Find sin(x + y)given: sin x = − 2/3 and x is in Quadrant III; and sin y = 1/3 and y is in Quadrant II.
Answers
Given
sin x = − 2/3 and x is in Quadrant III; and sin y = 1/3 and y is in Quadrant II.
Find
sin(x + y)
Explanation
sin x = − 2/3 and x is in Quadrant III
as, cos x is negative in Quadrant III
\(\begin{gathered} \cos x=-\sqrt{1-\sin^2x} \\ \\ \cos x=-\sqrt{1-(-\frac{2}{3})^2} \\ \\ \cos x=-\sqrt{1-\frac{4}{9}} \\ \\ \cos x=-\sqrt{\frac{5}{9}} \\ \\ \cos x=\frac{-\sqrt{5}}{3} \end{gathered}\)sin y = 1/3 and y is in Quadrant II.
cos y is negative in Quadrant II.
\(\begin{gathered} \cos y=-\sqrt{1-\sin^2xy} \\ \\ \cos y=-\sqrt{1-(\frac{1}{3})^2} \\ \\ \cos y=-\sqrt{1-\frac{1}{9}} \\ \\ \cos y=-\sqrt{\frac{8}{9}} \\ \\ \cos y=\frac{-2\sqrt{2}}{3} \end{gathered}\)as we know the formula of
sin (x + y)= sinx cosy + cosx siny
now put values ,
\(\begin{gathered} \sin(x+y)=\sin x\cos y+\cos x\sin y \\ \\ \sin(x+y)=(-\frac{2}{3})(\frac{-2\sqrt{2}}{3})+(\frac{-\sqrt{5}}{3})(\frac{1}{3}) \\ \\ \sin(x+y)=\frac{4\sqrt{2}}{9}-\frac{\sqrt{5}}{9} \\ \\ \sin(x+y)=\frac{4\sqrt{2}-\sqrt{5}}{9} \end{gathered}\)Final Answer
\(\sin(x+y)=\frac{4\sqrt{2}-\sqrt{5}}{9}\)Related Questions
HELPP!!! ASAP!!! What is the domain of F(x) = 2|x-1| + 3?
O A.
{x | X23)
OB.
{x | x< 1)
O c.
{x | x5-1)
O D.
{x | x = all real numbers)
Answers
Answer:
D.
Step-by-step explanation:
The function is an absolute value. That just means that all the y-values (in this case) will be positive, but there is nothing that limits the x-values. So, D. {x | x = all real numbers}.
Hope this helps!
I need help I’ll give u brainlest
Answers
Answer:
\(252\) cubic yards
Step-by-step explanation:
\(V=lwh\)
Volume = length * width * height
\(V=7*4*9\)
\(V=252\)
Answer:
252 yd³
Step-by-step explanation:
Volume of rectangular prism = length * width * height
= 9 * 7 * 4 yd³
= 252 yd³
I NEED HELP!!!! I DONT UNDERSTAND WHAT TO DO SO IF YOU COULD SOLVE IT FOR ME THAT WOULD BE GREAT!!! THXXXX
Answers
The measure of the angles are:
∠1 = 90
∠2 = 90
∠3 = 132
We have,
The angle between the tangent and the radius of a circle is 90.
So,
∠1 = 90
∠2 = 90
And,
48 + 90 + 90 + ∠3 = 360 ______(1)
Solve for ∠3 from (1).
48 + 90 + 90 + ∠3 = 360
48 + 180 + ∠3 = 360
∠3 = 360 - 228
∠3 = 132
Thus,
The measure of the angles are:
∠1 = 90
∠2 = 90
∠3 = 132
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Find the volume.
# 1
Answers
Answer:
50 m
Step-by-step explanation:
Formula:
V = lwh
V = (5)(4)(5/2)
V = 20 (5/2)
V = 50
easy math problem help me out tysm !
Answers
Answer: 26
Step-by-step explanation:
Since we are given the value of y, all we need to do is plug it into the equation and solve it. Make sure if you plug this into a calculator that you put the substituted number in parenthesis that way it squares the number correctly without a negative sign.
(-3)²-5(-3)+2
9 - 5(-3) +2
9 - -15 + 2
9 + 15 + 2
24 + 2
26
Hope this helps!
HELP ME PLZ PEOPLE!!
Answers
Answer:
I may be wrong but i think it's -27
Step-by-step explanation:
-3 ( p - q) exponet of 2
Pemdas : Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Parentheses
-3 (p - q) exponet of 2
-3 ( 5 - 2 ) exponet of 2
-3 ( 3 ) exponet of 2
Exponents
-3 ( 3 ) exponet of 2
-3 ( 3 ) exponet of 2 = -3 (3 x 3 = 9)
-3 (9)
Multiplication
-3 (9)
Answer: -27
PLEASE HELP!!!
