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]
what is the vertex to the graph below
Answer:
[tex]y = 4 {ax}^{2} \\ by \: comparison \: with \: y = 1.5 {x}^{2} \\ 4a = 1.5 \\ a = \frac{1.5}{4} \\ a = \frac{3}{8} \\ vertex = \frac{3}{8} \: \: o r\: \: 0.375[/tex]
Answer:
(0,0)
Step-by-step explanation:
The vertex of the parabola is the minimum ( or maximum) point
Since this is an open upwards parabola, it is the minimum point
The minimum is (0,0) so that is the vertex
For a standard normal distribution, find the approximate value of P (-0.78 < z < 1.16). Use the portion of the standard normal table below to help answer the question.
A. 22%
B. 66%
C. 78%
D. 88%
Answer:
B: 66%
Step-by-step explanation:
Is this a function?
(2,3) (3,3) (4,3) (5,3)
Answer:
Step-by-step explanation:
Yes, it is, because the inputs {2, 3, 4, 5} are all different.
Dr. Porterfield has a choice of bread (pink, purple), meat (ham, turkey, beef) and Cheese (American, Swiss, Portugues, Japanese) at a sandwich shop. What is the probability he will select a sandwich on purple bread with either beef or turkey and has Japanese cheese
Answer:
The probability is 0.08[tex]\overline 3[/tex]
Step-by-step explanation:
The choice of bread Dr Porterfield has = Pink, purple
The number of types of breads = 2
The choices of meat = Ham, turkey, beef
The number of types of meat = 3
The choice of cheese = American, Swiss, Portuguese, Japanese
The number of types of cheese = 4
The probability of selecting purple bread from pink or purple = 1/2
The probability of selecting beef or turkey from the 3 choices of meat = 2/3
The probability of selecting Japanese cheese from the fourvtypes of cheese = 1/4
Therefore, the probability he will select a sandwich on purple bread with either beef or turkey and has Japanese cheese = (1/2) × (2/3) × (1/4) = 2/24 = 1/12 = 0.08[tex]\overline 3[/tex]
Find l.
I= [?] ft
9 ft
4 ft
PLEASE PLEASE HELP MEEEEEE IM DESPERATE
Answer:
[tex]\sqrt{85}[/tex] ft
Step-by-step explanation:
Use the Pythagorean theorem to find the unknown side in any right triangle,
Essentially, look at it as if it was flat.
a is half of the diameter, so 2 ft.
b is your height, 9ft
[tex]a^{2} +b^{2} =c^{2} \\2^{2} +9^{2} =c^{2} \\4+81= c^{2}\\\sqrt{85}=c[/tex]
can you please help me to understand the pythagorean theorem, and Trigonometry . i don't really understand it
Answer:
The Pythagoras theorem has three places namely; hypotenus, adjacent, and opposite
Answer:
Step-by-step explanation:
Pythagorean theorem will be applied to right triangles. The formula is a^2+b^2=c^2 where a and b represent the legs of the truss de c is the hypotenuse. Now let’s say I had a leg that was 4 inches and a second leg that was 8 inches. I would then have to try and find the hypotenuse. So plug it into the equation
4^2+8^2=c^2
Now 4 to the power of 2 is 16 and 8 is 64
16+64=c (note we got ride of the ^2 for the c)
So 80=c
Now what we want to do is take the square root of 80 since our c needs to be rooted. So the square root of 80 would be your answer.
Hope this helps
what is the answer of this question
Answer:
i) [tex]2.2 * 10^{-7[/tex]
ii) [tex]6.4 * 10^{-5[/tex]
What is the length of CD?
Round to one decimal place.
C
5.6
4
A
B
D
5.1
Answer:
CD = 4.4
Step-by-step explanation:
AD bisects <CAB into two equal angles. Therefore, based in the angle bisector theorem, the segments are proportional to each other. This implies that:
CD/CA = DB/AB
CD = ?
CA = 5.6
DB = 4
AB = 5.1
Therefore:
CD/5.6 = 4/5.1
Cross multiply
CD*5.1 = 4*5.6
CD*5.1 = 22.4
Divide both sides by 5.1
CD = 22.4/5.1
CD = 4.39215686
CD = 4.4 (1 decimal place)
WILL GIVE BRAINLIEST.
Use the Pythagorean identity and tangent identity to find Tanθ if sinθ= -1 and 0 ≤θ<2π radians. (ie. find all tanθ on the unit circle when sinθ= -1).
Answer:
[tex]\tan(\theta) =[/tex] undefined
Step-by-step explanation:
Given
[tex]\sin(\theta) = -1[/tex]
Required
Determine [tex]\tan(\theta)[/tex]
We know that:
[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]
This gives:
[tex](-1)^2 + \cos^2(\theta) = 1[/tex]
[tex]1 + \cos^2(\theta) = 1[/tex]
Collect like terms
[tex]\cos^2(\theta) = 1 -1[/tex]
[tex]\cos^2(\theta) = 0[/tex]
Take square roots
[tex]\cos(\theta) = \sqrt 0[/tex]
[tex]\cos(\theta) = 0[/tex]
By tan identity
[tex]\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex]
[tex]\tan(\theta) = \frac{-1}{0}[/tex]
[tex]\tan(\theta) =[/tex] undefined
PLEASE ANSWER QUICKLY
Answer:
60 - 40 = 20
20
Step-by-step explanation:
59.15 - 41.81 = 17.34
17.34 ≈ 20
Mr. Fox organizes a field trip to a museum. He orders 52 student tickets and 2 adult tickets. The cost of a student ticket is s and the cost of an adult ticket is a. The tickets Mr. Fox orders are for the students and teachers from 2 classes that he is taking to the museum. Each class pays for the same number of student tickets and each class pays for the same number of adult tickets. Write 52s + 2a as the product of the number of classes and the total cost per class. Use the number pad, a, and s to enter your answers in the boxes.
PLEASE DO NOT SEND ANY FAKE LINKS
thank you
Answer:
52·s + 2·a = [2] × ([26·s] + [a])
Step-by-step explanation:
The number of classes Mr. Fox takes to the museum = 2 classes
The number of tickets Mr. Fox orders = The number of students and teachers in the two classes
The number of students paid for by one of the classes = The number of students paid for by the other class
The number of adult paid for by one of the classes = The number of adult paid for by the other class
The expression for the total cost of the ticket is 52·s + 2·a
Let 'c' represent the total cost for each class
Therefore, given that each class pays for the same number of students and adults, we have;
2 × c = 52·s + 2·a
∴ c = (52·s + 2·a)/2 = 26·s + a
Therefore, given that we have 2 classes, we get;
52·s + 2·a = 2 × (26·s + a)
1. Sandra just opened up her own pie shop. She makes $38 on every pie that.
she sells and her monthly expenses are $850. How many pies does Sandra nded to
sell this month so that she can earn a total of $100 after she pays her monthly
expenses?
Answer:
25
Step-by-step explanation:
If you take the 100+850= 950 then you take that because that is the expenses and what she wants to make you will then divide 950/38=25 so sandra will need to sell 25 pie in order to cover the monthly cost and what she wants to earn.
Answer:
25 pies
850 + 100 = $950
So Sandra needs $950 in total.
If you divide 950 by 38 (how much a pie costs) then you get 25.
hope this helps :)
12 inches
What is the circumference of the above circle? Use t = 3.14
inches (do not round your answer)
Answer:
37.68
Step-by-step explanation:
D=12
PI=3.14
C=(D)(PI)
C=(12)(3.14)
C=37.68
The perimeter of a rectangle is 35 cm. The rectangle's area (in sq. cm) as a function of its length (in cm) is graphed.
What is the approximate average rate at which the area decreases, as the rectangle's length goes from 13 cm to 16 cm?
