Answers
Answer:
The values of [tex]r_{2}[/tex] and [tex]\alpha_{2}[/tex] are 2 and 150º.
Step-by-step explanation:
The complete statement is:
Find [tex]\alpha_{2}[/tex] and [tex]r_{2}[/tex] such that [tex]\sin \theta - \sqrt{3}\cdot \cos \theta = r_{2}\cdot \cos (\theta - \alpha_{2})[/tex].
We proceed to use the following trigonometric identity:
[tex]\cos (\theta - \alpha_{2}) = \cos \theta \cdot \cos \alpha_{2} +\sin \theta \cdot \sin \alpha_{2}[/tex] (1)
[tex]\sin \theta -\sqrt{3}\cdot \cos \theta = r_{2}\cdot \cos \theta \cdot \cos \alpha_{2}+r_{2}\cdot \sin \theta \cdot \sin \alpha_{2}[/tex]
By direct comparison we derive these expressions:
[tex]r_{2}\cdot \sin \alpha_{2} = 1[/tex] (2)
[tex]r_{2}\cdot \cos \alpha_{2} = -\sqrt{3}[/tex] (3)
By dividing (2) by (3), we have the following formula:
[tex]\tan \alpha_{2} = -\frac{1}{\sqrt{3}}[/tex]
[tex]\tan \alpha_{2} = -\frac{\sqrt{3}}{3}[/tex]
The tangent function is negative at second and fourth quadrants. That is:
[tex]\alpha_{2} = \tan^{-1} \left(-\frac{\sqrt{3}}{3} \right)[/tex]
There are at least two solutions:
[tex]\alpha_{2,1} = 150^{\circ}[/tex], [tex]\alpha_{2,2} = 330^{\circ}[/tex]
And the value of [tex]r_{2}[/tex]:
[tex]r_{2}^{2}\cdot \sin^{2}\alpha_{2} + r_{2}^{2}\cdot \cos^{2}\alpha_{2} = 4[/tex]
[tex]r_{2}^{2} = 4[/tex]
[tex]r_{2} = 2[/tex]
The values of [tex]r_{2}[/tex] and [tex]\alpha_{2}[/tex] are 2 and 150º.
Related Questions
PLEASE HELP ILL GIVE BRAINLIEST
Answers
Answer:
(-2,0) (1,0) (6,0)
Step-by-step explanation:
I used synthetic division which is a lot to explain so I would recommend googling it
Answer:
-12X - 2
Step-by-step explanation:
I don't know I have never done this i'm just going with my gut.
Write the prime factorization of the number.
$74=$
Answers
Answer:
90
Step-by-step explanation:
The expression 4x/5-2x/3 is equivalent to?
Answers
Answer: The answer B
Step-by-step explanation: so the answer i got was x 5 so its B
Let C represent the cost in dollars and R represent the revenue in dollars. What is the break-even point? Use a table to help if necessary.
C=24x+80
R=44x
Break Even point (_ , _)
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given
C=24x+80
R=44x
To determine
What is the break-even point?
Given that
C represents the cost in dollars
R represents the revenue in dollars.
At the break-even point Cost (C) equals Revenue (R), so
R = C
44x = 24x+80
44x-24x = 80
20x = 80
divide both sides by 20
20x/20 = 80/20
x = 4
Thus, at x = 4 the value of Cost (C) equals Revenue (R).
i.e.
C = 24x+80 = 24(4)+80 = $176
R = 44x = 44(4) = $176
Answer:
(4, 176)
Step-by-step explanation:
Cause im smart and its right :3
Here is a list of numbers: 7, 19, 3, 18, 15, 3, 14 ,20 ,2 ,12 State the median.
Answers
Answer:
13.
Step-by-step explanation:
2, 3, 3, 7, 12, 14, 15, 18, 19, 20
3,3,7,12,14,15,18,19
3,7,12,14,15,18
7,12,14,15
12,14
^ Mean: 13
Uhh it's easy, did you really pay attention at ALL during the lesson. Literally don't judge on here but really!!!?
A car dealership has SUVs and sedans in a ration of 5:9. How many sedans does the car dealership have if there are 140 SUVs
Answers
To solve this, all you need to do is compare the ratio to the amount of SUVS there are.
