Answers
Answer:
[tex]\textsf{D)} \quad x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}[/tex]
Step-by-step explanation:
To find the solutions of the given trigonometric equation, begin by factoring out the common term sin 2x:
[tex]\begin{aligned}2 \sin 2x \cos x - \sin 2x & = 0\\\sin 2x(2 \cos x - 1)&=0\end{aligned}[/tex]
Set each factor equal to zero and solve for x using the unit circle.
[tex]\begin{aligned}\sin 2x & = 0\\2x & = \sin^{-1}(0)\\2x&=0+ 2\pi n, \pi + 2 \pi n\\ x&=\pi n, \dfrac{\pi}{2}+\pi n \end{aligned}[/tex]
[tex]\begin{aligned}2\cos x - 1 & = 0\\2 \cos x& = 1\\\cos x&=\dfrac{1}{2}\\x&=\cos^{-1}\left(\dfrac{1}{2}\right)\\x&=\dfrac{\pi}{3}+2\pi n, \dfrac{5\pi}{3}+2 \pi n\end{aligned}[/tex]
Therefore, the solutions in the given interval -π/2 < x ≤ π/2 are:
[tex]\boxed{x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}}[/tex]
Related Questions
prove that Sn=n(n+1) for the sequence an=2n,where n is any positive integers
Answers
Answer:
Proved
Step-by-step explanation:
Given
[tex]a_n = 2n[/tex]
Required
Prove that [tex]S_n = n(n+1)[/tex]
The given sequence is an arithmetic sequence.
The Sn of this sequence is:
[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]
Calculate a1
[tex]a_n =2n[/tex]
[tex]a_1 =2*1[/tex]
[tex]a_1 =2[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]
[tex]S_n = \frac{n}{2}(2 + 2n)[/tex]
Factor out 2
[tex]S_n = \frac{n*2}{2}(1 + n)[/tex]
[tex]S_n = n(1 + n)[/tex]
[tex]S_n = n(n + 1)[/tex] --- Proved
simplify the expression 4x+2-1/2x
Answers
answer 41x
Step-by-step
It's math,I'll send u a picture!
Answers
Answer:
suree.
Step-by-step explanation:
PLEASE HURRY!
Type the correct answer in each box.
The table shows Alice's age (a) and her daughter Martha's age (m). Complete the table and the equation.
Alice’s Age in Years
(a) Martha’s Age in Years
(m)
28 6
33 _
37 15
41 19
48 _
This equation relates Alice’s and Martha's ages in years.
Alice’s age (a) = Martha’s age (m) + _
Answers
Answer:
33-11
48-26
Alice’s age (a) = Martha’s age (m) + 22
Step-by-step explanation:
In order to find the blank spots you would need to find the difference in the filled spots. We are trying to figure out the difference which is subtraction.
28 - 6 = 22
To make sure we are correct we would do another problem.
37 - 15 = 22
So in order to find Martha's age when Alice was 33, we would subract 22.
33 - 22 = 11
Same when Alice was 48.
48 - 22 = 26
And the last equation is asking the difference between them, which would be 22.
Answer: 11 and 26
Step-by-step explanation:
hope this helps :)
El triple del mayor de tres números pares consecutivos, más 6 es igual al doble del menor. Encuentra el número mayor. Porfaaaa :(
Answers
Answer:
-14. Aunque podría estar equivocado. Espero poder ayudar
Step-by-step explanation:
In triangle ABC, one angle measures 68°, another measures 19°, what is the measure of the third angle? *
Answers
Answer:
93°
Step-by-step explanation:
In triangle ABC
one angle = 68°
Another angle = 19°
Let the third angle be X Then
x + 68° + 19° = 180° { being sum of angles of triangle }
x = 180° - 87°
x = 93°
The measure of the third Angle is 93°
Hope it will help :)
Translate the following phrases into mathematical statements.
r ) is less than or equal to ten.
s )is more than negative one
t ) isn't the same as negative
five.
x ) is at most negative three.
y )is never one.
Answers
Answer:
[tex]r \le 10[/tex]
[tex]s > -1[/tex]
[tex]t \ne 5[/tex]
[tex]x \le -3[/tex]
[tex]y \ne 1[/tex]
Step-by-step explanation:
Required
Translate to mathematical statements
a) r is less than or equal to ten.
less than or equal means [tex]\le[/tex]
So, the expression is:
[tex]r \le 10[/tex]
b) s is more than negative one
More than means >
So, the expression is:
[tex]s > -1[/tex]
c) t isn't the same as negative five.
isn't the same means not equal to ([tex]\neq[/tex])
So, the expression is:
[tex]t \ne 5[/tex]
d) x is at most negative three.
At most means [tex]\le[/tex]
So, the expression is:
[tex]x \le -3[/tex]
e) y is never one.
is never means not equal to ([tex]\neq[/tex])
So, the expression is:
[tex]y \ne 1[/tex]
Which choice is equivalent to the product below? Square root of 8 Times Square root 5?
