Determine the coordinate of endpoint B.
Coordinate of endpoint B
Answers
Ancient world study guide
Answers
Answer:
context
Step-by-step explanation:
ill help in comments if you can explain this makes no sense
Find the value of x in the equation below.
48 = 6x
Answers
Answer:
x=8
Step-by-step explanation:
This is a simple one-step algebraic equation. In algebra, to find x you must isolate the variable. To do this, use the property of equality. This property states that an equation is still true if you do the same thing to both sides. For example, the equation would still be true if you added 1 to both sides.
To isolate x divide both sides by 6. This equals 48/6 = 6x/6. Which simplifies to 8=x.
Plz help!! Math isn’t my thing. I’ll give brainliest.
Answers
Answer:
(2, - 6 )
Step-by-step explanation:
Use the mid point formula and equate to each coordinate of the midpoint
with endpoints (x₁, y₁ ) and (x₂, y₂ ) then
midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
let S = (x, y) , then
[tex]\frac{x+0}{2}[/tex] = 1 ( multiply both sides by 2 )
x = 2
and
[tex]\frac{y+2}{2}[/tex] = - 2 ( multiply both sides by 2 )
y + 2 = - 4 ( subtract 2 from both sides )
y = - 6
Then S (2, - 6 )
A spinner contains six sections of equal probability. Two sections are purple, two sections are red, one section is yellow and one section is blue. If you spin blue, you win $20. If you spin yellow, you win $10. If you spin red, you win $1 and if you spin purple you win nothing. How much would you need to be charged in order to make this a fair game
Answers
Answer: i wold charg 5 dollers
Step-by-step explanation:
sorry if im rong i dont know
if i under stood the question
HELP ME PLZ. I have no clue how to do this.
Answers
Answer:
32
Step-by-step explanation:
3x+1=8x-24
25=5x
x=5
3 times 5 plus 1 is 16 and so the length is 32
comment section:
XM=MY because MN is segment bisector
XM=3x+1=3*5+1=16=MY and since XM+MY=XY 16+16=32
Somebody help !!!!!!!!!!!!!!!!
Answers
Hey there! I'm happy to help!
The equation y=0.5x simply means that Joseph is hiking 0.5 miles every hour. This is because the x value is the independent variable or the thing you change, which in this case is the time you take hiking. The distance, the y-value, is dependent on that time.
Now, let's look at Kelly's graph. This graph isn't a grid, so we will have to eyeball some of the numbers on the graph. It appears that after 10 hours, Kelly has traveled eight miles. This is because if you go up from the 10 and meet the line and then go to the left. you will be about at the line right below the 10 on the y-axis, and if you count the lines, you will see that we are counting by 2, so it has to be eight.
So, we see that Kelly takes 10 hours to go eight miles. We know that Joseph's distance is half of his time (4 hours would be 2 miles, 6 hours would be 3 hours, etc.)
So, if we say that Joseph hikes for ten hours, he will have hiked five miles as that is half of ten. We see, though, that Kelly made it eight hours in that time, so Kelly is going faster here.
Have a wonderful day and keep on learning! :D
Or, y = x.
If Joseph hikes at the rate of y = 1/2x, and kelly hikes at the rate of y = x,
Kelly hikes faster than Joseph
how do I solve -2a = -24
Answers
Answer:
12
Step-by-step explanation:
you would divide -2 on both sides to isolate the variable a leaving you with 12
Answer:
12
Step-by-step explanation:
-2a= -24
or, a= -24/-2
:. a= 12
Can someone help I do not understand how to do this
Answers
Answer:
a) C = 1.40 + .4M
b) $4.60
c) 46.5 <= M (miles)
Step-by-step explanation:
a) Cost = initial fee + 0.40 * miles OR
C = 1.40 + .4M
b) C = 1.40 + .4M
C = 1.40 + .4 * 8
C = 1.40 + 3.20 = 4.60
c) C <= 20 so
20 <= 1.40 + .4M
20 - 1.40 <= .4M
18.60/.4 <= M
46.5 <= M
Which system of inequalities is shown?
Answers
Answer:
C. y>x
y>4
Step-by-step explanation:
the line passes y intercept (0,4) is y = 4
the line passes (0,0) and (5,5) is y = x
so, the system of inequalites of the shaded area is : y>x and y>4 (option C)
Write an algebraic expression for each verbal expression. 1. the sum of k and 8
2. 17 less than a number x times 9
6. four times the difference of a cubed and 8
PLZ HELP ASAP
Answers
Answer:
k + 8 = y
9x - 17
4(x²-8)
Express 6/2+i
with a real dersominator,
a. Find the conjugate of the denominator
b. Express with a real denominator
Answers
Is the correct answer
The quotient of 15 y
Answers
What do I need to know about 8th grade
Answers
Ida is walking dogs to help pay for sports equipment. She gets paid $10 for every dog walked and made a total of $70 on Saturday. Write an equation to show how many dogs Ida walked Saturday.
Answers
Answer:
10d = 70 where d is the number of dogs walked
Step-by-step explanation:
10d = 70 where d is the number of dogs walked
Divide each side by 10
10d/10 =70/10
d= 7
Answer: 10x = 70
Step-by-step explanations
Tom wins at chess 180 times in every 250.Daisy wins three quarters of the time.Jacob wins 328 times in every 400?Work out who has the best percentage score.
Answers
Answer:
Jacob has the best percentage score of 82%
Step-by-step explanation:
Tom wins at chess 180 times in every 250
Daisy wins 3/4 of 180 times
Jacob wins 328 times in every 400
Tom's percentage score = [tex]\frac{180}{250} * 100[/tex] = 72%
Daisy wins [tex]\frac{3}{4} * 180 = 135[/tex] times
Daisy's percentage score = [tex]\frac{135}{250} * 100[/tex] = 54 %
Jacob's percentage score = [tex]\frac{328}{400} * 100[/tex] = 82%
∴ Jacob has the best percentage score.