Triangle ABC has vertices at A(-5,2), B(1,3), and C(-3,0). Determine the coordinates of the vertices for the image of the pre image is translated 4 units right.
A. A’(-9,2),B’(-3,3), C’(-7,0)
B. A’(-4,6),B’(0,7),C’(1,0)
C. A’(-1,2),B’(5,3),C’(1,0)
D. A’ (-5,-2), B’(-1,-1), C’(-3,-4)
Answers
The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).
What is translation on a coordinate plane?Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.
During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.
Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.
So,
\(\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}\)
\(\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}\)
\(\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}\)
Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).
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Use a unit rate to find the unknown value.
Answers
Answer:
it's 6
Step-by-step explanation:
You can think of it 2 ways the first one is called the "bat and ball" method which is 12x15 then u divide it by 30. The other methos only works on very few if you look at the 30/15 one 15 is half of 30 so when you look at 12 half of that would be 6. Hope this helps :)
Whoever answers it first gets the title brainliest.
Answers
Answer:
2.24
Explanation:
2.5 - 2.4 / 1.2(0.13) = 2.24
29.For n ≥ 3, a pattern can be made by overlapping n circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-n rotational symmetry.
For instance, the diagram shows the pattern where n = 7.
If the total length of visible ares is 60 units, what is n?
Answers
The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.
To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).
In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.
Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:
2n = 60
Solving this equation, we find:
n = 60/2 = 30
Thus, the value of n is 30.
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What are the domain and range of the relation given in the table? x y −12 0 −8 12 0 0 1 8
Answers
Answer:
domain: {−12,−8,0,1}
range: {0,8,12}
The domain and range of the relation given in the table are:
The domain: {-12, -8, 0, 1}
And range: {0, 8, 12}
What is domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
We have the relation,
x → y
-12 → 0
-8 → 12
0 → 0
1 → 8.
The range of the relation: All achievable values.
So, the domain: {-12, -8, 0, 1}
And range: {0, 8, 12}
Therefore, range and domain is given below.
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Explain the Pythagorean Theorem, and provide two additional examples (other than football) of how it can it apply to sports
Answers
Given:
The objective is to explain Pythagorean Theorem with two examples by applying it to sports.
Explanation:
The Pythagorean Theorem states that. in a right triangle the sum of the squares of a two perpendicular legs will be equal to the square of the largest side of the triangle.
Consider a right triangle ∆ABC right angled at B.
By applying the Pythagorean Theorem to the above right triangle,
\(AC^2=AB^2+BC^2\text{ . . . . . .(1)}\)Example 1:
Consider a tennis player standing striking the ball to the service line of opponent field.
Let the height of the tennis player will be h = 3m.
The distance between the tennis player and the opponent service line is x = 18m.
Then, the distance at which the tennis player strikes the ground can be calculated as,
From the above diagram the distance d can be calculated using equation (1) as,
\(d^2=h^2+x^2\text{ . . . . . . (2)}\)On plugging the values in equation (2),
\(\begin{gathered} d^2=3^2+18^2 \\ d^2=9+324 \\ d=\sqrt[]{333} \\ d\approx18.25m \end{gathered}\)Example 2:
Consider a basket ball player ready to take a free throw standing at a horizontal distance of 20 ft from the ring and holding the ball at with distance of 10ft below the ring.
Then, the hypotenuse distance of the ring can be calculated using equation (1) as,
\(\begin{gathered} x^2=10^2+20^2 \\ x^2=100+400 \\ x=\sqrt[]{500} \\ x\approx22.36ft \end{gathered}\)Hence, the explanation for Pythagorean Theorem with two examples are provided.
What are the points of the image of the line in Q4 after the dilation?
Answers
Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)
How is this so ?To rotate a point 90 degrees clockwise about a given point,we can follow these steps -
Translate the coordinates of the given point so that the center of rotation is at the origin. In this case,we subtract the coordinates of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).
Perform the rotation by swapping the x and y coordinates and changing the sign of the new x coordinate. In this case,we swap the x and y coordinates of (-5, 3) to get (3, -5).
Translate the coordinates back to their original position by adding the coordinates of the center (0,1) to the result from step 2. In this case, we add (0,1) to (3, -5) to get (3, -4).
Therefore, the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).
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Which single-stroke lettering style does the ANSI standard recommend for lettering?
A.
uppercase Roman Sans Serif
B.
uppercase Gothic Serif
C.
uppercase Gothic Sans Serif
D.
small capital Gothic Serif
E.
small capital Roman Serif
Answers
Answer:
C. uppercase Gothic Sans Serif
Step-by-step explanation:
You want to know the recommended lettering style for drawings conforming to ANSI standards.
LetteringLettering on working drawings — those made to describe the manufacture or production of a product — must be legible and free of any ornamentation (sans serif). ANSI standards recommend an uppercase single-stroke Gothic style (Arial font).