Options:
1: 10 1/3
2: 10 2/3
3: 11
4: 11 1/3
Answer:
2
What is the extract trying to achieve? in The Explorer’s Daughter
A geometric sequence has the terms with values a5=58 and a10 = 440.4375.
Part A: Determine what the common ratio is.
Answer:
1.5
Step-by-step explanation:
58(r)^5 = 440.4375
r^5 = 440.4375 / 58
r^5 = 7.59375
r = 1.5
What's the degree of x^2+9x-8
Answer:
2
Step-by-step explanation:
The degree of a function is the highest power any single term is raised to.
x^2 is the term that has the highest degree, so in this case, the degree is 2.
For example; in x^5-x^4-3x^3; the degree would be 5 because the highest power x is raised to is 5.
0.835 - 0.423
Answers
¥
¥
0.512
0.412
0.402
0.418
Answer:
B. [tex]0.412[/tex]
Step-by-step explanation:
[tex]0.512 + 0.423 = 0.935[/tex]
[tex]0.402+ 0.423 = 0.825[/tex]
[tex]0.418+0.412 =0.83[/tex]
[tex]0.412+ 0.423 = 0.835[/tex]
help me plzz sorry for asking this much
Answer: the answer is D. this took sometime but if you find another question like this solve it like this|
Step-by-step explanation: if you're already given the perimeter then that is the area so how to find the lengths if you're given the width is to multiply or divide! if you're using multiplication then use the width to divide so let's say you're area (perimeter) is 32! that means if you're given 4cm as the lengths then you have to use table knowledge to find the width now if we know the 4x table then that means there is 8 x 4=32 so that means that the width is 8 thats an example!
Can someone help me with this please ??
Answer:
1. x= 16,7
2. x= 8,7
Step-by-step explanation:
Use pythagoras..
r² = x² + y²
c² = a² + b²
hypothesis² = side² + side²
1. c² = a² + b²
x² = 14² + 9²
x² = 196 + 81
x² = 277
x = square root of 277
x = 16,64
2. c²= a² + b²
10²= x² + 5²
100 = x² + 25
100 - 25 = x²
75 = x²
x = square root of 75
x = 5/3 = 8,66
Solve
1 . 10(d+2)
0.25. Show your reasoning.
Which equation can be used to find mArc M N? mArc M N + 150 = 180 mArc M N + 150 = 360 mArc M N – 150 = 180 mArc M N – 150 = 360
Answer:
A: mArc M N + 150 = 180
Step-by-step explanation:
on edge2021!! hope this helps!!~
Find the circumference of the circle.
Answer:
2pie R so it would be 15.7
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:
_____________________
If a certain object has a density of 223 g/cm3 and a mass of 26 grams
Determine the volume, in cm3, of the object.
