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3 years ago

The slope of the tangent to the curve y^3x + y^2x^2 = 6 at (2,1)

1 answer:

7 0

Y^3x + y^2x^2 = 6

Using implicit differentiation 

3 y^2.y'.x+y^3+2 y.y'.x^2+2 y^2.x=0

y'(3 y^2.x+2 y. x^2) = -y^3-2 y^2.x 

y' = -[y^2(y+2 x)]/[x y(3 y+2 x)] 

= -[y(y+2 x)]/[x(3 y+2 x)] 

Substituting x =2 and y = 1:

y' = -(1)(1+4)/[2(3+4)] 
 = -5/14 

The slope of the tangent of the curve at (2,1) will be:
m = -5/14

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two times a number is subtracted from 25 the result is the same as when it is added to six times.find the number

ExtremeBDS [4]

Answer:

6.3

Step-by-step explanation:

1. 25 - 2n = n + 6

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2 years ago

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aleksley [76]

Answer: c. 150g of sugar dissolved in 300ml water

Step-by-step explanation:

The concentration of sugar syrup will decide which syrup is sweetest. Concentration is defined as the amount of solute dissolved per unit volume of solution.

a) 50g of sugar dissolved in 150ml water

$Concentration=\frac{50g}{150ml}=0.33g/ml$

b) 100g of sugar dissolved in 500ml water

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c) 150g of sugar dissolved in 300ml water

$Concentration=\frac{150g}{300ml}=0.5g/ml$

d) 250g of sugar dissolved in 1000ml water

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3 years ago

The area of a rectangle is 60 cm2 If the width of the

aleksklad [387]

The length of the rectangle is 10 cm and perimeter of the rectangle is 32 cm.

Step-by-step explanation:

Given,

The area of rectangle = 60 sq cm

Width (b) of the rectangle = 6 cm

To find the length and perimeter of the rectangle.

Formula

The area of the rectangle = l×b

The perimeter of the rectangle = 2(l+b)

According to the problem,

l×b = 60

or, l×6 = 60

or, l = 60÷6 = 10

Length (l) = 10 cm

Perimeter = 2×(10+6) cm = 32 cm

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3 years ago

Evaluate tan45/sin30 . In your final answer, include all calculations.

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From the identity $\displaystyle{ \tan x= \frac{\sin x}{\cos x}$ , and from the values:

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We also know that $\sin30^{\circ}= \frac{1}{2}$ .

Thus, $\displaystyle{ \frac{\tan 45^{\circ}}{\sin30^{\circ}} = \frac{1}{\frac{1}{2}}=2.$

Answer: 2

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