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Yakvenalex [24]
3 years ago
8

A line that includes the point (7, -2) has a slope of 1. What is its equation in slope-intercept

Mathematics
1 answer:
kompoz [17]3 years ago
6 0

Answer:

Y = x - 9

Step-by-step explanation:

A slope of 1 = x

So we have

Y = x

To find y intercept we do

7 - (-2) = 9

So we have a y-intercept of 9

Y = x - 9

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To explain this answer, the data showed the coherent rate of like and dislike, hence the data showed among the population ages, 26-53 years old disliked the movie as chosen as the above answer. Keeping the keenness to specificities in statistics is an important aspect in interpreting and discussing the results of a specific descriptive data. In which this case, explains and clearly showed the data on first what is the rating and second who in the group was involved in this certain event or phenomenon.</span>



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2. Calculate an expression for dy/dx and d2y/dx2 in terms of t if the parametric pair is given as tan(x) = e^at and e^y = 1 + e^
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I assume a is a constant. If tan(x) = exp(at) (where exp(x) means eˣ), then differentiating both sides with respect to t gives

sec²(x) dx/dt = a exp(at)

Recall that

sec²(x) = 1 + tan²(x)

Then we have

(1 + tan²(x)) dx/dt = a exp(at)

(1 + exp(2at)) dx/dt = a exp(at)

dx/dt = a exp(at) / (1 + exp(2at))

If exp(y) = 1 + exp(2at), then differentiating with respect to t yields

exp(y) dy/dt = 2a exp(2at)

(1 + exp(2at)) dy/dt = 2a exp(2at)

dy/dt = 2a exp(2at) / (1 + exp(2at))

By the chain rule,

dy/dx = dy/dt • dt/dx = (dy/dt) / (dx/dt)

Then the first derivative is

dy/dx = (2a exp(2at) / (1 + exp(2at))) / (a exp(at) / (1 + exp(2at))

dy/dx = (2a exp(2at)) / (a exp(at))

dy/dx = 2 exp(at)

Since dy/dx is a function of t, if we differentiate dy/dx with respect to x, we have to use the chain rule again. Suppose we write

dy/dx = f(t)

By the chain rule, the derivative is

d²y/dx² = df/dx

d²y/dx² = df/dt • dt/dx

d²y/dx² = (df/dt) / (dx/dt)

d²y/dx² = 2a exp(at) / (a exp(at) / (1 + exp(2at)))

d²y/dx² = 2 (1 + exp(2at))

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2 years ago
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