Answer:
Line PU has points R and S between points P and U, lines QR and ST are parallel, line QR intersects line PU at point R, line ST. intersects line PU at point S, the measure of angle PRQ is 135 degrees, and the measure of angle UST is 15 ( x plus 2 ) degrees. X = −1 x = 7 x = 9 x = 13
Step-by-step explanation:
The given equation of the ellipse is x^2
+ y^2 = 2 x + 2 y
At tangent line, the point is horizontal with the x-axis
therefore slope = dy / dx = 0
<span>So we have to take the 1st derivative of the equation
then equate dy / dx to zero.</span>
x^2 + y^2 = 2 x + 2 y
x^2 – 2 x = 2 y – y^2
(2x – 2) dx = (2 – 2y) dy
(2x – 2) / (2 – 2y) = 0
2x – 2 = 0
x = 1
To find for y, we go back to the original equation then substitute
the value of x.
x^2 + y^2 = 2 x + 2 y
1^2 + y^2 = 2 * 1 + 2 y
y^2 – 2y + 1 – 2 = 0
y^2 – 2y – 1 = 0
Finding the roots using the quadratic formula:
y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1
y = 1 ± 2.828
y = -1.828 , 3.828
<span>Therefore the tangents are parallel to the x-axis at points (1, -1.828)
and (1, 3.828).</span>
Assume that the volume of the prism, V prism = Area of the base (A) x height (h). Using the equation for solving the volume of pyramid which is V pyramid = 1/3 x (base x height). For this example the prism and the pyramid's base is equal (A) and the height of pyramid is half the height of the prism (h/2). Hence, volume pyramid = 1/3 x (A) x (h/2) = (A x h)/6.
Answer:
n = -2/5
Step-by-step explanation:
n/8 - 7n/16 = 1/8
2n/16 - 7n/16 = 2/16 (making common denominators)
-5n/16 = 2/16 (Simplifying the equation)
-5n = 32/16 (Multiplying both sides by 16)
-5n = 2
n = -2/5
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Your scale model will be just under 3.135 inches x 1 inch even.