Answer:
[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]
Step-by-step explanation:
we would like to solve the following trigonometric equation on interval of [0,2π)
[tex] \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} [/tex]
remember that,
[tex] \displaystyle \cos(t) = \cos(2\pi - t) [/tex]
so the equation has two solutions
[tex] \begin{cases} \displaystyle \cos \left(2 \theta + \frac{\pi}{3} \right ) = \frac{ \sqrt{3} }{2} \\ \cos \left(2\pi - (2 \theta + \frac{\pi}{3} )\right ) = \frac{ \sqrt{3} }{2} \end{cases}[/tex]
take inverse trig both sides which yields:
[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ 2\pi - 2 \theta - \frac{\pi}{3} = \frac{\pi}{6} \end{cases}[/tex]
simplify the second equation:
[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} \end{cases}[/tex]
add period of 2kπ:
[tex] \begin{cases} \displaystyle 2 \theta + \frac{\pi}{3} = \frac{\pi}{6} + 2k\pi \\ \frac{5\pi}{3} - 2 \theta = \frac{\pi}{6} + 2k\pi\end{cases} [/tex]
By making theta subject of the equation we acquire:
[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} - k\pi\end{cases} [/tex]
since [tex]k\in\mathbb{Z}[/tex] we get:
[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + k\pi \\ \theta = \frac{3\pi}{4} + k\pi\end{cases} [/tex]
as we want to Solve the trigonometric equation on the interval of [0,2π) we get
[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{11\pi}{12} + \pi \\ \theta = \frac{3\pi}{4} + \pi\end{cases} [/tex]
by simplifying we acquire:
[tex] \begin{cases} \displaystyle \theta = \frac{11\pi}{12} \\ \theta = \frac{3\pi}{4} \end{cases} \text{and} \begin{cases} \displaystyle \theta = \frac{23\pi}{12} \\ \theta = \frac{7\pi}{4} \end{cases} [/tex]
and we are done!
hence,
[tex] \displaystyle \theta = \frac{3\pi}{4},\frac{11\pi}{12}, \frac{7\pi}{4}, \frac{23\pi}{12} [/tex]
Which is the solution for the system of linear equations below?
y= -1/3x + 3
y = -x + 1
Answer:
x= −3 and y= 4
not sure if this is what your looking for tho
Step-by-step explanation:
Hellppp pleaseee
Please be quick lol
Answer:
20(pi)
Step-by-step explanation:
• equation for the circumference of a circle= 2(pi)r
• You are given the diameter ( 20ft) but you need the radius (r) for the equation.
• divide 20 by 2 to get the radius since it is half of the diameter.
• 20/2=10 so c= 2(pi)(10)
• 2(10)=20
• plug in pi and your final answer is 20(pi)
Determine if the relation is a function. Explain and
justify your answer.
By looking at the table, you can see that we have an x
that is paired with two different y's so this does not fit the
definition of a function which states that each x must
be paired with exactly one y.
Find the area of the triangle
Answer:
Hello! answer: 84 sq mm
Step-by-step explanation:
To find triangle area we would do
base × height × 1/2 or
base × height ÷ 2 So...
14 × 12 = 168 168 ÷ 2 = 84 therefore the area is 84 sq mm HOPE THAT HELPS!
6. Write an equation that represents the
relationship “4 more than a number is 5"?
Answer:
4+x=5
Step-by-step explanation:
4+x=5
What minus 9 equals 11
Answer:
20
Step-by-step explanation:
20 - 9 = 11
I hope this helps
Answer:
20
Step-by-step explanation:
Call the number you're trying to find n.
"What" becomes n.
n - 9 = 11
To "undo" the subtraction and reveal the value of n , ADD 9 to both sides of the equation. (Addition is the inverse operation of subtraction.)
n = 11 + 9 = 20
Sarah walks uphill at an average of 2 miles per hour, and downhill at an average of 4 miles per hour. She goes for a 6 mile hike up a hill, and then returns downhill by the same route. What is Sarah's average speed for the whole journey?
Answer:
48
Step-by-step explanation:
Answer:
Average of 3mph
Step-by-step explanation:
If Sarah goes uphill at 2mph and downhill at 4mph.
Then to find the average you can:
Add 2 plus 4
which equals 6
Then divide the sum of 6 by the number of values given, there are two values (2 and 4)
6 divided by 2 equals 3
So the average is 3mph
I WILL GIVE BRAINLIEST IF ANSWER CORRECT
Solve the following inequality: 3 < x/2 + 1 *
Answer: x>9
Step-by-step explanation:
3 < x/2+1
switch sides: x/2+1 > 3
Multiply sides by 3: 3x/2+1 > 3*3
Simplify: x>9
What's the slope for (1,-2) & (4,4)
Answer:
2
Step-by-step explanation:
When give two points, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 4- -2)/(4-1)
= ( 4+2)/(4-1)
= 6/3
= 2
Answer:
2
Step-by-step explanation:
When give two points, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 4- -2)/(4-1)
= ( 4+2)/(4-1)
= 6/3
= 2
The festival sends Dani a map of where people will launch their kites. A portion of the map is shown. How far apart does each kite flyer stand? Round to the nearest foot. Explain please hurry
Answer:
16 ft.
Step-by-step explanation:
Distance Formula:
A = (2,2)
B = (12,14)
So, sqrt(12^2 + 10^2) = 16 ft.
This is the same for B to C.
So, 16 ft.
