The solutions to the equation sin(x + pi/2) = 1/2 in the interval [3pi/2, 2pi] are x = 5pi/3 and x = 4pi/3.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
We can solve this equation using the following steps:
Subtract pi/2 from both sides to get sin(x) = 1/2.
Recall that the sine function is positive in the first and second quadrants.
Therefore, we need to find the angles in these quadrants where sin(x) = 1/2.
The two angles in the first quadrant where sin(x) = 1/2 are pi/6 and 5pi/6. The two angles in the second quadrant where sin(x) = 1/2 are 7pi/6 and 11pi/6.
Adding pi/2 to each of these angles gives the solutions to the original equation. These solutions are:
x = pi/6 + pi/2 = 2pi/3
x = 5pi/6 + pi/2 = 7pi/6
x = 7pi/6 + pi/2 = 5pi/3
x = 11pi/6 + pi/2 = 4pi/3
We now need to check which of these solutions lie in the interval [3pi/2, 2pi]. We find that the solutions in this interval are:
x = 5pi/3
x = 4pi/3
Therefore, the solutions to the equation sin(x + pi/2) = 1/2 in the interval [3pi/2, 2pi] are x = 5pi/3 and x = 4pi/3.
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Someone pls help????????????????
Answer:
18
Step-by-step explanation:
perimeter = sum of the lengths of the sides
perimeter = 5 m + 5 m + 2 m + 5 m + 1 m
perimeter = 18 m
88 is a solution to 1/8x=11 because
See below...
(1/8)x = 11
Muliply 8 on both sides...
x = 88
What are the answers to number 12 and 14? Pls help!!!! 15 points :)
Find the value of two numbers if their sum is 12 and their difference is four.
Answer:
8 and 4 is the answer!
Find the value of f(5) y = f(x) on a graph
graphing
f ( 5 )
y = f ( x )
1. On her birthday, Shruti bought 2 kg sweets and distributed 1 kg 500 g among her classmates. How much sweets were left with her?
Answer:
500g
Step-by-step explanation:
since she brought 2 kg of sweets, and distributed to her classmates, that means we wil sustract 2 from 1,5 and that will be 0.5 or 500g
I hope I helped you! :)))
Answer:
500g
Step-by-step explanation:
She initially had 2 kg and gave away 1 kg 500 to her classmates
1000 g = 1 kg
500 g = ?
500 g = half a kilogram
So, 1kg 500g is 1.5 kg
So, to get how much sweets were left with her, we subtract 1.5 kg from 2 kg.
2 - 1.5 = 0.5 kg
So, she was left with 0.5 kg or 500g of sweets
What is the change in the scale factor from the old scale to the new scale?
Old: 1 inch = 3.3 feet. New: 1 inch = 1.1 feet.
Answer:
3 to 1
Step-by-step explanation:
It is divided by 3.
What is the result of the construction shown?
A. Angle bisector
B. Copying an angle
C. Copying a line segment
D. Perpendicular bisector
Answer:
Option C: Copying an angle
Step-by-step explanation:
Angle bisector is a line through an angle that will split that angle to 2 equal angles. Thus, option A is wrong as no angle is being split.
Copying an angle involves reproducing a particular angle in another construction. The image shows us that there is an attempt to reproduce the perpendicular angle of 90°. Thus, option B is correct.
Copying a line segment involves creating the exact size of line in another construction. The image doesn't depict that. Thus option C is wrong.
Perpendicular bisector is when we draw a perpendicular line through a horizontal one to divide it into 2 equal parts. This is not the case here. Thus, option D is wrong.
What is the simplified form of cos ??
Answer:
[tex]\frac{\sqrt{2} }{2\\}[/tex]
Step-by-step explanation:
A triangle has a total of 180° (B is a 90° angle)
Take 180° - 90° to find the angle of A + C which equals 90°
take 90°/2 to get the angle of C which is 45°
and to check that take 45°+45°+90°= 180°
Now...
cos (C)
cos(45°) = [tex]\frac{\sqrt{2} }{2}[/tex] [Answer]
Please rate!!
Sorry if it’s blurry, please help
Answer:
-7 & 1
Step-by-step explanation:
[tex] - 7 \times 1 = -7 \\ \\ - 7 + 1 = - 6[/tex]
Hope it helps you in your learning process.
Determining Possible Side Lengths
The distance between Lincoln, NE, and Boulder, CO, is about 500 miles. The distance between Boulder, CO, and a third city is 200 miles.
Assuming the three cities make a triangle on the map, which values represent the possible distance, d, in miles, between Lincoln, NE, and the third city?
