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By rewriting the equation from step 1 substituting the value of k into it, the value of x is 22.5
A direct variation is a type of variation that has two types of variables in which a variable can be expressed in terms of the other with its constant.
For example;
If x varies directly as y
<h3>Step 1:</h3>Then
- x
y
- x = ky ; where k is constant
The original question says:
- if x varies directly as y, and x = 9 when y = 6, find x when y = 15
∴
x = ky
9 = k × (6)
k = 9/6
k = 1.5
<h3>Step 3:</h3>Now, we can rewrite the equation from step 1 substituting the value of k into it:
∴
x = ky
- when y = 15 and k = 1.5
The value of (x) will be:
x = 1.5 (15)
x = 22.5
Learn more about Direct variation here:
The approximations T8 and M8 for the given integral are:
- T8 = 33.386321; and
- M8 = 33.50794
An Integral is a variable of which a given function is the derivative, i.e. it gives that function when differentiated and may express the area under the curve of the function's graph.
<h3>What is the explanation to above answer?</h3>Given:
F(x) = 37 cox (x²)
Internal = [0,1] n = 8 in Δ x = 1/8
The sub intervals are:
[0, 1/8], [1/8, 2/8], [2/8, 3/8], [ 3/8, 4/8], [ 4/8, 5/8], [ 5/8, 6/8], [6/8, 7/8], [ 7/8, 1]
The mid points are given as:
1/16, 3/16, 5/16, 7/16, 9/16, 11/16, 13/16, 15/16
and X₀ = 0, X₁ = 1/8, X₂ = 2/8
Using the Trapezium Rule which states that: = Δx/2
= 1/1Q[f(0) + 2f (1/8) + 2f(2/8) + ....+ 2f(7/8) + f(1)]
= 0.902333
Now
T8 =
=
= 37 (0.902333)
T8 = 33.386321
It is to be noted that the midpoints rule is given as; = Δx [f(1/16) + (3/16) + .... + f(15/16)]
= 1/8[f(1/16) + f (3/16) + f(5/16) + f(7/16) + f(9/16) + f(11/16) + f(13/16) + f(15/16)]
= 0.905620
From the above,
M8 =
=
= 37 (0.905620)
M8 = 33.50794
Learn more about integral at;
brainly.com/question/19053586
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