Answer:
0.11659...cm3
Step-by-step explanation:
To find volume you would have to plug it in the formula Volume= Mass / density so if we plug it in it will be, X(volume): 26(mass)/223(density) you will get 0.11659...cm3
Find the surface area for the following figures PLease help
Answer:
RP=190
TP=136
C=1,099
Step-by-step explanation:
RECTANGULAR PRISM, the equation is A=2(wl+hl+hw)
A=5*5+7*5+7*5
A=25+35+35
A=95*2
A=190
TRIANGULAR PRISM, the equation is A=1/2bh for the top and bottom triangles and A=lw for the sides
A=1/2(6)(4)
A=1/2*24
A=12
A=7*5
A=35
A=7*6
A=42
12*2=24
35*2=70
24+70+42=136
CYLINDER, the equation is A=2πrh+2πr2
A=2*3.14(7)(18)+2*3.14(7)^2
A=6.28*126+6.28*49
A=791.28+307.72
A=1,099
subtract the sum of 5/9 and -2/9 from the sum of 7/12 and -5/12
[tex] [\frac{7}{12} + ( - \frac{5}{12} )] -[ \frac{5}{9} + ( - \frac{2}{9} )] \\ \\ = [ \frac{7}{12} - \frac{5}{12} ] - [ \frac{5}{9} - \frac{2}{9} ] \\ \\ = [ \frac{7 - 5}{12} ] - [ \frac{5 - 2}{9} ] \\ \\ = \frac{2}{12} - \frac{3}{9} \\ \\ = \cancel \frac{2}{12} - \cancel \frac{3}{9} \\ \\ = \frac{1}{6} - \frac{1}{3} \\ \\ = \frac{1 - 2}{6} \\ \\ = - \frac{1}{6} [/tex]
Hope This Helps You ❤️Answer:
[tex]\frac{-1}{6}[/tex]
Step-by-step explanation:
[tex]Sum \ of \ \ \frac{5}{9} \ and \ \frac{-2}{9} =\frac{5}{9} + \frac{-2}{9} = \frac{5-2}{9} = \frac {3}{9} = \frac{1}{3}[/tex]
[tex]Sum \ of \ \frac{7}{12} \ and \ \frac{-5}{12} = \frac{7}{12} \ + \ \frac{-5}{12} = \frac{7-5}{12} = \frac{2}{12} = \frac{1}{6}[/tex]
[tex]subtract \ first \ from \ second = \frac{1}{6} - \frac{1}{3} = \frac{1 -2}{6} = \frac{-1}{6}[/tex]
Rehana has some money after she spend Rs15 she has Three quarter of the initial amount left the amount left is
Answer:
Amount left = Rs 45
Step-by-step explanation:
Let the initial amount be x.
Translating the word problem into an algebraic expression, we have;
[tex] x - 15 = \frac {3}{4} * x [/tex]
[tex] x - 15 = \frac {3x}{4} [/tex]
Cross-multiplying, we have;
[tex] 4(x - 15) = 3x [/tex]
[tex] 4x - 60 = 3x [/tex]
Rearranging the equation (collecting like terms), we have;
[tex] 4x - 3x = 60 [/tex]
x = Rs 60
Next, we find the amount left;
Amount left = 60 - 15
Amount left = Rs 45
A bag contains 4 red, 11 green, and 5 blue balls. The balls are identical in size. A call is drawn at random. What is the probability of the ball being red
Answer:
/////////////////////////////////////////////
Step-by-step explanation:
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////lalks
The planet Neptune orbits the Sun. Its orbital radius is 30.1 30.130, point, 1 astronomical units ( AU ) (AU)left parenthesis, start text, A, U, end text, right parenthesis. Assuming Neptune's orbit is circular, what is the distance it travels in a single orbit around the Sun? Give your answer in terms of π
adius is 30.1 astronomical units (AU). assuming neptunes orbit is circular, ... The distance it travels in a single orbit around the sun is ... Its orbital radius is 30.130.130, point, 1 astronomical units (\text{AU})(AU)left parenthesis, start text, A, U, end text, right parenthesis.
Answer:
60.20 pi
Step-by-step explanation:
to find curicumfrance with raidus all u have to do is multiply 30.1 ( the radius ) by 2 to get the curicumfrance
30.1*2 = 60.20
then u would multifply 60.20 by 3.14 ( pi) but in this case we can just put the pi
so the answer is 60.20 pi
-Hope this helps
plz mark brainlyest, rate and thank me
quick math help pls!
Answer:
half of 45.7 is 22.85
22.85^2 = 522.1225
522.1225 x pi
Meaning
522.1225π, A
Answer:
[tex]522.12\pi[/tex] inches²
Step-by-step explanation:
The formula for finding the area of a circle is:
[tex]A=\pi r^2[/tex]
If you put 45.7/2 (because you have the diameter and NOT the radius) instead of r you get:
[tex]A=22.85^2\pi[/tex]
Now you calculate:
[tex]A=522.12\pi \\[/tex] inches²