<span>x² + y² + 14x − 4y − 28 = 0
x² +14x +y² - 4y =28
x²+2*7x +7² -7² + y² - 2*2y +2² - 2² = 28
(x+7)² + (y-2)² -7²-2² =28
</span>(x+7)² + (y-2)²=28+49+4
(x+7)² + (y-2)² =81 is the answer.
The formula to calculate work done is -
Work done ( in joule, J) = Force (in Newton) X Distance (in meters)
So, we will use the formula to calculate work done,
Here, force is given as = 7 newtons
Distance is given as = 3 meters
So, work done will be -
Work done ( in joule, J) = 7 Newtons X 3 Meters
<u>Work done ( in joule, J) = 21 J (in joule)</u>
Cone details:
Sphere details:
================
From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.
<u>Using Pythagoras Theorem</u>
(a)
TO² + TU² = OU²
(h-10)² + r² = 10² [insert values]
r² = 10² - (h-10)² [change sides]
r² = 100 - (h² -20h + 100) [expand]
r² = 100 - h² + 20h -100 [simplify]
r² = 20h - h² [shown]
r = √20h - h² ["r" in terms of "h"]
(b)
volume of cone = 1/3 * π * r² * h
===========================
To find maximum/minimum, we have to find first derivative.
(c)
<u>First derivative</u>
<u>apply chain rule</u>
<u>Equate the first derivative to zero, that is V'(x) = 0</u>
<u />
<u>maximum volume:</u> <u>when h = 40/3</u>
<u>minimum volume:</u> <u>when h = 0</u>
The domain and the range of a function is the set of input and output values of the function.
The domain is the set of all whole numbers.
The range is the set of all whole numbers.
Let the number of tickets be x, and the revenue be y.
So, the revenue function will be:
y = 125
The number of tickets cannot be less than 0.
So, the domain of the revenue function is
domain=0,∞
The above means that, the domain is the set of all whole numbers
Similarly, the revenue cannot be less than 0.
So, the range of the revenue function is
range = 0,∞
The above means that, the range is also the set of all whole numbers (in multiples of 125).
to know more about range and domain;
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-4x+154 should be the answer
