Yes they are equivalent because when you multiply by 10, you move the decimal place one spot to the right.
A third are spotted so that would mean 2/3 are not spotted so if you take 1200 divide it by 3 and then multiply it by 2 you get 800 which is your answer
Answer:
m < 49/12
Step-by-step explanation:
The portion of the quadratic formula under the square root sign is the discriminant.
If the discriminant is > 0 then there are two real roots.
b² -4ac > 0
-----------------------------
7² - 4(3)m > 0
49 - 12m > 0
Subtract 49 from both sides
-12m > -49
Divide both sides by -12
(when multiplying or dividing by a negative the inequality must be reversed)
m < 49/12
Answer:
The x-coordinate of the point changing at ¼cm/s
Step-by-step explanation:
Given
y = √(3 + x³)
Point (1,2)
Increment Rate = dy/dt = 3cm/s
To calculate how fast is the x-coordinate of the point changing at that instant?
First, we calculate dy/dx
if y = √(3 + x³)
dy/dx = 3x²/(2√(3 + x³))
At (x,y) = (1,2)
dy/dx = 3(1)²/(2√(3 + 1³))
dy/dx = 3/2√4
dy/dx = 3/(2*2)
dy/dx = ¾
Then we calculate dx/dt
dx/dt = dy/dt ÷ dy/dx
Where dy/dx = ¾ and dy/dt = 3
dx/dt = ¾ ÷ 3
dx/dt = ¾ * ⅓
dx/dt = ¼cm/s
The x-coordinate of the point changing at ¼cm/s
