Answers
Answer:
[tex]\displaystyle \sin\Big(\frac{x}{2}\Big) = \frac{7\sqrt{58} }{ 58 }[/tex]
[tex]\displaystyle \cos\Big(\frac{x}{2}\Big)=-\frac{3 \sqrt{58}}{58}[/tex]
[tex]\displaystyle \tan\Big(\frac{x}{2}\Big)=-\frac{7}{3}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \sin(x)=-\frac{21}{29}[/tex]
Where x is in QIII.
First, recall that sine is the ratio of the opposite side to the hypotenuse. Therefore, the adjacent side is:
[tex]a=\sqrt{29^2-21^2}=20[/tex]
So, with respect to x, the opposite side is 21, the adjacent side is 20, and the hypotenuse is 29.
Since x is in QIII, sine is negative, cosine is negative, and tangent is also negative.
And if x is in QIII, this means that:
[tex]180<x<270[/tex]
So:
[tex]\displaystyle 90 < \frac{x}{2} < 135[/tex]
Thus, x/2 will be in QII, where sine is positive, cosine is negative, and tangent is negative.
1)
Recall that:
[tex]\displaystyle \sin\Big(\frac{x}{2}\Big)=\pm\sqrt{\frac{1 - \cos(x)}{2}}[/tex]
Since x/2 is in QII, this will be positive.
Using the above information, cos(x) is -20/29. Therefore:
[tex]\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{1 + 20/29}{2}[/tex]
Simplify:
[tex]\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{49/29}{2}}=\sqrt{\frac{49}{58}}=\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}[/tex]
2)
Likewise:
[tex]\displaystyle \cos \Big( \frac{x}{2} \Big) =\pm \sqrt{ \frac{1+\cos(x)}{2} }[/tex]
Since x/2 is in QII, this will be negative.
Using the above information, cos(x) is -20/29. Therefore:
[tex]\displaystyle \cos \Big( \frac{x}{2} \Big) =-\sqrt{ \frac{1- 20/29}{2} }[/tex]
Simplify:
[tex]\displaystyle \cos\Big(\frac{x}{2}\Big)=-\sqrt{\frac{9/29}{2}}=-\sqrt{\frac{9}{58}}=-\frac{3}{\sqrt{58}}=-\frac{3\sqrt{58}}{58}[/tex]
3)
Finally:
[tex]\displaystyle \tan\Big(\frac{x}{2}\Big) = \frac{\sin(x/2)}{\cos(x/2)}[/tex]
Therefore:
[tex]\displaystyle \tan\Big(\frac{x}{2}\Big)=\frac{7\sqrt{58}/58}{-3\sqrt{58}/58}=-\frac{7}{3}[/tex]
Related Questions
The coordinates of the endpoints of MP are
M(-3,-2) and P (2,3).
Which measurement is closest to the length of MP in
units?
Answers
Answer:
I'm pretty sure it is A
can you help me ASAP
Simplify
3×4²+8-(6÷2)
Answers
Answer:
USE PEMDAS
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
Solution (x, y) i dont understand it
Answers
Answer:
(3, 3)
Step-by-step explanation:
I guess you're looking for a point that satisfies 2 functions (red and blue). That point is an intersection of these two functions, hence (3,3)
Answer:
[tex]\boxed{\boxed{(x,y)=(3,3)}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:system of linear equationgraphing system of linear equationtips and formulas:when we have two linear equation to find the value of x and y is called the system of linear equationwhen we have graph, the solutions of system of linear equation are the coordinates of two lines cross togetherlet's solve:since you can see at "tips and formulas" what linear equation is and what the solutions are when you have graph
if you see the graph attentively, you can see that the blue line and the red line cross together at (3,3) coordinates
therefore
the solution of the system of linear equation is
(x,y)=(3,3)
The sum of two numbers is 100. The different between them is 56. What is the larger number?
Answers
[tex]\pink{\bigstar}[/tex] The larger number is [tex]\large\leadsto\boxed{\tt\purple{78}}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
• Given:-Sum of two numbers is 100.Difference between the numbers is 56.⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
• To Find:-The larger number = ?⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
• Solution:-Let the two numbers be 'x' and 'y' respectively.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
According to the question:-
✯ Sum of two numbers is 100.
➪ [tex]\sf x + y = 100 \dashrightarrow\bold\red{[equation \: 1]}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Also,
✯ Difference between the numbers is 56.
➪ [tex]\sf x - y = 100 \dashrightarrow\bold\red{[equation \: 2]}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
• Adding equation [1] and equation [2]:-
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf (x + y) + (x - y) = 100 + 56[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf x + y + x - y = 156[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf 2x = 156[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf x = \dfrac{156}{2}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
★ [tex]\large{\bold\red{x = 78}}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
• Substituting the value of x in equation [1]:-
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf x + y = 100[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf 78 + y = 100[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
➪ [tex]\sf y = 100 - 78[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
★ [tex]\large{\bold\red{y = 22}}[/tex]
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Therefore, the numbers are 78 and 22.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
The larger number is 78.