__
Additional comment
The lettering is called "single-stroke" because each line is the width of one pencil line.
Hand-written lettering is generally formed by top down or left to right strokes, straight or curved as needed. The use of a lettering guide is recommended.
I NEED HELP AP STATS THANK YOU!!
Answers
Answer:
it is true :)
Step-by-step explanation:
Researchers measured the percent body fat and the preferred amount of salt (percent weight/volume) for several children. Here are data for seven children:
Preferred amount of salt x 0.2 0.3 0.4 0.5 0.7 0.9 1.1
Percent body fat y 20 30 22 30 38 23 30
Use your calculator or software: The correlation between percent body fat and preferred amount of salt is about which of the following?
a) τ = 0.08.
b) τ = 0.3.
c) τ = 0.8.
Answers
Answer: b) τ = 0.3
Step-by-step explanation:
Given the data :
Amount of salt (x)____% body fat(y)
0.2 _______________20
0.3 _______________30
0.4 _______________22
0.5 _______________30
0.7 _______________38
0.9 _______________23
1.1 ________________30
The correlation Coefficient as obtained from the online pearson correlation Coefficient calculator is 0.3281 = 0.3 (to one decimal place) which implies that a weak positive correlation or relationship exists between the preferred amount of salt taken to the percentage body weight of an individual. This is because the value is positive and closer to 0 than 1. The closer the weaker the degree of correlation. With positive values implying a positive relationship (that is an increase in variable A leads to a corresponding increase in B and vice-versa).
Arianys is going to invest $11,000 and leave it in an account for 9
years. Assuming the interest is compounded monthly, what interest
rate, to the nearest hundredth of a percent, would be required in order
for Arianys to end up with $20,000?
Answers
The compound interest rate of the investment is 1.10%
How to determine the compound interest rate?The given parameters about the compound interest are
Principal, P = $11,000
Amount, A = $20,000
Time, t = 9
Number of times, n = 12 i.e. monthly interest
To calculate the amount, we have:
A = P(1 + R/n)^nt
Substitute the known values in the above equation, so, we have the following representation
20000 = 11000 * (1 + r/12)^(12 * 9)
This gives
1.82 = (1 + r/12)^108
Take the 108th root of both sides
1 + r/2 = 1.0055
Subtract 1 from both sides
r/2 = 0.0055
Multiply by 2
r = 0.011
Express as percentage
r = 1.10%
Hence, the value of the interest rate is 1.10%
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Answer:
6.66%
Step-by-step explanation:
Compounded Monthly:
�
=
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(
1
+
�
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)
�
�
A=P(1+
n
r
)
nt
Compound interest formula
�
=
20000
�
=
11000
�
=
9
�
=
12
A=20000P=11000t=9n=12
Given values
20000
=
20000=
11000
(
1
+
�
12
)
12
(
9
)
11000(1+
12
r
)
12(9)
Plug in values
20000
=
20000=
11000
(
1
+
�
12
)
108
11000(1+
12
r
)
108
Multiply
20000
11000
=
11000
20000
=
11000
(
1
+
�
12
)
108
11000
11000
11000(1+
12
r
)
108
Divide by 11000
1.8181818
=
1.8181818=
(
1
+
�
12
)
108
(1+
12
r
)
108
(
1.8181818
)
1
/
108
=
(1.8181818)
1/108
=
[
(
1
+
�
12
)
108
]
1
/
108
[(1+
12
r
)
108
]
1/108
Raise both sides to 1/108 power
1.0055509
=
1.0055509=
1
+
�
12
1+
12
r
−
1
−1=
−
1
−1
Subtract 1
0.0055509
=
0.0055509=
�
12
12
r
12
(
0.0055509
)
=
12(0.0055509)=
(
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12
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12
(
12
r
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Multiply by 12
0.0666108
=
0.0666108=
�
r
6.66108
%
=
6.66108%=
�
r
Convert to percent (multiply by 100)
�
≈
r≈
6.66
%
6.66%
Round to the nearest hundredth of a percent
which of the following are solutions to the equation sin x cos x= -1/4
Answers
Answer:
x=-pie/12
sinxcosx=-1/4
multiply both sides by 2
sin2x = 2sinxcosx we know
now equation will be
sin2x = -1/2
2x=-pie/6
x=-pie/12
Matthew is saving money for a pet turtle the data in the table represents the total amount of money in dollars that he saved by the end of each week.
Answers
• 3.3
• 5.0
• 6.7
• 8.4
• 10.1
Which one is it?
Answers
Answer: 5.0
Step-by-step explanation:
Fill in the missing numbers to complete the Sequence below. 1, 2, 3, 7,-, 24,-.
