Answer:
(a) (x-2)^2 +(y-2)^2 = 16
(b) r = 2
Step-by-step explanation:
(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.
Circle centered at (h, k) with radius r:
(x -h)^2 +(y -k)^2 = r^2
The given circle is ...
(x -2)^2 +(y -2)^2 = 16
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(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:
r = 2
Answer:
x-intercepts are (0, 0) and (-6, 0)
Step-by-step explanation:
equation of a parabola in vertex form: y = a(x - h)² + k
where (h, k) is the vertex
Substituting the given vertex (-3, -18) into the equation:
y = a(x + 3)² - 18
If the y-intercept is (0, 0) then substitute x=0 and y=0 into the equation and solve for a:
0 = a(0 + 3)² - 18
⇒ 0 = a(3)² - 18
⇒ 0 = 9a - 18
⇒ 9a = 18
⇒ a = 2
Therefore, y = 2(x + 3)² - 18
To find the x-intercepts, set the equation to 0 and solve for x:
2(x + 3)² - 18 = 0
Add 18 to both sides: 2(x + 3)² = 18
Divide both sides by 2: (x + 3)² = 9
Square root both sides: x + 3 = ±3
Subtract 3 from both sides: x = ±3 - 3
so x = 3 - 3 = 0
and x = -3 - 3 = -6
So x-intercepts are (0, 0) and (-6, 0)
Answer:
The inverse function of f(x) is ... f⁻¹(x) = log (x/9.16)/log (1.0054)
Step-by-step explanation:
Starting equation... f(x) = 9.16(1.0054)ˣ
Visually rewritten... y = 9.16(1.0054)ˣ
Flipping x and y... x = 9.16(1.0054)ʸ
Isolating (1.0054)ʸ... x/9.16 = (1.0054)ʸ
Taking the log of both sides... log (x/9.16) = y log (1.0054)
Isolating y... log (x/9.16)/log (1.0054) = y
Solution... y = log (x/9.16)/log (1.0054)
Hi there!
We can calculate slope using the following formula:
Plug in the corresponding points:
Simplify:
Answer: 36.84
(lmk if this isnt right)
Step-by-step explanation:
To find the perimeter of the rectangle:
3+3+3+3+3+3=18
or
3(6)=18
To find the diameter of the circle:
12-(3+3)
12-6=6
You can combine the 2 half circles to make 1 full circle since they both have the same diameter. Use the circumference formula to solve.
C=πd
Substitute
C=3.14(6)
Multiply
C=18.84
Add the perimeter of the rectangle and the circumference of the circle.
18+18.84=36.84