Answers
Answer:
Step-by-step explanation:
For each statement, write what would be assumed and what would be proven in a proof by contrapositive of the statement. Then write what would be assumed and what would be proven in a proof by contradiction of the statement.
a. If x and y are a pair of consecutive integers, then x and y have opposite parity.
b. For all integers n, if n² is odd, then n is also odd.
Answers
Answer:
a)
Given Statement - If x and y are a pair of consecutive integers, then x and y have opposite parity.
Proof by Contrapositive:
Assumed statement: Suppose that integers x and y do not have opposite parity.
Proven Statement: x and y are not a pair of consecutive integers.
Proof -
x = 2u₁ , y = 2u₂
Then
(x, x+1) = (2u₁ , 2u₁ + 1) = (Even, odd)
If y = 2u₁ + 1
Not possible
⇒x and y are not a pair of consecutive integers.
Hence proved.
Proof by Contradiction:
Assumed statement: Suppose x and y are not a pair of consecutive integers.
Proven Statement: Suppose x and y do not have opposite parity.
Proof -
If x and y are not a pair of consecutive integers.
⇒ either x and y are odd or even
If x and y are odd
⇒x and y have same parity
Contradiction
If x and y are even
⇒x and y have same parity
Contradiction
(b)
Proof by Contrapositive:
Assumed statement: Let n be an integer such that n is not odd (i.e. n is an even integer)
Proven Statement: n² is not odd (i.e n² is even)
Proof -
Let n is even
⇒n = 2m
⇒n² = (2m)² = 4m²
⇒n² is even
Hence proved.
Proof by Contradiction:
Assumed statement: Let n be an integer such that n² be odd.
Proven Statement: suppose that n is not odd (i.e n is even)
Proof -
Let n² is odd
⇒n² is even
⇒n² = 2m
⇒2 | n²
⇒2 | n
⇒n = 2x
⇒ n is even
Contradiction
Hellllllllppppp meeeee
Answers
Answer:
x=18°
Step-by-step explanation:
5x-18=4x
subtract 4x from both sides
x-18=0
add 18 to both sides
x=18°
Given the linear equation & its graph, what is the slope?
Answers
Answer:
Slope: 5/3
Step-by-step explanation:
Linear equation:
y = mx + b
m is the slope
so if,
y = 5/3x - 4
5/3 is the slope.
Hope this helps :)
Let me know if there are any mistakes!!
Given two points (-3, 1) and (4, -1) are on a line. Write an equation in slope-
intercept form of the line.
y=____x+____
Answers
Answer:
y=-2/7x+1/7
Step-by-step explanation:
Find the slope first
-1-1/4+3
-2/7
m=-2/7
y=-2/7x+b
1=-2/7(-3)+b
b=1/7
PLEASEEEEEEEEEEEEE ANSWER THIS FASTTTTTTTTTTTTTTTT
Answers
Answer:
B 2:1
Step-by-step explanation:
Please help with this area assignment
Answers
Answer:
375
Step-by-step explanation:
15 times 25 equals 375
The sum of two numbers is 15. Twice the large
number plus 4 times the smaller number is 24.
Find the large number.
Answers
2x+4y=24
2x+4(15-x)=24
2x+60-4x=24
-2x=-36
x=18
the larger number is 18
a que numero micro corresponde 7/2
Answers
Answer:
31/2 d nada xdddddddddddddddddddddddddddd
The area of Ms. Anderson’s office floor measures 120
square feet. She puts down a carpet that covers 40%
of the floor. What is the area of Ms. Anderson’s floor not covered by the carpet?
Answers
Answer:
72 square feet not covered
Step-by-step explanation:
100%-40% = 60%
60% of 120 = 0.6x120 = 72
Answer:
72
Step-by-step explanation:
because i know
how do you write this number 0.1709 in words?
Answers
Answer:
0.1709 in words-
Point one seven zero nine
which is the graph of y - 3 = -2/3 (x+6)? PLEASE ANSWER QUICK IM TAKING A TIMED TEST
Answers
Answer:
the first graph
Step-by-step explanation:
the one with (0,-1) (-3,1) (3,-3)
I need help with this question
Answers
Answer:
2,540 miles
Step-by-step explanation:
The computation of the fewer miles is given below;
For Space explorer B
= 15,000 miles ÷ 5 hours
= 3,000 miles per hour
For space explorer A
y = 4,600 x
That means in one hour it covered 460 miles
So, the fewer miles would be
= 3,000 - 460
= 2,540 miles
Which professionals most directly use geometry In their work?
O A. accountants
© B. astronomers
O C. judges
© D.
pharmacists
O E. politicians
Answers
Answer:
Step-by-step explanation:
A rectangle has vertices A(1, 6), B(6, 6), C(6, 3) and D(1, 3). What is the "Area" of the rectangle?
Answers
Answer:
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
Length times width. 3 is length and width is 5
Fine the area of this figure.what two shapes can you decompose.
Answers
Steps are on paper
The senior class is making T-shirts as a fundraiser. The material needed to make each T-shirt costs $3.75. The students sell each shirt for $10.To increase sales, the students spend $350 on advertising. How many t-shirts must the students sell to breakeven?
Answers
Answer:
the number of t-shirts sold to breakeven is 56 t-shirts
Step-by-step explanation:
The computation of the number of t-shirts sold to breakeven is shown below:
= Fixed cost ÷ (Selling price - cost price)
= $350 ÷ ($10 - $3.75)
= $350 ÷ 6.25
= 56 t-shirts
Hence, the number of t-shirts sold to breakeven is 56 t-shirts
14000.00 rate 8% 60 days simple interest
Answers
Answer:186.66is answer
p=14000
r=8%
time=60days=2month/12=1/6year
Step-by-step explanation:
simple interest=ptr/100=14000×8×1/600=186.666
Ms. Halloween works in a factory. She receives a salary of $9.10 per hour and piecework pay of 15 cents per unit produced. Last week she worked 40 hours and produced 988 units. a. What was her piecework pay? What was her total hourly pay for the week? What was her total pay for the week? b. If her boss offered to pay her a straight $13 per hour and no piecework pay for the week, would she earn more or less than under the piecework pay system? c. What would her total weekly salary have been if she produced 0 units?
Answers
Answer:
1065.1
Step-by-step explanation:
Part a:
1. Halloween's piecework pay = $148.20
2. Halloween's total hourly pay for the week = $364
3. Halloween's total pay for the week = $512.20
Part b:
Total amount received for the week = $520 and she earns more when she get the straight salary on hourly basis.
Part c:
Halloween's hourly pay for 0 units production = $364
What is a salary?
Salary is a compensation or fixed amount of money paid to an employee by an employer in return for work performed.
For the given situation,
Halloween's salary received per hour = $9.10
Halloween's piecework pay per unit = 15 cents
Total work per week = 40 hours
Total unit produced per week = 988 units.
Part a:
1. Halloween's piecework pay = [tex](988)(15)[/tex]
⇒ [tex]14820 cents[/tex]
we know that $1 = 100 cents
⇒ [tex]\$148.20[/tex]
2. Halloween's total hourly pay for the week = [tex](40)(9.10)[/tex]
⇒ [tex]\$364[/tex]
3. Halloween's total pay for the week = [tex]364+148.20[/tex]
⇒ [tex]\$512.20[/tex]
Part b:
Halloween's boss offered to pay her a straight $13 per hour and no piecework pay for the week.
Total amount received for the week = [tex](40)(13)[/tex]
⇒ [tex]\$520[/tex]
Difference in pay = [tex]520-512.20[/tex]
⇒ [tex]\$7.80[/tex]
Thus, she earns more when she get the straight salary on hourly basis.
Part c:
If her production is 0 units, then she might get her hourly pay only.
⇒ [tex](40)(9.10)[/tex]
⇒ [tex]\$364[/tex]Hence we can conclude that
Part a:
1. Halloween's piecework pay = $148.20
2. Halloween's total hourly pay for the week = $364
3. Halloween's total pay for the week = $512.20
Part b:
Total amount received for the week = $520 and she earns more when she get the straight salary on hourly basis.
Part c:
Halloween's hourly pay for 0 units production = $364
Learn more about salary and wages here
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what is 445 + (67 x 958) x (3n - 31) x 67
Answers
Step-by-step explanation:
1
9
2
5
5
8
6
7
−
1
9
8
9
7
6
6
6
7
+
4
4
5
A pair of shoes that normally sells for $74.88 goes on sale for 25% off. What is the sale price?
Answers
Answer:
$56.16
Step-by-step explanation:
74.88 times 0.75 =56.16
Answer:
$56.16
Step-by-step explanation:
To find the sale price, multiply the original price by 0.75:
74.88(0.75)
= 56.16
So, the sale price is $56.16
write a real-world problem given the equation 2/3x = 12. Then solve the equation.
Answers
Answer:
You want to buy long pieces of paper at Dollar Tree for 66 cents. You have $12. How many long pieces of paper can you buy
Step-by-step explanation:
30. Which reason justifies the statement below?
A. Definition of Congruence
B. Angle Addition Postulate
C. Supplement Theorem
D. Definition of Vertical Angles
Answers
Yw
The correct reason for the statement ∠1 ≅ ∠2 will be;
⇒ Definition of Vertical Angles.
Option D is true.
What is Vertical angles?
When the two lines are crosses to each other at a point then the vertical angles are formed.
Given that;
∠1 and ∠2 are formed between two lines which crosses at a point.
Now,
The two lines are vertical lines which passes through a point and ∠1 and ∠2 are formed between them.
So, By definition of Vertical Angles;
∠1 ≅ ∠2
Therefore,
The correct reason for the statement ∠1 ≅ ∠2 will be;
⇒ Definition of Vertical Angles.
Learn more about the vertical angles visit:
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