Answer:
1/2
Step-by-step explanation:
The "Pythagorean relation" between trig functions can be used to find the sine.
<h3>Pythagorean relation</h3>
The relation between sine and cosine is the identity ...
sin(x)² +cos(x)² = 1
This can be solved for sin(x) in terms of cos(x):
sin(x) = √(1 -cos(x)²)
<h3>Application</h3>
For the present case, using the given cosine value, we find ...
sin(x) = √(1 -(√3/2)²) = √(1 -3/4) = √(1/4)
sin(x) = 1/2
__
<em>Additional comment</em>
The sine and cosine of an angle are the y and x coordinates (respectively) of the corresponding point on the unit circle. The right triangle with these legs will satisfy the Pythagorean theorem with ...
sin(x)² + cos(x)² = 1 . . . . . . where 1 is the hypotenuse (radius of unit circle)
A calculator can always be used to verify the result.
Answer:
(B , D) = (-2,5)
Step-by-step explanation:
The given quadratic expression is
![3x^{2} -x-10](https://tex.z-dn.net/?f=3x%5E%7B2%7D%20-x-10)
compare the given expression with ![ax^{2} +bx+c](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2Bbx%2Bc)
so we have ![a = 3 , b = -1 ,c = -10](https://tex.z-dn.net/?f=a%20%3D%203%20%2C%20b%20%3D%20-1%20%2Cc%20%3D%20-10)
now
and ![b= -1](https://tex.z-dn.net/?f=b%3D%20-1)
we need to find two numbers such that their product is -30 and sum is -1
-6 and 5 are such numbers
so we have
![3x^{2} -6x+5x-10](https://tex.z-dn.net/?f=3x%5E%7B2%7D%20-6x%2B5x-10)
grouping first two terms and last two terms
![(3x^{2} -6x)+(5x-10)](https://tex.z-dn.net/?f=%283x%5E%7B2%7D%20-6x%29%2B%285x-10%29)
factor out 3x from first two terms and 5 from last two terms
( factor out (x-2))
![(x+(-2))(3x+5)](https://tex.z-dn.net/?f=%28x%2B%28-2%29%29%283x%2B5%29)
hence B =-2 and D= 5
(B,D)= (-2,5)
Answer: 170,000 kg m/s
Step-by-step explanation:
Answer:
2 5/8
Step-by-step explanation:
simple met... I mean math :)
Answer:
10 units
Step-by-step explanation:
<u>General equation of an ellipse</u>
![\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1 \quad \textsf{where }(h \pm a,k)\: \textsf{and}\:(h, k \pm b)\: \textsf{are the vertices}](https://tex.z-dn.net/?f=%5Cdfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D%2B%5Cdfrac%7B%28y-k%29%5E2%7D%7Bb%5E2%7D%3D1%20%5Cquad%20%5Ctextsf%7Bwhere%20%7D%28h%20%5Cpm%20a%2Ck%29%5C%3A%20%5Ctextsf%7Band%7D%5C%3A%28h%2C%20k%20%5Cpm%20b%29%5C%3A%20%5Ctextsf%7Bare%20the%20vertices%7D)
<u>Major Axis</u>: longest diameter of an ellipse
<u>Minor Axis</u>: shortest diameter of an ellipse
<u>Major radius</u>: one half of the major axis
<u>Minor radius</u>: one half of the minor axis
If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.
If b > a the ellipse is vertical and b is the major radius, and a is the minor radius.
Given equation:
![\dfrac{(y-4)^2}{25}+\dfrac{x^2}{9}=1](https://tex.z-dn.net/?f=%5Cdfrac%7B%28y-4%29%5E2%7D%7B25%7D%2B%5Cdfrac%7Bx%5E2%7D%7B9%7D%3D1)
![\implies \dfrac{x^2}{9}+\dfrac{(y-4)^2}{25}=1](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bx%5E2%7D%7B9%7D%2B%5Cdfrac%7B%28y-4%29%5E2%7D%7B25%7D%3D1)
Comparing with the general equation:
- h = 0
- a² = 9 ⇒ a = 3
- k = 4
- b² = 25 ⇒ b = 5
As b > a then the ellipse is vertical and b is the major radius.
⇒ Major axis = 2 × Major Radius
= 2b
= 2 × 5
= 10
Also, the vertices are:
- (3, 4) and (-3 ,4)
- (0, 9) and (0, -1)