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3 years ago

If x√(1+y) + y√(1+x) = 0 , then dy/dx = ?

1 answer:

6 0

$DIFFERENTIAL \: \: \: CALCULUS \\ \\ \\ Given \: expression \: - \\ \: \\ x \sqrt{1 + y} \: = \: y \sqrt{1 + x} \\ \\ x \sqrt{1 + y} \: = \: - y \sqrt{1 + x} \\ \\ \\ Squaring \: both \: sides \: , \: We \: get \: - \: \\ \\ {x}^{2} (1 + y) = {y}^{2} (1 + x) \\ \\ {x}^{2} + {x}^{2} y - {y}^{2} - x {y}^{2} = 0 \\ \\ ( {x}^{2} - {y}^{2} ) + xy(x - y) = 0 \\ \\ (x - y)(x + y + xy) = 0 \\ \\ Therefore \: , \: either \: \: y=x \: \: or \: \\ \: \: \: \: \: \: \: \: \: \: \: x+y+xy=0 \\ \\ \\ Since \: , \: \: x=y \: \: doesn't \: satisfy \: the \\ given \: function \: , \: we \: reject \: it \\ \\ x + y + xy = 0 \\ \\ y \: \: = \: \: \frac{ - x}{1 + x} \\ \\ \frac{dy}{dx} \: \: = \: - \: \frac{(1 + x) - x.1}{ {(1 + x)}^{2} } \\ \\ \\ \frac{dy}{dx} = \frac{ - 1}{( {1 + x)}^{2} } \: \: \: \: \: \: \: \: \: Ans.$

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The cost of a High Definition television now averages $700, but the cost is decreasing about 15% per year. In how many years wil

Roman55 [17]

Answer: 7.7 years

Step-by-step explanation:

Given

The cost of HD TV is $700 and it is decreasing at the rate of 15% per year

After one year it becomes

$\Rightarrow 700-700\times 15\%\\\Rightarrow 700(1-0.15)$

after 2 year it becomes

$\Rightarrow 700(1-0.15)-700(1-0.15)\times 15\%\\\Rightarrow 700(1-0.15)(1-0.15)\\\Rightarrow 700(1-0.15)^2$

Suppose, after x years it becomes $200

$\Rightarrow 200=700(1-0.15)^x\\\\\Rightarrow \dfrac{2}{7}=0.85^x\\\\\text{Taking log both sides}\\\\\Rightarrow x=\dfrac{\ln (\frac{2}{7})}{\ln (0.85)}\\\\\Rightarrow x=7.7\ \text{years}$

Thus, it takes 7.7 years for the cost to come under $200.

3 0

2 years ago

How do I find this, what’s the formula to find the 20th term and can anyone explain the formula? Will award brainliest

harina [27]

Answer:

f(n) = n^2 +1
f(20) = 401

Step-by-step explanation:

The first differences of the sequence are ...

5-2 = 3
10-5 = 5
17-10 = 7
26-17 = 9
37-26 = 11

Second differences are ...

5 -3 = 2
7 -5 = 2
9 -7 = 2
11 -9 = 2

The second differences are constant, so the sequence can be described by a second-degree polynomial.

We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...

f(n) = an^2 + bn + c

Then the first three terms of the sequence are ...

f(1) = 2 = a·1^2 + b·1 + c
f(2) = 5 = a·2^2 +b·2 + c
f(3) = 10 = a·3^2 +b·3 +c

Subtracting the first equation from the other two gives ...

3a +b = 3

8a +2b = 8

Subtracting the first of these from half the second gives ...

(4a +b) -(3a +b) = (4) -(3)

a = 1 . . . . . simplify

Substituting into the first of the 2-term equations, we get ...

3·1 +b = 3

b = 0

And substituting the values for a and b into the equation for f(1), we have ...

1·1 + 0 + c = 2

c = 1

So, the formula for the sequence is ...

f(n) = n^2 + 1

The 20th term is f(20):

f(20) = 20^2 +1 = 401

_____

Comment on the solution

It looks like this matches the solution of the "worked example" on your problem page.

4 0

3 years ago

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ale4655 [162]

Answer:

1. Is

2. Is

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8 0

3 years ago

X.7=14 plz help me 4th grade work

OlgaM077 [116]

x*7=14

14/7=2

x=2

brainliest please

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3 years ago

You have 15 pennies in your pocket. Of those pennies, 3 are Canadian. Suppose you pick a penny out of your pocket at random. Fin

den301095 [7]

The best and most correct answer among the choices provided by your question is the fourth choice or letter D. The probability is 4/5.

P ( canadian)= 3/15 = 1/5
On the other hand, P (not canadian) = 1 - 1/5 = 4/5

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

4 0

3 years ago