Answer:
[tex]\displaystyle x=\left\{\frac{\pi}{6}+2n\pi, \frac{5\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi\right\}, n\in\mathbb{Z}[/tex]
Step-by-step explanation:
We are given the equation:
[tex]2\cos^2(x)=\sin(x)+1[/tex]
And we want to find all solutions for x.
First, we should put the equation into terms of only one trigonometric ratio.
Since we are given cos²(x), we can turn this into sine. Recall the Pythagorean Identity which states:
[tex]\sin^2(x)+\cos^2(x)=1[/tex]
Therefore:
[tex]\cos^2(x)=1-\sin^2(x)[/tex]
By substitution:
[tex]2(1-\sin^2(x))=\sin(x)+1[/tex]
Distribute:
[tex]2-2\sin^2(x)=\sin(x)+1[/tex]
Isolate the equation:
[tex]2\sin^2(x)+\sin(x)-1=0[/tex]
We can factor:
[tex](2\sin(x)-1)(\sin(x)+1)=0[/tex]
Zero Product Property:
[tex]2\sin(x)-1=0\text{ or } \sin(x)+1=0[/tex]
Solve for each case:
[tex]\displaystyle \sin(x)=\frac{1}{2}\text{ or } \sin(x)=-1[/tex]
We can use the unit circle.
sin(x) = 1/2 for every π/6 and 5π/6. So, it will continue every 2π.
sin(x) = -1 every 3π/2. And this will also continue every 2π.
Hence, our solutions are:
[tex]\displaystyle x=\left\{\frac{\pi}{6}+2n\pi, \frac{5\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi\right\}, n\in\mathbb{Z}[/tex]
Note:
If you only need the solutions within the interval [0, 2π), then it is:
[tex]\displaystyle x=\left\{\frac{\pi}{6}, \frac{5\pi}{6}, \frac{3\pi}{2}\right\}[/tex]
Help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
pythagorean theorem
12^2 + 5^2 = PQ^2
144 + 25 = 169
[tex]\sqrt{169}[/tex] = 13
answer = 13 units
Mr. Dieter wants to tile the family room in his basement. He has selected a pattern of square tiles that measure 9 inches by 9 inches each. The shape of the floor to be tiled is shown below. a. What is the area of the family room in square feet? b. How many of the 9 inch by 9 inch tiles will it take to cover the floor? (NOTE: You will need to convert the area in Part a from square feet to square inches.) c. If the tile is sold only in boxes of 12 tiles per box, how many boxes will Mr. Dieter have to buy to tile the family room?
Answer:
146 ft²
21.6 tiles
1.8 boxes
Step-by-step explanation:
Please find attached an image of the family room used in answering this question
the family room has the following shapes : 2 triangles and one rectangle
the area of the family room can be determined by calculating the area of each of the shape and adding the 3 areas together
area of a rectangle = length x breadth
16 x 7 = 112 ft²
Area of a triangle = 1/2 x base x height
Area of the smaller triangle = (1/2) x 4 x 3 = 6 ft²
Area of the bigger triangle = (1/2) x 8 x 7 = 28 ft²
Sum of the areas = 112 + 6 + 28 = 146 ft²
b.
1. First convert the area of the room to inches
1 ft = 12 in
146 x 12 = 1752 in²
2. the next step is to determine the area of the tile
area of a square = length²
9² = 81 in²
3. Divide the area of the room by the area of the tile
1752 / 81 = 21.6 tiles
c. total number of boxes that would be bought = 21.6 /12 = 1.8 boxes
SUPER EASY What is 4a + 5 × S simplified
Answer:
4a + 5S
Step-by-step explanation:
Which of the following is a prime number between 50 and 60?
A.
55
B.
53
C.
57
D.
51
Answer: B, 53
53 is the only prime number between 50 and 60
The table below shows the transportation method of all of the employees who work at the mall. What percent of employees walk to work?
Car: 758
Bus: 530
Walk: 7
Other: 105
Answer:
0.005 or 0.5% walk
Step-by-step explanation:
Total:
758 + 530 + 7 + 105 = 1400
To find how many employees walk:
7/1400 = 0.005
Given the two dilated figures, what is the length of AB
I think the answer is B
sorry if I am wrong
Please help i need help bad please i have so much work ugh
Step-by-step explanation:
Meeting ID: 436 406 7407
Passcode: 12345
AHH HELP RN PLEASE
IS THIS AN EXPONENTIAL FUNCTION??
