Answer:
1.625 kg
Step-by-step explanation:
Answer:
y = 3x² – 9b + 3 and the parabola opens upwards since a = 3 > 0.
Step-by-step explanation:
The general equation of a parabola is:
y = ax² + bx + c
So we have to solve for a, b and c to get our equation with the 3 given points.
When x = 0 and y = 3 we have
3 = a(0)² + b(0) + c, this means c = 3
When x = 4 and y = 15
15 = a(4)² + b(4) + 3 we have
16a + 4b = 12 which is
4a + b = 3
When x = 5 and y = 33 we have
33 = a(5)² + b(5) + 3 we have
25a + 5b = 30 which gives
5a + b = 6.
We have two equations
4a + b = 3
5a + b = 6
Eliminating b we have
a = 3, substituting a = 3 in the first equation we have
4(3) + b = 3
12 + b = 3
b = –9
Our equation therefore is:
y = 3x² – 9b + 3 and the parabola opens upwards since a = 3 > 0.
Answer:
A
Step-by-step explanation:
A proportional relationship either increases or decreases its points at the same rate. In the first set of ordered pairs, the x values all increase by 3 while the y values all increase by 6, which is twice the value of the x values' increasing. The second set of ordered pairs is not proportional because all pairs' x values increase by 2 while the y values increase by 8 until ordered pair (5, 20), so this set therefore is non-proportional. y = x + 3 is the correct equation because it represents that the y value is always 3 greater than the x value. All the shown ordered pairs for set 1 supports this (3 - 0 = 3, 6 - 3 = 3, 9 - 6 = 3, 12 - 9 = 3).
z= r(cosθ+i sinθ) is the required polar form where, r = √41 and θ =π- 
Step-by-step explanation:
Given,
-4+5i is a complex number.
To find the polar form.
Formula
z=x+iy
r² = mod of (x²+y²)
θ = 
So, the polar form will be z=r(cosθ+i sinθ)
Now,
r² =(-4)²+5² = 41
or, r = √41
θ =π- [ since the point is in second quadrant]
Hence,
z= r(cosθ+i sinθ) is the required polar form where, r = √41 and θ =π-
