Answer:Y=4x+26
Step-by-step explanation:
Didn't you mean y = ax^2? "^" denotes "exponentiation."
The first derivative of y = ax^2 represents the slope of the tangent line to the curve of y = ax^2. Here, dy/dx = 2ax. When x = 2, dy/dx = 2a(2) = 4a.
The point of tangency is (2,y), where y = a(2)^2, or y=4a; thus, the point of tangency is (2,4a). The equation of the tangent line to y=ax^2 at (2,4a) is found by (1) differentiating y=ax^2 with respect to x, (2) letting x = 2 in the result: dy/dx = 2ax => dy/dx (at 2,4a) = 2a(2) = 4a
The line 2x + y = b is supposed to be tangent to y = ax^2 at (2,4a).
The slope of 2x + y = b is found by solving 2x + y = b for y:
y = b - 2x => slope m = -2
Thus, dy/dx = 4a = - 2, and thus a = -2/4, or a = -1/2. All we have to do now is to find the value of b. We know that 2x + y = b, so if x=-2 and y=-8,
2(-2) + [-8] = b = -4 - 8 = -12
Thus, the equation of the parabola is y = ax^2 = (-1/2)x^2.
a = -2 and b = -8 are the required a and b values.
The answer is:
The farmer has ( 140 cows ) & ( 28 horses ). = 168 animals
5 × 28 = 140
Answer:
(12,10)
Step-by-step explanation:
Answer:
D. 30
Step-by-step explanation:
Having a population that doesn't follow normal distribution (skewed) can still have sampling distribution that is completely normal. This fact is presented in the Central Limit Theorem.
Central Limit Theorem: states that we can have a normal distribution of sample means even if the original population doesn't follow normal distribution, we just need to take a large sample.
So how much sample size do we need?
There is no straight forward answer to this rather we have to analyse the situation closely!
1. If the population distribution is already normal then a smaller sample size would be enough to ensure normal distribution.
2. If the population distribution is very skewed than a larger number of sample size is needed to ensure normal distribution. The rule of thumb is to take sample size equal to or more than 30 to be on safer side. This is the case in this problem hence option D fits the best.