< d
Answer:
300<d<700
Step-by-step explanation:
Answer:
300 < d < 700
Step-by-step explanation:
we know thatin the triangle ABCAB=500 milesBC=200 milesAC=xApplying the Triangle Inequality Theorem1) 500+200 > x------> 700 > x------> x < 700 miles2) 200+x > 500----> x > 500-200------> x > 300 milesthe solution for x is 300 < x < 700
Select the correct answer from each drop-down menu.
The length of arc PR is 12 centimeters and its measure is 60° on circle O.
The area of sector POR is approximately
centimeters
square centimeters, and the perimeter of sector POR is approximately
Answer: • 68.76
• 34.92
Step-by-step explanation:
edmentum answer
Trigonometry, I also need help with this, 66 points because why not?
Answer:
[tex]\cot(\theta)=\sqrt{2}[/tex]
[tex]\implies \dfrac{1}{\tan(\theta)}=\sqrt{2}[/tex]
[tex]\implies \tan(\theta)=\dfrac{1}{\sqrt{2}}[/tex]
[tex]\implies \theta=35.26438968...\textdegree \pm180\textdegree n[/tex]
[tex]\implies \theta=215.26438968...\textdegree[/tex]
⇒ Opposite side to angle = 1, Adjacent side to angle = √2
⇒ Hypotenuse = √(1² + √2²) = √3
[tex]\implies \cos(\theta)=\dfrac{A}{H}=-\dfrac{\sqrt{2}}{\sqrt{3}}=-\dfrac{\sqrt{6}}{3}[/tex]
[tex]\implies \sin(\theta)=\dfrac{O}{H}=-\dfrac{1}{\sqrt{3} }=-\dfrac{\sqrt{3}}{3 }[/tex]
[tex]\implies \tan(\theta)=\dfrac{O}{A}=\dfrac{1}{\sqrt{2}} = \dfrac{\sqrt{2}}{2}[/tex]
Complete the square
[tex]2x^2+16x-7[/tex]
Hey there!
[tex]\fbox{2x²+16x-7}[/tex]
[tex]\fbox{2(x + 4)² - 39}[/tex]
Solve for x. .
32
Answers
(2x - 12)
X = 35
x = 51
x = 80
x = 96
Step-by-step explanation:
plug in the values of x in the function
1. 58
2. 90
3. 148
4. 180
Frank traveled 5.3 kilometers from work to home in 30-minutes. Which of the following values is closest to the average speed, in miles per hour?
Frank's average speed is the rate of the distance traveled and the time
Frank's average speed is 6.58 miles per hour
How to determine the average speedThe given parameters are:
Distance = 5.3 kilometers
Time = 30 minutes
The average speed is then calculated as:
Average speed = Distance/Time
Substitute known values
Average speed = 5.3km/30 minutes
Convert time to hours
Average speed = 5.3km/0.5 hour
Convert the distance to miles
Average speed = 3.29 miles/0.5 hour
Evaluate the quotient
Average speed = 6.58 miles per hour
Hence, Frank's average speed is 6.58 miles per hour
Read more about average speed at:
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Select all tables that show a porportional relationship hurry pls thx
Answer:
the 4th table and the last one
Step-by-step explanation:
Given the figure below, find the values of x and z.
Answer:
make me brainlaiest.....
Answer:
The value of x = 5
The value of z = 107
Step-by-step explanation:
=> (6x+43)° +107° = 180° { linear pair }
=> 6x+43 +107 = 180
=> 6x + 150 = 180
=> 6x = 180-150
=> x = 30/6
=> x = 5
Now solve for z ,
107 = z { Vertically opposite angle }
what is the constant of proportionality in the equation x/y = 2/9
Answer:
The constant of proportionality is 4.5
Step-by-step explanation:
To demonstrate the constant of proportionality, we typically use variable k. The equation can look like y/x=k or y=kx
y/x=k
9/2= 4.5
The constant of proportionality is 4.5.
To check the work, we can use the other equation, y=kx.
y=kx
y=4.5(2)
y= 9
3x + 2 =x +4(x+2) solve for x
Answer:
x= -3
Step-by-step explanation:
I do not have one sorry,
What are all the things dilations do in geometry?
Answer:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation that creates a larger image is called an enlargement. A dilation that creates a smaller image is called a reduction. A dilation stretches or shrinks the original figure.
Write the equation of a line through points (5, 5) and (1, 0) in point-slope form.
