A polar coordinate is that which can be written as (r, θ) where r is the radius and θ is the angle.
The radius, r, is also the hypotenuse of the right triangle that can be formed. Hence, it can be calculated through the equation,
r² = x² + y²
If we are to simplify this for the r alone, we have,
r = sqrt (x² + y²)
Substituting the known values,
r = sqrt ((4)² + (-4)²) = 4√2
The x and y can be related through the trigonometric function, tangent.
tan θ = y/x
To solve for θ
θ = tan⁻¹(y/x) = tan⁻¹(-4/4) = -45° = 315°
Hence, the polar coordinate is <em>(4√2, 315°)</em>
Answer:
307 Meters
Step-by-step explanation:
The answer for the given equation is x = 3.5.
<u>Step-by-step explanation</u>:
Given, 2 / 3 (3x + 6) = 4x + 3
Step 1:
Rearranging the given equation by subtracting the right side of the equation to the left side.
2 / 3 (3x + 6) - 4x + 3 = 0
Step 2:
Taking out the like terms, the equation becomes
(2 / 3) 
3 (x + 2) - (4x - 3) = 0
⇒ 2 (x + 2) - (4x - 3) = 0
Step 3:
Solving the equation for the value of x,
⇒ 2x + 4 - 4x + 3 = 0
⇒ -2x + 7 = 0
⇒ -2x = -7
⇒ x = 7 / 2 = 3.5.
Hence the value of x = 3.5.
Answer:
the object will attain maximum height at 3.5 seconds.
Step-by-step explanation:
The height of the object (in feet), h, above the ground t seconds after it is fired is given by h(t)=−16t2+112t+128.
128 represents 128 feet above the ground and this is the height from which the object was fired.
The given equation is a quadratic equation and plotting of this equation on a graph would give a parabola whose vertex would be equal to the maximum height travelled by the rocket.
The vertex of the parabola is calculated as follows,
Vertex = -b/2a
From the equation,
a = -16
b = 112
Vertex = - - 112/32= 3.5
So the object will attain maximum height at 3.5 seconds.
