Answer:
a. dy/dx = -2/3
b. dy/dx = -28
Step-by-step explanation:
One way to do this is to assume that x and y are functions of something else, say "t", then differentiate with respect to that. If we write dx/dt = x' and dy/dt = y', then the required derivative is y'/x' = dy/dx.
a. x'·y^3 +x·(3y^2·y') = 0
y'/x' = -y^3/(3xy^2) = -y/(3x)
For the given point, this is ...
dy/dx = -2/3
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b. 2x·x' +x^2·y' -2x'·y^3 -2x·(3y^2·y') + 0 = 2x' + 2y'
y'(x^2 -6xy^2 -2) = x'(2 -2x +2y^3)
y'/x' = 2(1 -x +y^3)/(x^2 +6xy^2 -2)
For the given point, this is ...
dy/dx = 2(1 -0 +27)/(0 +0 -2)
dy/dx = -28
_____
The attached graphs show these to be plausible values for the derivatives at the given points.
For there to be 1 car, we consider two possible outcomes:
The first door opened has a car or the second door opened has a car.
P(1 car) = 2/6 x 4/5 + 4/6 x 2/5
P(1 car) = 8/15
For there to be no car in either door
P(no car) = 4/6 x 3/5
P(no car) = 2/5
Probability of at least one car is the sum of the probability of one car and probability of two cars:
P(2 cars) = 2/6 x 1/5
= 1/15
P(1 car) + P(2 cars) = 8/15 + 1/15
= 3/5
Answer:
The maximum value of the confidence interval for this set of survey results is 51.73%.
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
These bounds depend on the sample proportion and on the margin of error.
The lower bound is the sample proportion subtracted by the margin of error.
The upper bound is the margin of error added to the sample proportion.
In this question:
Sample proportion: 46.1%
Margin of error: 5.63%.
Maximum value is the upper bound:
46.1+5.63 = 51.73
The maximum value of the confidence interval for this set of survey results is 51.73%.
Y = -3/2x + 4...slope is -3/2
A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So that means the slope we will need is 2/3...see how I flipped the slope and changed the sign.
Now we use y = mx + b....slope(m) = 2/3....(3,9)...x = 3 and y = 9.
Time to sub...we r looking for b, the y intercept.
9 = 2/3(3) + b
9 = 2 + b
9 - 2 = b
7 = b
so the perpendicular equation is : y = 2/3x + 7...but we need it in Ax + By = C form....
y = 2/3x + 7....multiply by common denominator of 3 to get rid of fractions
3y = 2x + 21...subtract 2x from both sides
-2x + 3y = 21....<== ur answer...normally, I would have multiplied this by -1 to make x positive...but that is not an answer choice