Mark me as Brainliest if this is correct! I really appreciate it! :D
What’s #1?????? Plz help
Answer:
C) [tex]400\pi[/tex]
Step-by-step explanation:
The formula for area is
A=pi * radius ^2
If the diameter is 40, the radius is 20
Therefore
[tex]A=\pi 20^{2} \\A=\pi 400[/tex]
Write an equation for the function that includes the points (1, 18) and (2, 54).
Answer:
y = 36x - 18
Step-by-step explanation:
(1,18) (2,54)
y2 - y1 / x2 - x1
54 - 18 / 2 - 1
36 / 1
= 36
y = 36x + b
18 = 36(1) + b
18 = 36 + b
-18 = b
5.
Geometric Sequence goes from one term to the next by always multiplying by the same
value.
Examples:
1, 2, 4, 8, 16,...... common multiplier is multiply by 2
27, 9, 3, 1, 2,........ Common multiplier is multiplied by 13
t(n) = ab"
b= common multiplier
n = term # (the nth term)
a= zeroth term
Given the sequence 70, 49, 34.3, 24.01, ....
a. What is the common multiplier?
b. What is the zeroth term?
c. What is the value of the 25th term t(25)?
Answer: See explanation
Step-by-step explanation:
a. What is the common multiplier?
This will be gotten by dividing the second term by the first term. This will be:
= 49/70 = 0.7
Common multiplier = 7/10 or 0.7
b. What is the zeroth term?.
a = 70
The zeroth term is 70
c. What is the value of the 25th term t(25)?
nth term = ar^n-1
25th term = ar^25-1
= ar^24
= 70 × 0.7^24
= 70 × 0.0001916
= 0.013412
What is the missing term?
Answer:
Missing term = 6x
Step-by-step explanation:
We got:
=> 4x by multiplying +4 and x (x * 4 = 4x)
=> 12 by multiplying +4 and +3 (4 * 3 = 12)
=> 2x² by multiplying 2x and x (2x * x = 2x²)
Similarly we will get the "missing term" by multiplying 2x and +3
=> Missing term = 6x, (2x * 3 = 6x)
Hope this helps!
Which expression is equivalent to (2x+3)(3x2−2x+5)?
Answer:
See the steps below:)
Step-by-step explanation:
Expression is equivalent to (2x+3)(3x²−2x+5) is 6x³+5x²+4x+15.
What are equivalent expressions ?An expression can be of many types numerical expressions, Algebraic expressions.We can also form these mathematical expressions from a given statement or by observing a real world scenario.
Equivalent expressions are same expressions in different forms.To check whether an expression is equivalent to another expression or not we just need to do some algebraic manipulations.Like distributing or taking common and other algebraic and arithmetic operations.
According to the given problem we have to write an expression which is equivalent to the expression (2x+3)(3x²-2x+5).
(2x+3)(3x²-2x+5)
= (2x+3)(3x²-2x+5)
=2x(3x²-2x+5)+3(3x²-2x+5) (now we will distribute)
=6x³-4x²+10x+9x²-6x+15
=6x³+5x²+4x+15.
Learn more about equivalent expressions here :
https://brainly.com/question/3644212
#SPJ6
Which of the following is equal to tan O using coordinates on the unit circle?
A) y/x
B) y
C) x/y
D) x
Answer:
A) y/x
Step-by-step explanation:
_____________________
What exactly is a root of a logarithmic function again?
Answer:
Root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.
plis help me answer this question plis also give expolaniaton
Answer:
Option c and d is right.
Step-by-step explanation:
CHECK BY MULTIPLYING THEM.
Answer:
Answer C and D are correct.
Step-by-step explanation:
In c, 2m + m=3m, and then adding the 2 leaves you with 3m+2.
In d, m+m+m=3m, and then again you add the two.
PLEASE HELP I NEED THE ANSWER ASAP ILL GUVE BRAINLIST
Hope this helps. please mark me brainliest if it did
Answer:B $225
Step-by-step explanation:
$2,700.00 divided by 12 = $225
12 = 1 year
PLEASE ANSWER QUICKLY
Answer:
60 - 40 = 20
20
Step-by-step explanation:
59.15 - 41.81 = 17.34
17.34 ≈ 20
corresponding points of (-1, 1/2)
Answer:
(-2,0), (-1,1), (0,2)
Step-by-step explanation:
Find the corresponding time in the different countries in relation to the Philippine time. Choose the correct answer from the give choices.
easy algebra question below first correct answer gets brainliest
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fshgfjgf
jgf
Answer:
Interesting... go on.
Step-by-step explanation:
Solve the equation.
5x + 6 = 2x – 3
Answer:
x = -3
Step-by-step explanation:
5x + 6 = 2x – 3
5x-2x+6=-3
3x=-9
x=-9/3
x=-3
By the end of February, Rachel's family had used 7,800 kilowatt hours (kWh) of electricity since they had moved in. On average, her family uses 900 kWh of electricity every month. Let x represent the number of months since the end of February and let y represent the electric meter reading, in kWh.
By rounding each number to 1 singnificant figure. estimate answers to:
a.) 8.2×6.7/0.46
b.) 23.4x13.9/0.18
(need answers for b.)
thank you!
Answer:
1000
Step-by-step explanation:
b.) 23.4x13.9/0.18= 1000
( Picture Included )Help please, and don’t comment unnecessary things.
Answer:
Angle 1 and Angle 8 are alternate exterior angles.
Step-by-step explanation:
If this helps please mark as brainliest
What is the measure of angle R?
110°
140°
125°
70°
what are some good notes I can use to study for my algebra exam tomorrow?
Answer:
all you need to do is look over your notes continue to partice as much as you can
Step-by-step explanation:
you got this