Answers
The missing numbers are 13 and 50
How to determine the numbers
Given the numbers;
1, 2, 3, 7, -, 24, -.
Find the numbers by preceding numbers together, thus;
1 + 1 =2
1 + 2 = 3
1 + 2 + 3 = 7
1 + 2 + 3 + 7 = 13
1 + 2 + 3 + 7 + 13 + 24 = 50
Thus, the missing numbers are 13 and 50
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Find m<1 then classify the angle.
Answers
Answer:
81 degrees
This is an acute angle since it’s less then 90 degrees
Step-by-step explanation:
All three angles of a triangle always equal 180 degrees
180-(78+31)
180-109
81 degrees
Hopes this helps please mark brainliest
What is the next number in the sequence: 3, 8, 12, 48, 29, __
Answers
Answer:
144
Step-by-step explanation:
Answer:
116
Step-by-step explanation:
3x4=12
12x4=48
8x4=32
32-3=29
29x4=116
Hope it's clear
Let g(x) be the indicated transformation of f(x) = −|3x| − 4. Stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g(x).
Answers
The final rule for g(x) is g(x) = 3|3x| + 12.
To stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3, we multiply the function by 3. This will result in a vertical stretching of the graph.
So, the rule for g(x) is g(x) = 3f(x).
Now, let's find the expression for g(x) using the given function f(x) = −|3x| − 4:
g(x) = 3f(x)
g(x) = 3(-|3x| - 4)
g(x) = -3|3x| - 12
This is the expression for g(x), which represents the transformed graph.
To reflect the graph of g(x) across the x-axis, we change the sign of the function. This means that the negative sign in front of the absolute value will become positive, and the positive sign in front of the constant term will become negative.
Therefore, the final rule for g(x) is g(x) = 3|3x| + 12.
Now, let's consider the graph of g(x). The graph will have the same shape as f(x), but it will be stretched vertically by a factor of 3 and reflected across the x-axis.
The original graph of f(x) = −|3x| − 4 is a V-shaped graph that opens downward and passes through the point (0, -4). The transformed graph of g(x) will have a steeper V-shape, opening downward, and passing through the point (0, 12) instead of (0, -4).
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Steven conjectures that for |x|>5, it is true that x^3>125. Is his conjecture correct? Why or why not?
Answers
Answer:
yes
Step-by-step explanation:
it is correct because, since x>5, anything relating x and 5 together will always put x greater than 5.
If one length of a board is 1 1/3 feet long, how many lengths of board is needed to cover 12 feet?
Answers
Answer:
9
Step-by-step explanation:
12÷1 \(\frac{1}{3}\)=9
Which two inequalities to compare |-5| and 4?
Answers
Answer:
|-5|>4
Step-by-step explanation:
Negative 5 in absolute value is 5 since any number in absolute value turns out positive or at the very least 0. 5 is greater than 4, so |-5|>4.
PLEASE HELP ASAP!! WILL GIVE BRAINLIEST
A regular polygon has 12 sides. If one of its angles measures (8h − 30)°, what is the value of h?
h = 10.75
h = 18.75
h = 20.25
h = 22.5
Answers
Answer: h = 22.5
Step-by-step explanation:
Total angle area of a 12 sided polygon is 1800
1. One angle would be 1800/12= 150
8h - 30 = 1502. Add 30 one each side to cancel out and only leave 8h.
8h = 1803. To get rid of the 8 we divide the the other side by 8.
h = 22.5The answer is 22.5
Answer: D 22.5 i got it right on the exam
Step-by-step explanation:
Round to hundredths and ten-thousandths place for number 132.4893
hurryyyyy plz
Answers
Answer:
132.4900
Step-by-step explanation:
The hundredths place is the second digit after the decimal point (i.e. 132.4893). To round, we look at the digit in the thousandths place. Since 9 is more than 5, we round up and change the remaining digits to 0, making the answer 132.4900.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
If mZA = (4x - 2)° and mZB= (6x-20), what is the value of x?
Answers
To find the value of x, we can set the two angle measures equal to each other and solve for x.
Given:
mZA = (4x - 2)°
mZB = (6x - 20)°
Setting them equal to each other:
4x - 2 = 6x - 20
Now, we can solve for x:
4x - 6x = -20 + 2
-2x = -18
Dividing both sides by -2:
x = -18 / -2
x = 9
Therefore, the value of x is 9.
Answer:
The answer is 9.
Step-by-step explanation:
We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:
mZA + mZB + mZC = 180°
Substituting the given values, we get:
(4x - 2)° + (6x - 20)° + mZC = 180°
Simplifying the left side, we get:
10x - 22 + mZC = 180°
Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:
mZA = mZB
Substituting the given values and simplifying, we get
4x - 2 = 6x - 20
Solving for x, we get:
x = 9
Therefore, the value of x is 9.