1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MissTica
2 years ago
7

1+sin^2 x = 2-cos^2 x

Mathematics
1 answer:
Alinara [238K]2 years ago
3 0
1+sin²x=2-cos²x
Remenber:   sin²x+cos²x=1      ⇒sin²x=1-cos²x
 
1+sin²x=1+(1-cos²x)=2-cos² x       (this is true)

You might be interested in
Follow the rule to find the output for an input of -4. output = input x 17
vladimir2022 [97]

Answer:

output = - 68

Step-by-step explanation:

given

output = input × 17

when input = - 4 , then

output = - 4 × 17 = - 68

6 0
2 years ago
On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s^2. A cannonball is launched from the or
almond37 [142]

Answer:

a) \vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j, b) \theta = \frac{\pi}{4}, c) y_{max} = 84.375\,m, t = 3.75\,s.

Step-by-step explanation:

a) The function in terms of time and the inital angle measured from the horizontal is:

\vec r (t) = [(v_{o}\cdot \cos \theta)\cdot t]\cdot i + \left[(v_{o}\cdot \sin \theta)\cdot t -\frac{1}{2}\cdot g \cdot t^{2} \right]\cdot j

The particular expression for the cannonball is:

\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j

b) The components of the position of the cannonball before hitting the ground is:

x = (90\cdot \cos \theta)\cdot t

0 = 90\cdot \sin \theta - 6\cdot t

After a quick substitution and some algebraic and trigonometric handling, the following expression is found:

0 = 90\cdot \sin \theta - 6\cdot \left(\frac{x}{90\cdot \cos \theta}  \right)

0 = 8100\cdot \sin \theta \cdot \cos \theta - 6\cdot x

0 = 4050\cdot \sin 2\theta - 6\cdot x

6\cdot x = 4050\cdot \sin 2\theta

x = 675\cdot \sin 2\theta

The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:

\frac{dx}{d\theta} = 1350\cdot \cos 2\theta

1350\cdot \cos 2\theta = 0

\cos 2\theta = 0

2\theta = \frac{\pi}{2}

\theta = \frac{\pi}{4}

Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:

\frac{d^{2}x}{d\theta^{2}} = -2700\cdot \sin 2\theta

\frac{d^{2}x}{d\theta^{2}} = -2700

Which demonstrates the existence of the maximum associated with the critical point found before.

c) The equation for the vertical component of position is:

y = 45\cdot t - 6\cdot t^{2}

The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:

\frac{dy}{dt} = 45 - 12\cdot t

45-12\cdot t = 0

t = \frac{45}{12}

t = 3.75\,s

Now, the second derivative is used to check if such solution leads to a maximum:

\frac{d^{2}y}{dt^{2}} = -12

Which demonstrates the assumption.

The maximum height reached by the cannonball is:

y_{max} = 45\cdot (3.75\,s)-6\cdot (3.75\,s)^{2}

y_{max} = 84.375\,m

7 0
3 years ago
Will rank the correct answer brainliest!
andreyandreev [35.5K]

Answer:

Step-by-step explanation:

diameter=2*radius

=2*9

=18 in

given central angle=72 degree

arc length=central angle /360° *πd

=72/360 *3.14*18

=1/5 *56.52

=56.52/5

=11.304

8 0
2 years ago
Read 2 more answers
What term is used to describe the study of using limited resources to fulfill wants and needs?
amid [387]

Answer: C, management

6 0
2 years ago
Read 2 more answers
Please Help!
Artist 52 [7]
X<4 hope this helped dude
5 0
3 years ago
Other questions:
  • Ellen has property whose boundary lines form a triangle, as shown in the diagram. Her house lies at Vertex A and she is going to
    12·1 answer
  • All of the following are terminating decimals except _____.
    9·2 answers
  • What is the greatest common factor of 16a and 20ab<br><br> 2d and 10d
    8·2 answers
  • Which ordered pair is a solution to the equation y=4x
    13·1 answer
  • The length of ZX is 2 units. What is the perimeter of triangle XYZ? 5 + + 2 units 5 + 3 units 5 + + 2 units 10 + 2 units
    16·1 answer
  • 24 students in a class took an algebra test. If 18 students passed the test what percent passed?
    11·2 answers
  • Evaluate x2+9/x2 for each of the given values.
    6·2 answers
  • Which is true:<br>0/4 = 0<br>or, <br>4/0 = 0​
    8·2 answers
  • In the Ambrose family, the ages of the three children are three consecutive integers. If
    10·1 answer
  • On cold days, nick likes to make hot chocolate. He uses 6 table spoons of coco and 2 table spoons of sugar
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!