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aev [14]
3 years ago
6

Solve the system by substitution. y=2x^2-3x-1 y=x-3

Mathematics
2 answers:
padilas [110]3 years ago
6 0
The answer is B(1,-2). This is the only point where the two lines intercept. & if you plug the numbers into the equations they fit.
vekshin13 years ago
4 0

Answer:  The correct option is (B) (1, -2).

Step-by-step explanation:  We are given to solve the following system of equations by substitution method :

y=2x^2-3x-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

Substituting the value of y from equation (ii) in equation (i), we get

x-3=2x^2-3x-1\\\\\Rightarrow 2x^2-4x+2=0\\\\\Rightarrow x^2-2x+1=0\\\\\Rightarrow (x-1)^2=0\\\\\Rightarrow x-1=0,~~~x-1=0\\\\\Rightarrow x=1,1.

Substituting x = 1 in equation (ii), we get

y=1-3=-2.

Thus, the required solution is (x, y) = (1, -2).

Option (B) is correct.

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"A rectangle has a height of 5 cm and its base is increasing at a rate" of 3/2 cm/min. When its area is 60 cm2, at what rate is
sukhopar [10]

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The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

Step-by-step explanation:

Dimensions of the rectangle

Height = 5cm

Rate of base = 3/2 cm/min

Area = 60cm^2

We know the area of a rectangle of given by = base* Height

b*h = 60

b*5 = 60

b = 12cm

Applying Pythagoras theorem while drawing a diagonal to the rectangle

  b^2 +h^2 =  D^2\\

 5^2 +12^2 = 13^2

so our diagonal will be 13cm  

Upon differentiating the area of the rectangle  we get

b*h = A=60cm^2

using  the chain rule of differentiation

h*db/dt + b*dh/dt  = 0

b*dh/dt = -h*db/dt

12*dh/dt = -5*3/2

dh/dt = -5/8 cm//min

so the height of the rectangle is decreasing at the rate of -5/8cm/min

now we have all the measurements we need

b = 12 , db/dt = 3/2cm/min

h = 5 , dh/dt = -5/8 cm/min

b^2 +h^2  = D^2

Upon differentiating we get

2b*db/dt + 2h*dh/dt = 2D*dD/dt

b*db/dt + h*dh/dt = D*dD/dt

12*3/2 + 5*(-5/8) = 13*dD/dt

18 -25/8 = 13*dD/dt

\frac{144-25}{8} = 13*dD/dt

dD/dt = \frac{119}{104} cm/min

Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

6 0
3 years ago
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