What is the value of the expression
1 answer:
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Answer:
(p, q) = (8, 82)
Step-by-step explanation:
When a circle is centered at the origin, the radius to point (a, b) will have slope m = b/a. The tangent is perpendicular to the radius, so the tangent at point (a, b) will have slope -a/b. In point-slope form, the equation of the tangent line will be ...
y -k = m(x -h) . . . . . point-slope equation of line with slope m through (h, k)
y -b = (-a/b)(x -a)
Rearranging this to standard form, we have ...
b(y -b) = -a(x -a)
by -b² = -ax +a²
ax +by = a² +b²
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For (a, b) = (5, 4), the standard form equation of the tangent can be written ...
5x +4y = 5² +4² = 41
Your given equation has an x-coefficient that is twice the value shown in this equation, so we need to multiply this equation by 2:
2(5x +4y) = 2(41)
10x +8y = 82
Comparing to 10x +py = q, we see that ...
p = 8
q = 82
Answer:
The vertical distance from the top of the slide go the ground is 24.25 feet
Step-by-step explanation:
Here, we want to calculate the vertical distance from the top of the slide to the ground.
To answer this properly, we shall need the aid of a diagram. Please check the attachment for this;
Mathematically, to calculate this vertical distance, we shall be employing the use of a trigonometric ratio since the shape we are considering is a right-angled triangle
The vertical distance faces the angle given and we can refer to it as the opposite. The length of the slide refers to the hypotenuse
So the trigonometric ratio we are to use will consider the opposite and the hypotenuse
This is the sine
Mathematically sine of an angle = length of the opposite/length of the hypotenuse
let’s call the length of the opposite x
sin 60 = x/28
x = 28 sin 60
x = 24.248 which is 24.25 feet