Help soon pls :)
Answer:
Step-by-step explanation:
Find the slope of the line between (5,5)and (1,0) using m=(y2-y1)/(x2-x1)
which is the change of y over the change of x.
m=5/4
Use the slope 5/4 and a given point (5,5) to substitute for x1 and y1 in the point-slope form y−y1=m(x−x1), which is derived from the slope equation m=(y2-y1)/(x2-x1)
y-5=5/4*(x-5)
Simplify the equation and keep it in point-slope form y-5=5/4*(x-5)
Solve for y.
y=5x/4-5/4
Reorder terms.
y=5/4 x-5/4
List the equation in different forms.
Slope-intercept form: y=5/4 x-5/4
Point-slope form: y-5=5/4*(x-5)
Describe and correct the error a student made in identifying the common difference of the following sequence.
29, 22, 15, 8, 1, ...
Given:
The sequence is 29, 22, 15, 8, 1, ...
To find:
The common difference.
Solution:
We have,
29, 22, 15, 8, 1, ...
It is an AP.
First term : [tex]a_1=29[/tex]
Second term : [tex]a_2=22[/tex]
Now,
Common difference : [tex]d=a_2-a_1[/tex]
[tex]d=22-29[/tex]
[tex]d=-7[/tex]
Therefore, the correct common difference is -7.
Note: Here calculation by student is not given, so we cannot find the error of the student.
An angle measures 1.2° more than the measure of its complementary angle. what is the measure of each angle?
Answer:
44.4°
Step-by-step explanation:
Two complementary angles add up to 90°. Let's call one of the two x, and the second 90-x (in fact, [tex]x+(90-x) = 90[/tex]).
At this point we can use the second condition: the first angle, plus 1.2°, is equal to the complementary.
[tex]x+1.2=90-x \rightarrow 2x=88.8 \rightarrow x = 44.4[/tex]
Starting from the same place, Ryu walks due west and Samantha walks due east.
On the number line, 0 represents their starting point, negative values represent the distance traveled west and positive values represent the distance traveled east. All values are given in feet.
A number line ranging from minus 660 to plus 660. Tick marks are every 60 units. A point labeled Samantha is located at two tick marks to the right of zero. A point labeled Ryu is located at 8 tick marks to the left of zero.
How many feet apart are Ryu and Samantha on the number line?
Enter your answer in the box.
For Samantha, 2 tick marks east is 120 units east because 1 tick is 60 units.
For Ryu, 8 tick marks west is 480 units west because 1 tick is 60 units.
They are walking to form a line. Just add their distances from 0.
120 + 480 = 600.
--------------------------0----------------------------
Ryu: 480 Samantha: 120
480 + 120 = 600.
600 units, or feet.
Scott had a balance of $1910.30 in his bank account on August 1st. On August 12th, he wrote a check to the local car shop for $75.00, then on August 21st his friend gave him a check for deposit $41.50. Then he bought groceries for 210.25. How much money does she have in her bank account?
Answer: $1,666.55
Step-by-step explanation:
The amount of money that Scott will have in the bank will be the total of the money that was in the bank at the beginning of August plus any money received, less any money that was disbursed.
= Beginning balance + check from friend - check to local car shop - cash spent on groceries
= 1,910.30 + 41.50 - 75.00 - 210.25
= $1,666.55
Figure is assuming groceries were paid for by cash from bank account.
Stuffed animals each weighing 1 over 4 pound are on a scale. The scale shows 1 1 over 2 pounds. How many stuffed animals are on the scale?
Answer:
6 stuffed animals
Step-by-step explanation:
if 1/4= 1 then 1x6= 1 1/2
Answer: The answer is: 6
Step-by-step explanation: I have my ways ;>
Have a nice day!
-Sunny
yoko made $323 for 17 hours of work. at the same rat how much would she make for 8 hours of work
Answer:
$152
Step-by-step explanation:
To find Yoko's hourly pay, we will divide the $323 she made after working by 17, which is the number of hours she worked:
323 ÷ 17 = 19
We now know that Yoko makes $19 an hour (dang, she's probably a doctor or something) however, we're not done yet.
We will multiply $19 by 8 hours of work to see how much she'll make after 8 hours:
19 × 8 = 152
Yoko makes $152 after 8 hours of work.
Please rate 5 stars and/or say thanks if I helped!
~Roi
brainliest answer will be given
Which intersection forms a parabola?
Answer
A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone.
Step-by-step explanation:
Parabola is a symmetrical open plane bend framed by the crossing point of a cone with a plane parallel to its side. The way of a shot affected by gravity in a perfect world takes after a bend of this shape.