Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.
<h3>Variation</h3>
y = k × x
where,
k = constant of proportionality
y = -40
x = -5
y = k × x
-40 = k × -5
-40 = -5k
k = -40/-5
k = 8
when,
y = 8 and x = 2.5
y = k × x
8 = k × 2.5
8 = 2.5k
k = 8/2.5
k = 3.2
when,
y = 5 and x = 4
y = k × x
5 = k × 4
5 = 4k
k = 5/4
k = 1.25
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Answer:
A i think
Step-by-step explanation:
I'll explain how to do the first one:-
y = cos-1(x2)
This can be described as ' a function of a function' x^2 is a function of x and cos-1(x^2) is a function of x^2.
We need to apply the chain rule.
Personally I find this easier to understand if i let u = x^2, so
If y = f(u) and u is a function of x then
dy/dx = dy/ du * du/dx
Here u = x^2 and y = cos-1(u)
du/dx = 2x
so dy/dx = d(cos-1(x^2) dx = dy/du * du/dx
= -1 / √(1 - u^2) * 2x
= -2x / √(1 - u^2)
= -2x / √(1 - (x^2)^2)
= -2x / √(1 - x^4)
I hope this helps. but if not. you might like to employ the formulae in the question - The square boxes contain the 'u' s in my answer. These formulae are equivalent to my explanation.
Answer:
Im pretty sure the answer is 327.96
Step-by-step explanation:
Answer:
Suppose we have a polynomial of degree N with a leading coefficient A and roots {x₁, x₂, ..., xₙ}
We can write this polynomial as:
P(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)
such that the terms:
(x - x₁), (x - x₂), etc...
are called the factors.
In this case, we know that the roots OF THE FACTORS
are:
(x = - 2)
(x = - (1 + √5))
(x = + 3i)
If the root of the polynomial is x = -2, then the factor should be:
(x + 2)
which is zero when we evaluate x in -2
Then the correct option is the first one.
