Answer:
D
Step-by-step explanation:
the center is (0,8)
(to solve this just flip the signs on the constants being added to x and y (there is an invisible constant of 0 being added to the x))
the radius is 7 (or √49)
9514 1404 393
Answer:
- kayak: 12 mph
- current: 2 mph
Step-by-step explanation:
Bunny's rate downstream is ...
(70 mi)/(5 h) = 14 mi/h = k + c
Bunny's rate upstream is ...
(70 mi)/(7 h) = 10 mi/h = k -c
The kayak speed is the average of these:
(14 mi/h +10 mi/h)/2 = ((k +c) +(k -c))/2
(24 mi/h)/2 = 2k/2
12 mi/h = k
Then the current speed is ...
c = k -10 = 12 -10 = 2 . . . . mi/h
The still-water speed of the kayak is 12 mi/h; the speed of the current is 2 mi/h.
_____
<em>Additional comment</em>
World-class kayak paddlers will not maintain a speed more than 8 mi/h for that distance and/or time (140 miles in 12 hours). Bunny is exceptional.
A greatest common factor is the largest number that goes into two or more numbers (in this case two). To find the GCF of two numbers, we have to find the prime factorization (how to express a number as a product of prime numbers) and then see which numbers are common in both of the prime factorizations.
11. The prime factorization of 12 is 3 * 2 * 2. The prime factorization of 18 is 3 * 3 * 2. Looking at the prime factorizations, we can see that both of them have 3 and 2. That means that the GCF is 3 * 2 which is 6.
12. The prime factorization of 48 is 2 * 2 * 2 * 2 * 3. The prime factorization of 80 is 2 * 2 * 2 * 2 * 5. We see that the numbers shared are 2, 2, 2, and 2. That means that the GCF is 2 * 2 * 2 * 2 or 16.
Answer:
Step-by-step explanation:
Number of vertices
3
Variable constraints
a>0 and b>0
Diagonal lengths
(data not available)
Height
b
Area
A = (a b)/2
Centroid
x^_ = (a/3, b/3)
Mechanical properties:
Area moment of inertia about the x-axis
J_x invisible comma x = (a b^3)/12
Area moment of inertia about the y-axis
J_y invisible comma y = (a^3 b)/12
Polar moment of inertia
J_zz = 1/12 a b (a^2 + b^2)
Product moment of inertia
J_x invisible comma y = -1/24 a^2 b^2
Radii of gyration about coordinate axes
r_x = b/sqrt(6)
r_y = a/sqrt(6)
Distance properties:
Side lengths
a | sqrt(a^2 + b^2) | b
Hypotenuse
sqrt(a^2 + b^2)
Perimeter
p = sqrt(a^2 + b^2) + a + b
Inradius
r = 1/2 (-sqrt(a^2 + b^2) + a + b)
Circumradius
R = 1/2 sqrt(a^2 + b^2)
Generalized diameter
sqrt(a^2 + b^2)
Convexity coefficient
χ = 1
Mean triangle area
A^_ = (a b)/24
