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3 years ago

What is an equation of the line that passes through the point (-1,-7) and is perpendicular to the line x+y=6x

Mathematics

1 answer:

julia-pushkina [17]3 years ago

7 0

Answer: y = -1/5x - 36/5

Hope this is right with the weird fractions. Work in pic:

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If w = 5 cos (xy) − sin (xz) and x = 1/t , y = t, z = t^3 ; then find dw/dt

Scrat [10]

In this question, we find the derivatives, using the chain's rule.

Doing this, the derivative is:

$\frac{dw}{dt} = \frac{5}{t}(\sin{1} - \cos{1}) - 2t\cos{t^2}$

Chain Rule:

Suppose we have a function $w(x,y,z), x = x(t), y = y(t), z = z(t)$ , and want to find it's derivative as function of t. It will be given by:

$\frac{dw}{dt} = \frac{dw}{dx}\frac{dx}{dt} + \frac{dw}{dy}\frac{dy}{dt} + \frac{dw}{dz}\frac{dz}{dt}$

Thus, we have to find the desired derivatives, which are:

w of x:

$\frac{dw}{dx} = -5y\sin{(xy)} - z\cos{(xz)}$

Considering $x = \frac{1}{t}, y = t, z = t^3$

$\frac{dw}{dx} = -5t\sin{(1)} - t^3\cos{(t^2)}$

w of y:

$\frac{dw}{dy} = -5x\cos{(xy)}$

Considering $x = \frac{1}{t}, y = t$

$\frac{dw}{dy} = -\frac{5}{t}\cos{1}$

w of z:

$\frac{dw}{dz} = -x\cos{(xz)}$

Considering $x = \frac{1}{t}, z = t^3$

$\frac{dw}{dz} = -\frac{1}{t}\cos{(t^2)}$

Derivatives of x, y and z as functions of t:

$\frac{dx}{dt} = -\frac{1}{t^2}$

$\frac{dy}{dt} = 1$

$\frac{dz}{dt} = 3t^2$

Derivative of w as function of t.

Now, we just replace what we found into the formula. So

$\frac{dw}{dt} = \frac{dw}{dx}\frac{dx}{dt} + \frac{dw}{dy}\frac{dy}{dt} + \frac{dw}{dz}\frac{dz}{dt}$

$\frac{dw}{dt} = (-5t\sin{(1)} - t^3\cos{(t^2)})(-\frac{1}{t^2}) - (\frac{5}{t}\cos{1}) - (\frac{1}{t}\cos{(t^2)})3t^2$

Applying the multiplications:

$\frac{dw}{dt} = \frac{5}{t}\sin{1} + t\cos{t^2} - \frac{5}{t}\cos{1} - 3t\cos{t^2}$

Applying the simplifications:

$\frac{dw}{dt} = \frac{5}{t}(\sin{1} - \cos{1}) - 2t\cos{t^2}$

Which is the derivative.

For more on the chain rule, you can check brainly.com/question/12795383

8 0

3 years ago

Helppp asapppp!!!!right Answers please

evablogger [386]

Translation is 4 units left and 2 units down

6 0

3 years ago

There are 13 books on a shelf. 7 of these books are new. The rest of them are used.

emmainna [20.7K]

Answer:

6 of them are used books

Step-by-step explanation:

6+7=13. 7 new book and add 6 more book that will be used, it will equal out in addition = 13

3 0

3 years ago

there are 23 tables in the library. each table has 4 chairs. 3rd graders sit in all the chairs at 3 tables. fourth graders sit i

hichkok12 [17]

Answer:

14 tables left

Step-by-step explanation:

23-6-3= 14

5 0

3 years ago

The table shows the price for different quantities of sponge brushes offered at a wholesale art supply store. Which is the BEST

Hitman42 [59]

Answer:

The BEST value would be 70 brushes.

Step-by-step explanation:

First, get all the values per brush for all brushes listed.

20 / 11.80 = $1.70

35 / 17.15 = $2.04

50 / 27.50 = $1.81

70 / 45.50 = $1.53

80 / 36.00 = $2.22

So, as you can see we have the values for what a single brush would cost from each selection. 70 brushes would be the BEST value.

7 0

3 years ago

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