Verify: (sinx+cosx)^2=1+sin(2x)
Answers
Since (a + b)² = (a + b)(a+b):
(sinx + cosx)(sinx + cosx) = 1 + sin(2x)
Now, multiply each member with another:
sin²x + sinxcosx + sinxcosx + cos²x = 1 + sin(2x)
⇒ sin²x + cos²x + 2sinxcosx = 1 + sin(2x)
Since sin²x + cos²x = 1 (Pithagorean identity):
1 + 2sinxcosx = 1 + sin(2x)
Since 1 + 2sinxcosx = 1 + sin(2x) (Double-angle identity):
1 + sin(2x) = 1 + sin(2x)
Related Questions
Find the mean of the numbers 10, 11, 12, 14, 12, 11, 13, 12, 14, and 11.
Find zHelp me please
Abcd is a rectangle. Find the length of each diagonal. .AC= 3y/5 BD=3y-4
12. The square and rectangle shown below have the same perimeter length Show that the length of the rectangle (3x + 1) centimetres
Answers
Write the steps you will use to solve the equation and explain each step.
Answers
Me personally I substitute random numbers till I find the correct number, this takes longer but it works best for my understanding. X= 1. 10(1)-40+15=-15. 10-40 is -30, -30+15=-15. So, x=1
Original Equation.
5(2x - 8) + 15 = -15
First do what is in the parenthesis.
2 x 1 = 2
2 - 8 = -6
5(-6) + 15 = -15
Multiply 5 x -6 to get -30
-30 + 15 = -15
add 15 + -30 to get -15
-15
x = 1
Hope This Helps!
Can I get Brainliest?
Answers
The squeegee passes by the other window washer in ____ seconds to the nearest tenth.
seconds. If necessary, round your answer
Answers
Answer:
The squeegee passes by the other window washer in 3.9 seconds to the nearest tenth
Step-by-step explanation:
From the question,
The first person drops a squeegee from a height of 95 feet, to determine how long it takes the squeegee to pass by another person at a height of 20 feet, that is, we are to determine how long it will take the squeegee to travel a height distance of 95 feet - 20 feet
95 feet - 20 feet = 75 feet.
Hence, we are to determine how long it will take the squeegee to travel a height distance of 75 feet.
From one of the equations of motion due to free fall
h = ut + 1/2gt²
Where h is the height
u is the initial velocity
g is the acceleration due to gravity (Take g = 9.8 m/s²)
and t is the time
For the question,
h = 75 feet
u = 0 m/s ( Since the squeegee is dropped from rest)
Therefore
75 = 0(t) + 1/2(9.8)(t²)
75 = 4.9t²
∴ t² = 75/4.9
t² = 15.306
t =√15.306
t = 3.9 secs
Hence,
The squeegee passes by the other window washer in 3.9 seconds to the nearest tenth.
Final answer:
Using the kinematic equations for free fall, we find that it takes approximately 2.2 seconds for the squeegee to pass by the other window washer working at a height of 20 feet.
Explanation:
The question is related to the subject of physics and involves the free fall motion of an object under the influence of gravity. We can use the kinematic equations to solve for the time it takes for the squeegee to pass the window washer working at 20 feet.
The initial height h0 from which the squeegee was dropped is 95 feet, and the height h where the other window washer is located is 20 feet. Therefore, we are interested in the time it will take the squeegee to cover the distance d = h0 - h, which equals 75 feet.
Assuming acceleration due to gravity g is approximately 32.2 feet per second squared (in the downward direction), and initial velocity u is 0 since the squeegee is dropped, we can use the formula to find the time t.
Plugging in the values, we get:
- t = sqrt(4.6584)
- t ≈ 2.16 seconds
To the nearest tenth, it takes the squeegee approximately 2.2 seconds to pass by the other window washer.
Learn more about Free Fall Physics here:
#SPJ3
A) X = 1/3
B) X = 17/5x
C) X = 1/5
D) X = 1/6
Answers
Answers
Answer:
The system of inequalities 45 > 4x + 9 and 53 ≤ 4x + 9 doesn't have any solution, because the restrictions on x are contradictory (x can't be both less than 9 and greater than or equal to 11).
Step-by-step explanation:
These are a set of compound inequalities. Let's solve these equations step by step. The first inequality 45 > 4x + 9, we start to solve it by subtracting 9 from both sides of the inequality, which gives us 36 > 4x. Then, we divide each side by 4 to get x < 9.
The second inequality is 53 ≤ 4x + 9. We solve this by subtracting 9 from both sides to get 44 ≤ 4x. Then, we divide each side by 4 to find x ≥ 11.
However, these two results are contradictory (as x cannot be both less than 9 and greater than or equal to 11 simultaneously). So, there is no solution to this system of inequalities.