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Finger [1]
3 years ago
5

What is the equation of the line that passes through the point (-6,-6)and has a slope of -\frac{1}{3}− ?

Mathematics
1 answer:
Gnesinka [82]3 years ago
3 0

9514 1404 393

Answer:

  y +6 = (-1/3)(x +6)

Step-by-step explanation:

Given a point and a slope, it is appropriate to use the point-slope form to represent the equation:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

For your point and slope, the equation is ...

  y -(-6) = -1/3(x -(-6))

  y +6 = -1/3(x +6)

__

Of course, this can be rearranged to whatever form you need.

  y = -1/3x -8 . . . . slope-intercept form

  x +3y = -24 . . . . standard form

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Finding Derivatives Implicity In Exercise,Find dy/dx implicity.<br> x2e - x + 2y2 - xy = 0
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Answer:

the question is incomplete, the complete question is

"Finding Derivatives Implicity In Exercise,Find dy/dx implicity . x^{2}e^{-x}+2y^{2}-xy"

Answer : \frac{dy}{dx}=\frac{y-(2-x)xe^{-x}}{(4y-x)}

Step-by-step explanation:

From the expression  x^{2}e^{-x}+2y^{2}-xy" y is define as an implicit function of x, hence we differentiate each term of the equation with respect to x.

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for the expression \frac{d}{dx}(x^{2}e^{-x}) we differentiate using the product rule, also since y^2 is a function of y which itself is a function of x, we have

(2xe^{-x}-x^{2}e^{-x})+4y\frac{dy}{dx}-x\frac{dy}{dx} -y=0\\\\(2-x)xe^{-x}+(4y-x)\frac{dy}{dx}-y=0 \\.

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5 0
3 years ago
Heart failure is due to either natural occurrences (89%) or outside factors (11%). Outside factors are related to induced substa
Firdavs [7]

Answer:

a) 11% probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors.

b) 0.0871 = 8.71% probability that third patient with heart failure that enters the emergency room is the first one due to outside factors.

c) The mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors is 9.09.

Step-by-step explanation:

We have these following probabilities:

89% probability that a patient has heart failure due to natural occurrences.

11% probability that a patient has heart failure due to outside factors.

A) What is the probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors?

We assume that causes of heart failure between individuals are independent, which means that the probabilities are the same for each patient. So:

11% probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors.

B) What is the probability that third patient with heart failure that enters the emergency room is the first one due to outside factors?

First two due to natural occurrences, each with 89% = 0.89 probability.

Third due to outside factors, with 11% = 0.11 probability. So

0.89*0.89*0.11 = 0.0871

0.0871 = 8.71% probability that third patient with heart failure that enters the emergency room is the first one due to outside factors.

C) What is the mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors?

11% with outside factors, so the mean number of patients before the first with outside factors is given by

m = 1/0.11 = 9.09

The mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors is 9.09.

4 0
3 years ago
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