Answer:
Step-by-step explanation:
The equation of a circle with center (a,b) and radius r, is
From the question, the center of the circle is located at (-6,2) and the radius is
We substitute the center and radius to get:
Simplify to obtain:
The first composite shape we would need to find is the rectangle. We would use the formula length multiplied by width. The second composite shape is a hemisphere. The area of a hemisphere is Pi multiplied by the radius squared and then divide it by 2. To find the area of both of these figures, add up the area for each one and then you will get the
area of both.
Answer:
y + 1 = -14(x - 2)^2y = -14(x - 2)^2 - 1
Step-by-step explanation:
Answer:
13 ft/s
Step-by-step explanation:
t seconds after the boy passes under the balloon the distance between them is ...
d = √((15t)² +(45+5t)²) = √(250t² +450t +2025)
The rate of change of d with respect to t is ...
dd/dt = (500t +450)/(2√(250t² +450t +2025)) = (50t +45)/√(10t² +18t +81)
At t=3, this derivative evaluates to ...
dd/dt = (50·3 +45)/√(90+54+81) = 195/15 = 13
The distance between the boy and the balloon is increasing at the rate of 13 ft per second.
_____
The boy is moving horizontally at 15 ft/s, so his position relative to the spot under the balloon is 15t feet after t seconds.
The balloon starts at 45 feet above the boy and is moving upward at 5 ft/s, so its vertical distance from the spot under the balloon is 45+5t feet after t seconds.
The straight-line distance between the boy and the balloon is found as the hypotenuse of a right triangle with legs 15t and (45+5t). Using the Pythagorean theorem, that distance is ...
d = √((15t)² + (45+5t)²)
Answer:
If your solving for x on the first one it’s x =−5/2y+8
If your solving for y on the second one it’s y =−4x+3
Step-by-step explanation:
