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Tpy6a [65]
3 years ago
7

Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x)= −1x + 1

Mathematics
2 answers:
Simora [160]3 years ago
8 0

They have the same slope. The slope of f(x) is 3 because it is the m in f(x)=mx+b. In the graph of g(x), the slope can be found by change in y divided by change in x, or rise over run. Between x=0 and x=1, the y value increases by three, from 2 to 5. The slope of g(x) is 3/1=1.

Hope this helps!

Arlecino [84]3 years ago
6 0

Answer with explanation

The Function , f(x)= -1 x +1

Slope of f(x)=-1

Equation of function , g(x),that is, line passing through ,(0,3) and (2,-1) can be obtained by

Equation of line passing through two points , (x_{1},y_{1}), (x_{2},y_{2}) is,

      \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

→\frac{y-3}{x-0}=\frac{3+1}{0-2}\\\\ \frac{y-3}{x}=\frac{4}{-2}\\\\y-3=-2 x\\\\ 2 x+y=3

g(x)= 2 x+y=3

y= -2 x+3

Slope of g(x)= -2  

-1 > -2

So, Slope of f(x) > Slope of g(x)

Option a: The function f(x) has a larger slope.

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Answer:

C: -|x| + 3

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From the graph, we see that when y = 2, x is either +1 or -1

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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
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Answer:

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

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Applying Pythagoras theorem while drawing a diagonal to the rectangle

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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

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Upon differentiating we get

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

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

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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.

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