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seropon [69]
3 years ago
12

1. Evaluate the function f(x)=3x-1 using the domain of -2, 0, 3, and 5. Results are to be shown in a table.

Mathematics
2 answers:
GaryK [48]3 years ago
7 0

Answer:

Step-by-step explanation:

1) . The given function is f(x) = 3x - 1

Using the domain or value of x = -2, 0, 3, and 5 we have to formulate a table for the value of the function.

f(-2) = 3(-2) - 1

      = -7

f(0) = 3×0 - 1

     = -1

f(3) = 3(3) - 1

     = 9 - 1

     = 8

f(5) = 3(5) - 1

     = 15 - 1

     = 14

x     -2     0    3     5

y      -7    -1     8    14

2). Since f(x) = 3x - 1

Now we can rewrite the function in the form of an equation.

y = 3x - 1

To formulate the inverse of the given function we will flip x by y.

x = 3y - 1

then we will solve it for the value of y.

3y = x + 1

y = \frac{1}{3}(x + 1)

Or f^{-1}(x)=\frac{1}{3}(x+1)

Now this inverse function will be defined for all real numbers.

Therefore, domain of f^{-1}(x) will be all real numbers.

IceJOKER [234]3 years ago
6 0

Answer:

See explanation

Step-by-step explanation:

You are given the function f(x)=3x-1

The domain of the function are all possible values of variable x, so you can find f(x) for x=-2, 0, 3, 5:

f(-2)=3\cdot (-2)-1=-6-1=-7\\ \\f(0)=3\cdot 0-1=0-1=-1\\ \\f(3)=3\cdot 3-1=9-1=8\\ \\f(5)=3\cdot 5-1=15-1=14

The table is

\begin{array}{cc}x&f(x)\\-2&-7\\0&-1\\3&8\\5&14\end{array}

The inverse function f^{-1}(x) has the domain which is the range of the function f(x) (all possible values of f(x)), so the domain of inverse function is {-7,-1,8,14}

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On a morning of a day when the sun will pass directly​ overhead, the shadow of a 60​-ft building on level ground is 25 ft long.
AysviL [449]

Answer:

The shadow is decreasing at the rate of 3.55 inch/min

Step-by-step explanation:

The height of the building = 60ft

The shadow of the building on the level ground is 25ft long

Ѳ is increasing at the rate of 0.24°/min

Using SOHCAHTOA,

Tan Ѳ = opposite/ adjacent

= height of the building / length of the shadow

Tan Ѳ = h/x

X= h/tan Ѳ

Recall that tan Ѳ = sin Ѳ/cos Ѳ

X= h/x (sin Ѳ/cos Ѳ)

Differentiate with respect to t

dx/dt = (-h/sin²Ѳ)dѲ/dt

When x= 25ft

tanѲ = h/x

= 60/25

Ѳ= tan^-1(60/25)

= 67.38°

dѲ/dt= 0.24°/min

Convert the height in ft to inches

1 ft = 12 inches

Therefore, 60ft = 60*12

= 720 inches

Convert degree/min to radian/min

1°= 0.0175radian

Therefore, 0.24° = 0.24 * 0.0175

= 0.0042 radian/min

Recall that

dx/dt = (-h/sin²Ѳ)dѲ/dt

= (-720/sin²(67.38))*0.0042

= (-720/0.8521)*0.0042

-3.55 inch/min

Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min

8 0
3 years ago
Hello someone please help me
Naya [18.7K]

Answer:

(2, -8)

Step-by-step explanation:

6 0
3 years ago
Two numbers that differ by 46
Reil [10]

the complete question is

Find two numbers whose difference is 46 and whose product is a minimum


Let

x------->larger number

y-------> smaller number

P-------> product of the two numbers


we know that

x-y=46\\ y=x-46-----> equation 1

P=x*y-----> equation 2


substitute equation 1 in equation 2

P=x*[x-46]\\ P=x^{2} -46x


using a graph tool

see the attached figure


Find the value of x for that the product P is a minimum

the vertex is the point (23,-529)

that means, for x=23

the product is a minimum P=-529


find the value of y

y=x-46\\ y=23-46\\ y=-23


therefore


the answer is

the numbers are 23 and -23

7 0
3 years ago
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Rise over run is 7 over 2 so 7/2 is the slope
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If you scale a figure by less than 1 or less than 100%, does the new copy increase or decrease in size? *​
nasty-shy [4]

Answer:

Decrease

Step-by-step explanation:

It gets smaller because it is 100% is full size, so less would make it smaller

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