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Leni [432]
3 years ago
5

Find dy/dx by implicit differentiation for x – y = xy.

Mathematics
2 answers:
frez [133]3 years ago
8 0

Answer:

\frac{dy}{dx} = \frac{1-y}{1+x}

Step-by-step explanation:

Differentiate xy using the product rule, then

Given

x - y = xy

1 - \frac{dy}{dx} = x. \frac{dy}{dx} + y. 1 = x\frac{dy}{dx} + y ( subtract 1 from both sides )

- \frac{dy}{dx} = x \frac{dy}{dx} + y - 1 ( subtract x \frac{dy}{dx} from both sides )

- \frac{dy}{dx} - x \frac{dy}{dx} = y - 1 ( multiply through by - 1 )

\frac{dy}{dx} + x\frac{dy}{dx} = 1 - y

\frac{dy}{dx} (1 + x) = 1 - y ← divide both sides by (1 + x)

\frac{dy}{dx} = \frac{1-y}{1+x}

Crazy boy [7]3 years ago
4 0

Answer:

- \frac{dy}{dx} = x. \frac{dy}{dx}

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The sector of a circle with a 12 inches radius has a central angle measure of 60°.
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5 0
3 years ago
large cheese pizzas cost $5 each and large one topping pizzas cost $6 each. write an equation that represents the total cost, T
Gelneren [198K]

Answer:

T = 5c +5d,    where unit of the equation is $.

Step-by-step explanation:

Cost of 1 large cheese  pizza = $5

No. of large cheese pizza = c

therefore

cost of c  large cheese pizza = c*Cost of 1 large cheese  pizza = $5c

Cost of 1 large one topping  pizza = $6

No. of large one topping pizza = d

therefore

cost of d  large one topping pizza = d*Cost of 1 large one topping  pizza =             cost of d  large one topping pizza = $6d  

Total cost of  c  large cheese pizza and cost of d  large one topping pizza

= $5c +$6d

total cost is represented by T

thus, T = $5c +$5d  Answer

4 0
3 years ago
In ∆PQR, ∠P = 90degrees , PQ= 12 cm, PR=16cm. Find ∠Q
siniylev [52]

Answer:

∠Q  = 53.13 degrees

Step-by-step explanation:

Given that ∆PQR, ∠P = 90degrees , this means that the triangle is a right angled triangle

Hence using the notation

SOH CAH TOA

where S is sine, C is cosine, T is tangent and O, A and H represents the size of the opposite, adjacent and hypotenuse sides

Considering  ∠Q and the given sides

PR=16cm is the opposite side,

PQ= 12 cm is the adjacent side hence we use TOA

Tan Q = 16/12 =

Q = Arc tan 16/12

= 53.13 degrees

5 0
2 years ago
Can someone please explain how to solve this.<br><br> p^-4 x -5p
solong [7]
P^-4 x -5p

In properties of exponents, if the exponent is negative then you move the variable with the negative exponent to the denominators place and it changes to positive and the numerator becomes 1.

p^-4=1/(p^4)

Also, if no exponent is present it is understood to be 1.

Keeping this in mind,
p^-4 x -5p
1/(p^4) x -5p^1            substituted p^-4 by 1/p^4 and added ^1 to -5p
-5p^1/p^4                     multiplied-5p^1 to 1 
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6 0
3 years ago
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