The height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 – 5t2, where t is the tim
2 answers:
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Answer:
see explanation
Step-by-step explanation:
Using the Cosine rule
a² = b² + c² - 2abcosA ← Rearranging for cosA gives
cosA =
(a)
let a = 10, b = 7, c = 8 and A = α, then
cosα = =
=
, thus
α = (
) ≈ 83° ( to the nearest degree )
(b)
let the angle opposite side 7 be x
Using the Sine rule
=
( cross- multiply )
10sinx = 7sin83 ( divide both sides by 10 )
sinx = , thus
x = (
) = 44°
The third angle can be found using the sum of angles in a triangle
third angle = 180° - (83 + 44)° = 180° - 127° = 53°
The 3 angles are 83°, 44°, 53°
<span>4. The x-coordinate of the solution is 9.
</span><span>5. The y-coordinate of the solution is −8 .
</span><span>6.The ordered pair that is the solution to the system lies in Quadrant IV .</span><span>
Proof:
Solve the following system:
{4 x + 3 y = 12 | (equation 1)
{2 x + 3 y = -6 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x + 3 y = 12 | (equation 1)
{0 x+(3 y)/2 = -12 | (equation 2)
Multiply equation 2 by 2/3:
{4 x + 3 y = 12 | (equation 1)
{0 x+y = -8 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{4 x+0 y = 36 | (equation 1)
{0 x+y = -8 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 9 | (equation 1)
{0 x+y = -8 | (equation 2)
Collect results:
Answer: {x = 9 , y = -8
</span>
</span><span>5. The y-coordinate of the solution is −8 .
</span><span>6.The ordered pair that is the solution to the system lies in Quadrant IV .</span><span>
Proof:
Solve the following system:
{4 x + 3 y = 12 | (equation 1)
{2 x + 3 y = -6 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x + 3 y = 12 | (equation 1)
{0 x+(3 y)/2 = -12 | (equation 2)
Multiply equation 2 by 2/3:
{4 x + 3 y = 12 | (equation 1)
{0 x+y = -8 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{4 x+0 y = 36 | (equation 1)
{0 x+y = -8 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 9 | (equation 1)
{0 x+y = -8 | (equation 2)
Collect results:
Answer: {x = 9 , y = -8
</span>