Answer:
dy/dx = ![\frac{4x-1}{1-15y^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B4x-1%7D%7B1-15y%5E%7B2%7D%20%7D)
Step-by-step explanation:
-y + 2x²- x = -5y³
2x² - x = y - 5y³
4x - 1 = dy/dx - 15y².dy/dx
dy/dx(1 - 15y²) = 4x - 1
dy/dx = ![\frac{4x-1}{1-15y^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B4x-1%7D%7B1-15y%5E%7B2%7D%20%7D)
3a) The figure has 5 sides and 5 vertices
3b) None of the sides are congruent, so the figure is not are guitar polygon
This is the concept of applications of volume. We are required to calculate BTUs per cubic foot. This will be given by the formula:
(BTU)/volume
Total BTU=15*750=11,250
(assuming the bus is a perfect cuboid) volume of the bus will be;
volume=length*width*height
=38*8.5*6.25
=2018.75 ft^2
Thus the BTUs per foot will be:
11250/2018.75
5.57 BTUs/ft
Answer:
Step-by-step explanation:
From the figure attached,
If the figures shown are congruent (Equal in shape and size), length of all the sides must be equal.
Therefore, sides sides CD and GH must be equal in measures.
Distance between the two points
and
is given by,
d = ![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Length of the side CD having ends C(-4, 4) and D(0, 5) will be,
CD = ![\sqrt{(-4-0)^2+(4-5)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-4-0%29%5E2%2B%284-5%29%5E2%7D)
CD = ![\sqrt{(16+1)}](https://tex.z-dn.net/?f=%5Csqrt%7B%2816%2B1%29%7D)
= ![\sqrt{17}](https://tex.z-dn.net/?f=%5Csqrt%7B17%7D)
Length of GH having ends G(0, -4) and H(4, -5) will be,
GH = ![\sqrt{(0-4)^2+(-4+5)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%280-4%29%5E2%2B%28-4%2B5%29%5E2%7D)
= ![\sqrt{16+1}](https://tex.z-dn.net/?f=%5Csqrt%7B16%2B1%7D)
= ![\sqrt{17}](https://tex.z-dn.net/?f=%5Csqrt%7B17%7D)
Therefore, m(CD) = m(GH)
Similarly, we can prove all corresponding sides of two figures equal in measure.
This shows ABCD ≅ EFGH.