Answer:
this =2.x3
Step-by-step explan
ation:
gramwergssa
Plzzz help meeee!!! I CANT DO THISSSSSS AT ALLLLLLLL!!!!!:/:/:/:/AHHH
Answer:
Step-by-step explanation:
11q + 5 <= 49
11q <= 44
q <= 4
answer is B
A square box lid has an area of 50 square inches. Which is the best estimate of the length of one side?
Answer: 7.1 inches
Step-by-step explanation:
The area of a square is simply the square of one of its length. Therefore since we are informed that the area of the square box is given as 50 inches².
Then the best estimate of the length of one side will be the square root of 50 which will be:
= ✓50
= 7.1 inches approximately
Dishwasher detergent is sold in individual packs is sold in 20, 60 and 90 pack containers which container do you think has the lowest unit rate of dollars per pack and why
Answer:
I think 90
Step-by-step explanation:
Would help if you provided more information
If ava makes $15 in 2 hours, what is her rate of pay?
Answer:
$7.50 per hour
Step-by-step explanation:
15/2=7.5
Answer:
she makes $ 7.50 an hour
Step-by-step explanation:
mark brainliest
Please help
Find x:
5
31
10
60
Answer:
x=31....................
Find the radius of a circle with an area of 1017.36 in?, Use 3.14 for pi
area of a circle = πr², where r = the radius of the circle
We can rearrange the formula to solve for r:
[tex]r=\sqrt{\frac{\mathrm{area}}{\pi}}.[/tex]
Given an area of 1017.36 in² and using 3.14 for our value for π, the radius of our circle would be:
[tex]r=\sqrt{\frac{\mathrm{area}}{\pi}} = \sqrt{\frac{\textrm{1017.36 }\mathrm{in^2}}{3.14}} \\ r = 18 \text{ } \mathrm{in^2}.[/tex]
need help I will give brainiest
Answer: 97
Step-by-step explanation:
10+3+3+33+33+15
Plsss help I’m super stuck on this
Answer:
its b
Step-by-step explanation:
took the quiz
Answer:
I would go with D
Step-by-step explanation:
You can look at the graph and answer it
what is the quotient of the fractions below? 7/2 divided by 1/3
What is the distance between the points (0,0) and (6,8)?
Please him me with this
Answer:
x=3
Step-by-step explanation:
To do this we need to do
10-4=6
Then we do
6/2=3
x=3
can someone help me with this??????
Answer:
anong grade po yan
Step-by-step explanation:
idont know
X/x-3 + 2x+2/x^2-2x-3
Answer:
x+2/x-3
Step-by-step explanation:
= x/x-3 + 2(x+1)/(x-3)(x+1)
= x+2/x-3
Answer plz ASAP, I will give brainliest no links
Answer:
A: (10k+m)(10k−m)
Step-by-step explanation:
ASAP PLEASE HELP!!!!
-44 +40−44+40minus, 44, plus, 40
Answer:
-12
Step-by-step explanation:
lol, hope this isn't a troll
Answer:
-12
Just combine the numbers
Stacy saved some dimes. Leo saved 3 times as many dimes as Stacy. If Leo saved a total of 72 dimes, how many dimes did Stacy save? Let n represent the number of dimes that Stacy saved.
Answer:
Leo: 3n Dimes
Leo: 72 Dimes
Stacy: 72/3 Dimes
Stacy: 24 Dimes
which expression is equivalent to 3 to the power of 9
Answer:
3^9
Step-by-step explanation:
Also 3 to the power of 9 is 19,683
Hope This Helps :b
Answer:
What he said which is the answer I just want to get more points
The area of a rectangular plot of land is 58 of a square mile. If this plot of land is 34 of a mile wide, what is the length, in miles, of this plot of land
Answer:
5/6 miles
Step-by-step explanation:
(5/8)/(3/4) = 5/6 miles
Please help show work
(Don’t mind my answer I accidentally clicked)
anything helps :)
plz someone solve this problem
6 ×½ = 3
Answer:
[tex]6[/tex]×[tex]\frac{1}{2} =3[/tex]
Step-by-step explanation:
Yeah.
Which measurement is most accurate to describe the weight of an adult?
1.5 tons
50 lb.
160 oz.
180 lb.
Answer:
180 lb for an adult
Answer:
180 lb.
Step-by-step explanation:
This is due to the fact that 1.5 tons is literally 3,000 pounds and someone would have to be morbidly obese to weigh that much, 50 lbs. is underweight for an adult, 160 oz is 10 lbs which is even more underweight, which leaves 180 lbs as the last resort as well as the one that makes the most sense.
Brainliest please