Answer:
[tex]here \: given \: that \: sum = 100 \\ diffrence = 56 \\ take \: the \:large \: number = x \\another = y \\ thenx - y = 56 \\ y = x - 56 \\ here \: x + y = 100 \\ x + x - 56 = 100 \\ 2x - 56 = 100 \\ 2x = 156 \\ x = \frac{156}{2} \\ x = 78 \\ large \: number \: = 78 \\ thank \: you[/tex]
Why is
power sharing desirable ?
Answers
Answer:
Why power sharing is desirable? It helps to reduce the possibility of conflict and clashes between social groups. Secondly, a democratic rule involves sharing power with those affected by its exercise, and who have to live with its effects.
Step-by-step explanation:
PLEASE ANSWER WITH A PROPER ANSWER QUICKLY
If the first equation is multiplied by 3 and then the equations are added, the result is _____.
3 x + y = 3
x - 3 y = -2
8 x = 7
10 x = 7
10 x = 11
Answers
Which model represents the factors of x2+9x+8
Answers
Answer:
(x+1)(x+8)
Step-by-step explanation:
Those are the factors of x^2+9x+8
What is 50% in decimal form?
Answers
Answer:
0.5
Step-by-step explanation:
divide 50 by 100
and get 0.5
2a+b=5 and 6y+4y=48 show that 20a+10b has a greater value than 3x+2y
Answers
Answer:
Step-by-step explanation:
There is an error in the question. 6x+4y = 48
Multiply first equation by 10:
20x+10y = 50
Divide second equation by 2:
3x+2y = 24
50>24, so 20x+10y > 3x+2y
work out the total number of mobile phones sold in the 3 years
Answers
Answer: your wuestion isn’t specific enough.
Step-by-step explanation:
what is distance between C(−5,−2) and D(0,−4)
Answers
Answer:
[tex]\displaystyle d = \sqrt{29}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point C(-5, -2)
Point D(0, -4)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(0+5)^2+(-4+2)^2}[/tex][√Radical] (Parenthesis) Add: [tex]\displaystyle d = \sqrt{(5)^2+(-2)^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{25+4}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{29}[/tex]2. To use the weight machines at a
health club, you must be at least
12 years old. Brandon writes the
inequality a > 12, where a represents
age in years, to represent this. Is
Brandon correct? Explain.
Answers
Answer:
no, he is not correct because if you must be at least 12, then the inequality should include 12
it should be written as:
a ≥ 12
Step-by-step explanation:
^
whats -11 + x =19
i just dont know what we do can someone help me?
Answers
The new camera you want to buy is $84.95. This weekit is on sale for 30% off. You also need to pay 7.25% sales tax. What is the inalcost of the camera? This is very easy so Ima give you guys about 50 points because im cool lol
Answers
Answer:
283.2325$
Step-by-step explanation:
84.94-25.48= 59.47
59.47x.0725= 4.13
59.47+4.13= $63.78
Find the midpoint of a and b where a has coordinates (2,3) and b has coordinates (8,9).
Please help.
Answers
Answer:
please follow me bro i have followed u
A hiker in Africa discover a skull that contains 63% of its original amount of C-14
Answers
please help!! will give brainliest!!
SR=___
Answers
Answer:
7
Step-by-step
on 2x-14 you got to divide by 2 on both sides and 2x/2 is 0 so that is how it is 7
Is the product the same when multiplying 22 x (-5) and multiplying (-5) x 22? Explain
Answers
Answer: Yes it's the same due to communitive property of multiplication
Step-by-step explanation:
22 times -5 is -110
-5 times 22 is -110
Answer: Yes Bc Of Communitive Property
Step-by-step explanation:
Find the product and simplify
(2x+3)(x+6)
Answers
answer: 2x^2 + 15x + 18
I hope that the attachment helps you..
SOLUTION: a diver jumps from a diving board that is 24 feet above the water. the height of the diver is given by h= -16(t-1.5)(t+1) where the height h is measured in feet and the time t
Answers
Answer:
The diver will hit the water at 1.5 seconds
Step-by-step explanation:
Given
[tex]h= -16(t-1.5)(t+1)[/tex]
Required (Missing from the question)
When will the diver hit the water?
To do this, we simply solve for t
When the diver hits the water, the height is 0 (at that point)
So, substitute 0 for h in [tex]h= -16(t-1.5)(t+1)[/tex]
[tex]0= -16(t-1.5)(t+1)[/tex]
Divide both sides by -16
[tex]\frac{0}{-16} =\frac{-16(t-1.5)(t+1)}{-16}[/tex]
[tex]\frac{0}{-16} =(t-1.5)(t+1)[/tex]
[tex]0 =(t-1.5)(t+1)[/tex]
[tex](t-1.5)(t+1)=0[/tex]
Split
[tex]t - 1.5 = 0[/tex] or [tex]t + 1 = 0[/tex]
Solve for t
[tex]t = 1.5[/tex] or [tex]t = -1[/tex]
But time (t) can not be negative.
