According to the graph what is the value of the constant in the equation below

Mathematics

1 answer:

pochemuha3 years ago

6 0

As you can see in the picture, all the points lie on the same line, so they are collinear. The line follows an equation with the general form of:

y = mx + b
where m and b are the constants

The b parameter is the y-intercept. This is the point at which the line intersects the y-axis. From the graph, b = 0. The other constant is the slope m. You can choose any two points, the answer would just be the same.

m = (y₂ - y₁)/(x₂ - x₁)
Suppose point 1 is (2,1) and point 2 is (3,1.5).

m = (1.5 - 1)/(3 - 2) = 1/2 or 0.5

Therefore, the answer is either 0 or 0.5. From the choices, the answer would be letter C.

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Use logarithmic differentiation to find dy/dx if y=(cosx)sinx. Write the derivative in terms of x only. Show all your work.

gladu [14]

Step-by-step explanation:

y = (cos x)^(sin x)

Take log both sides.

ln y = ln ((cos x)^(sin x))

ln y = (sin x) ln (cos x)

Take derivative.

1/y dy/dx = (sin x) (1/cos x) (-sin x) + (cos x) ln (cos x)

dy/dx = y [ (cos x) ln (cos x) − sin x tan x ]

dy/dx = (cos x)^(sin x) [ (cos x) ln (cos x) − sin x tan x ]