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grandymaker [24]
3 years ago
8

Multivariable Calculus Question:

Mathematics
1 answer:
vovangra [49]3 years ago
3 0
f(2,-1)=2^2-(-1)^2=3

so we're considering the level curve

x^2-y^2=3

The tangent line to this curve at (2, -1) will be the value of \dfrac{\mathrm dy}{\mathrm dx} at this point. Differentiating yields

2x-2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac xy

and so the slope of the tangent would be \dfrac2{-1}=-2.

The tangent line then has equation

y-(-1)=-2(x-2)\implies y=-2x+3
You might be interested in
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325. Writ
QveST [7]

Answer:


Step-by-step explanation:

Part A

We will use the slope intercept form of the line and then convert later.

Equation

y = mx + b is the general form

Givens

Two data points

(4,180)

(9,325)

Solution

325 = 9x + b

<u>180 = 4x + b</u>                Subtract

145 = 5x                      Divide by 5

145/5 = 5x/5               Do the division

29 = x                          This represents the cost / day

180 = 4x + b                 Substitute x = 29 to find b

180 = 4*29 + b             Combine

180 = 116 + b                Subtract 116 from both sides.

180 - 116 = b

64   = b

Solution for y = mx + b

y = 29x + 64

In Standard form this is

- 29x + y = 64 But the first number must be plus

29x - y = - 64 <<<< Answer A

Part B

y = 29x + 64

f(x) = 29x + 64

Part C

The graph is shown below. Various points are filled in using y = 29x + 64. The y intercept is (0,64) which is labeled. Let x = 1 , 2, 3, 4, ... 10 (which is arbitrary). This may be more easily done on a spreadsheet if you know how to use one to make graphs.


8 0
3 years ago
Can someone aswer this Please
IRISSAK [1]

Answer:

9 . 5/3

10. - 5/11

................................

4 0
2 years ago
8 divided by 2 (2+2). 1 or 16
laiz [17]

Answer:

16

Step-by-step explanation:

8/2(2+2)  

Following the order of operations (PEMDAS), combine the terms in your parentheses:

8/2(4)

Remember that we follow the order of operations from left to right.

Divide 8 into 2:

4(4)

Multiply:

16

8 0
3 years ago
For the month of November in a certain​ city, 88​% of the days are cloudy. Also in the month of November in the same​ city, 54​%
Gnoma [55]

Answer:

There is a 61.36% probability that a randomly selected day in November will be foggy if it is cloudy.

Step-by-step explanation:

We have these following probabilities:

An 88% probability that the day is cloudy.

An 54% probability that the day is both foggy and cloudy.

What is the probability that a randomly selected day in November will be foggy if it is cloudy​?

This is the percentage of days that are cloudy and foggy divided by those that are cloudy. So:

P = \frac{0.54}{0.88} = 0.6136

There is a 61.36% probability that a randomly selected day in November will be foggy if it is cloudy.

4 0
3 years ago
Help plz................
Pani-rosa [81]
You have the formula. Put in the numbers and solve for r.

The interest earned in 4 years on 5000 is (6500 -5000) = 1500.
.. I = Prt
.. 1500 = 5000*r*4
.. 1500/20000 = r = .075 = 7.5% . . . . . . matches selection B
7 0
3 years ago
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