So:
[tex]t = 1.5[/tex]
Hence, the diver will hit the water at 1.5 seconds
40 is what precent 50?⇒
Answers
Answer:
Answer is 80%
Step-by-step explanation:
40% is 80% of 50.
I hope it's helpful!
Answer:
80%
Step-by-step explanation:
40 /50 x 100% = 80%
Nick is making bread dough. The recipe requires 3/4 cup of flour and 1 1/8 teaspoon of salt. Nick wants to make the recipe using 1 cup of flour. To maintain the ratio, how much salt is required when 1 cup of flour is used?
(explain)
Answers
The recipe requires 3/4 cup of flour and Nick wants to make the recipe using 1 cup of flour.
The recipe requires 1 1/8 teaspoon of salt and Nick wants to know how much salt he heeds.
Consider short description:
3/4 cup of flour - 1 cup of flour,
1 1/8 teaspoon of salt - x teaspoon of salt.
Mathematically, you can wrte a proportion:
3/4 divided by 1 1/8
then 3/4 times x = 1 time 1 1/8
3x/4 =9/8
24x = 36
X = 36/24 = 3/2 = 1 1/2
Answer:
x = 1 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
make equal equations first
[tex]\frac{3/4}{1 and 1/8}[/tex] = [tex]\frac{1}{x}[/tex]
cross multiply to get: 3/4x = 1 [tex]\frac{1}{8}[/tex]
divide by 3/4 on both sides: x = 1 [tex]\frac{1}{2}[/tex]
The coordinate of the midpoint of the line AB are (1,2)
The length of the line AB is 10 units.
if the gradient of AB is 0, Find the coordinates of A and B
Answers
ye, cant help here. sorry dude wish i could. i need points tho so
rewrite the expression that is equivalent to x^2/3.
-pasagot po please-.-
Answers
Answer:
[tex]\sqrt[3]{x^{2}}[/tex]
Step-by-step explanation:
[tex]x^{2/3} = \sqrt[3]{x^{2}}[/tex]
What is the exact perimeter of the trapezoid?
Answers
but the answer rounded to the nearest thousandth is 54.806
A small radio transmitter broadcasts in a 50 mile radius. If you drive along a straight line from a city 65 miles north of the transmitter to a second city 58 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Answers
Answer:
29% of the drive
Step-by-step explanation:
The plot of the problem is:
Transmitter at origin (0,0)
City to the north at (0,70)
City to the east at (74,0)
The path from city to city is a line with slope:
m = (-70)/74 = -35/37
and y-intercept at y = 70, so the equation is y = (-35/37)*x + 70.
The transmitter reach the area enclosed by the next circle:
x^2 + y^2 = 53^2
See the picture attached
The intersection is gotten from the picture or solving:
x^2 + [(-35/37)*x + 70]^2 = 53^2
the points approximately are: (24.1, 47.2) and (45.8, 26.7)
From Pythagorean theorem the total distance of the trip is:
d1 = √(70^2 + 74^2) ≈ 101.9 miles
And the distance when the signal is picked up is:
d2 =√ [(45.8 - 24.1)^2 + (47.2 - 26.7)^2] ≈ 29.9 miles
You will pick up a signal from the transmitter in (d2/d1)*100 = 29% of the drive.
Keisha's cat had kittens. The line plot below shows the weight, in pounds, of each kitten.
What is the total weight of all the kittens that weighed 3/8
pound?
Answers
Answer:
the answer would be 1 7/8
Step-by-step explanation:
first you would count up the number of kittens that weighted 3/8 of a pound. You should have the number of 5, next you would multiply 5 × 3/8= 1.875 (as a decimal). Then you would convert that number into a mixed number (fraction) because all the answers are in mixed number form. You should get 1 7/8 because:
(1875÷125)(1000÷125) = 158 when reduced to the simplest form. As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 18751000 is also equal to 1 7/8 when expressed as a mixed number.
I hope this helps!
you wish to purchase dog food foe your kennel. you find 2 equal brands. bowser dog food comes in 50lb. bags for 32.50 per bag . Woof woof dog food comes in 40 lb. bags which cost 26.95 each
Answers
Answer:
Woof Woof dog food is a better deal. It costs $1.48 per pound.
Bowser dog food costs $1.54 per pound.
In 2008, there were 285 cell phone subscribers in the small town of Berrydale. The number of subscribers increased by 75% per year after 2008. How many cell phone subscribers were in Berrydale in 2017?
Answers
Answer:
Step-by-step explanation:
[tex]F=I(1.75^t)\\ \\ F=285(1.75)^{y-2008}\\ \\ F=285(1.75)^{2017-2008}\\ \\ F=285(1.75)^9\\ \\ F=43871.99\\ \\ F\approx 43872[/tex]
EZ: Find the Equation Using Two Points
(0,200) & (120,0)
Answers
Answer:
[tex]y = \frac{-5}{3}x+200[/tex]
Step-by-step explanation:
Find the value of the slope.
Find the value of the y-int.
good luck, i hope this helps :)