5/9 (SUVs to sedans)
140/? (SUVs to sedans)
140 ÷ 5 = 28
9 x 28 = 252
140/252
There are 252 sedans in the car dealership! :D
Answer:
252 Sedans
Step-by-step explanation:
your welcome ;)
Quickkk please help and how all work
y = x +4
2x - y = 6
Answers
Jerome served $725 worth of meals last weekend. How much did Jerome earn last weekend?
Answers
Answer:
725 dollars probably
Step-by-step explanation:
it really depends on how much is cut away from his check from business expenses and how much his boss would take
Please help me with I’m desperate
Answers
Answer:
Radius
314 cm²
Step-by-step explanation:
They gave you the diameter which you can find the radius from, and you need the radius to find the area. The radius is 10, and that squared is 11. Multiply 3.14 times 100 to get 314.
Jake's coupon took $2 off the price of a book. If the coupon took off 10% of the price,
how much did the book originally cost?
Answers
Best Buy is having a HUGE sale. All items are 60% off. How much will you pay for a tv that originally cost $1200 including 5% sales tax?
Answers
Answer:
$480
Step-by-step explanation:
According to the problem, calculation of the given data are as follows,
Original cost including sales tax = $1,200
Discount = 60%
So, we can calculate the cost of TV after discount by using following formula:
Cost of TV after discount = $1,200 - ( $1,200 × 60%)
= $1,200 - $720
= $480
Hence, Cost of TV after discount is $480.
After a 80% reduction, you purchase a new washing machine on sale for $132. What was the original price of the washing machine?
The original price was $
Answers
132 =.2x
X =$660
$200
Step-by-step explanation:
80% 200 is equal $132
Pls help?!!! 3 = a — 1
Answers
Answer:
4
Step-by-step explanation:
3= a -1
+1 = a. you pass the negative 1 to the other side.
and it turns to a + 1 and then you add it which
gives you 4
4= a
I am having trouble on algebraic expressions and numerical expression what is the easiest way to solve my problem and im in 6 th grade
Answers
Hi. you've asked an incomplete question. However, I provided some explanation about algebraic expressions and numerical expression.
Step-by-step explanation:
First, we may wonder: What is a numerical expression? In simple words, they are mathematical expressions that contain numbers and operations (like +, -, ÷, ×).
For example, 7+70, 90-10, 60÷10, 5×4 are numerical expressions.
While an algebraic expression on the other hand is a mathematical expression that contains at least one variable.
Variables are letters or symbols (like x, y, p, q, etc) that represent an unknown number or value in a mathematical expression.
For example, 7x+70, 90y-10 are algebraic expressions since they contain at least one variable.
A baseball diamond is a square that is 90 feeton
each side. What is the distance from home to
second base?
Answers
Answer:
x = 127 ft
Step-by-step explanation:
Answer:45 ft
Step-by-step explanation:X^2= (90ft)^2 + (90ft)^2
1a. Write the equation: You work during the summer mowing lawns. You charge 13
dollars per lawn. You made $819 for the summer. *
Your answer
1b. Describe your steps to find the number of lawns you mowed. *
Your answer
1c. How many lawns did you mow? Write a complete sentence.
Answers
Answer:
819÷13=63
Step-by-step explanation:
you divide 819 by 13 and you get 63
Answer:
1b) 819 ÷ 13 =63
1c) 63 lawns were mowed
-6= n/2-10 what is n?
Answers
Answer:
8
Step-by-step explanation:
8/2 equals 4 minus 10 is -6
Answer:
-6= n/2 -10
-12=n-20
-12-n=-20
-n=-20+ 12
-n=-8
n=8
Step-by-step explanation:
1. multiply both sides of the equations by 2
2.Move the N varaiableto the left hand side and change its sign
3. Calculate the sum of -20+12
4. change the signs from negative N to positive N giving you the value of 8
n=8
Solved.
:)
Imagine that you are given the graph of a brand new parent function, y = P(x), that you have never seen before. You are then asked to graph y = P(x) + 3. Explain how you would go about graphing this new function.
Answers
Answer:
You would move each point on y=P(x) up by three. Or add 3 to each y coordinate
Step-by-step explanation:
This is because we're not manipulating the value of x before it gets multiplied by P.
For example:
If x is set to equal 5 and P equal to 2, then the parent function would have a coordinate of (5,10) since 2(5)=10 but the new function would have a coordinate of (5,13) since 2(5)+3= 13 due to order of operations (2×5 =10, then we add 3).
Answer:
Step-by-step explanation:
Step 1:
Plot y=P(x) from x=-a to x=a with x=0 as the middle point of the distance between a and -a.
Step 2:
Add the value of +3 to each point of y=P(x), ie, y=P(x)+3 meaning that the graph y=P(x) will be pulled up three units on the y axis.
what is the value of the expression 4⁴?
Answers
Answer:
256
Step-by-step explanation:
solve 4/6 + 1/3
options:
6/6 or 1
7/6
5/3
12/6 or 2
Answers
Need help, Simplify
2(-6+2) ÷ 4 =
Answers
Answer:
2
Step-by-step explanation:
2(-6+2)= -8 then divide it by 4 and you get -2
then 4 turns it positive
hope this helps ;}
8 / 4 Multiply 2 and -4 first because it is in the question first.
Divide 8 / 4 = 2
Word problem ideas for
4x+10
2(x-6)
Answers
Answer:
15
Step-by-step explanation:
Mark's favorite tree is a large oak
tree in his front yard. Mark wanted to
know how tall the tree is. At the
same time of day, he measured the
length of his shadow and the length
of the shadow cast by the tree. Mark,
who is 5 feet tall, cast a shadow 10
feet long. He found that the tree's
shadow was 140 feet long. How tall is
the tree?
Answers
Answer: The shadow of the tree is 280 feet long.
Step-by-step explanation:
We can use a ratio to solve this:
Use the Height to shadow for each. This works because the fractions must reduce to the same equivalent.
5/10 = 140/x
We can see that 5/10 is 1/2, so we need another fraction using 140 as the numerator that is equal to 1/2. That's easy here: Multiply 140 × 2 to get the new denominator, 280 that replaces x. That is the length of the shadow.
If you have a less obvious ratio, you can use Cross Multiplication to solve the unknown value in the ratio:
5/10 = 140/x Cross multiply the numerator of the left side times the denominator on the right side, and the denominator on the left side by the numerator on the right side:
5 × x = 10 × 140
5x = 1400 Divide both sides by 5 (the 5s "cancel" on the left)
5x/5 = 1400/5
x = 280
I hope this helps, especially when you see more questions like this in the future.
Can someone please help me ASAP!!?
Answers
Answer:
Option A
Step-by-step explanation:
Domain is the set of x values or input values of a function.
Range is the set of y values or output values of a function.
Given relation is,
2x + y = 4
Set if input values of domain → {-5, 0, 6}
Table for the input - output values,
x -5 0 6
y 14 4 -8
Therefore, range of the given relation will be the set of output values.
{14, 4, -8}
Option A is the answer.
is x2 greater then x
Answers
Answer:
yes
Step-by-step explanation:
please help om failing math..
Answers
What is the location of D on the decimal number line below?
Write your answer as a decimal.
D
2
х
?
Answers
Answer:
1 point
Step-by-step explanation:
3x +y = -5
2x + 3y = -8
Answers
Answer:
Step-by-step explanation:
for 3x +y = -5
it's [tex]x = \frac{-5 -y}{3}[/tex]
and for 2x + 3y = -8 it's
[tex]x = \frac{-8 - 3y}{2}[/tex]
a student throws a baseball with a speed of 8m/s and a kenetic energy of 25J.what is the mass of the baseball
Answers
Answer:
25/32 kg
Step-by-step explanation:
The kinetic energy K of a body in motion measured in joules is given as
K = 1/2 mV^2
Where n is the mass in kg and V is the speed in m/s
Hence given that K is 25J and speed V is 8 m/s,
25 =1/2 * m * 8^2
25 = m *32
Divide both sides by 32
m = 25/32 kg
How many 3/5's are in 4?
Answers
Answer:
6.6
Step-by-step explanation:
Answer:
6.6
Step-by-step explanation:
