7, 14, 21, 28, 35, 42, 49... 7 cars will need. to be washed to reach $49
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>
25% is being taken off the original price, p, of each patio chairs.
That means the price of each patio chair is the full price, p, minus <span>25% of the original price.
1) To find 25% of the original price, multiply p (original price) by the decimal form of 25%, or 0.25. That means 25% off original price = 0.25p.
2) Now subtract 0.25p from the original price of the chairs to find the price of each (1) chair. p - 0.25p
Shylah is buying 4 chairs at that discounted price. That means you need to multiply the discounted price, </span> p - 0.25p, by 4. Shylah is paying 4(p-0.25p) total for the 4 chairs, which is answer choice B.
Since you can choose more than one choice, you can simplify 4(p-0.25p) by subtracting what is in the parathesis, then multiplying, following the order of operations:
4(p-0.25p)
= 4(0.75p)
= 3p
That is answer choice A.
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Answer: Choices A and B, <span>3p and 4(p−0.25p).</span>
