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Oliga [24]
3 years ago
9

Tiana looks at a map to find the best route from her house to her friend's house. the map has a scale of 4 centimeters = 3 miles

. The distance of the route is 8 centimeters on the map
Mathematics
1 answer:
Luden [163]3 years ago
8 0

Answer: 6

Step-by-step explanation:

4 centimeters times what gives u 8 centimeters

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A linear function and an exponential function are graphed below. Find possible formulas for the functions f(t), in blue, and g(t
Zielflug [23.3K]

Answer:

f(t) = -t + 21

g(t) = 18*e^( - t / 12 + 1/4 )

Step-by-step explanation:

Given:

- The graphs for the similar question is attached.

- The same graph would be used as reference but with different coordinates for point of intersection of f(t) and g(t) @ ( 3 , 18 ) & ( 15 , 6 ).

Find:

- The formulas for functions f(t) and g(t).

Solution:

- First we will determine f(t) the blue graph which is a "linear" function. The general equation for the linear function is given as:

                                    f(t) = m*t + c

Where, m: is the gradient  ( constant )

            c: The f(t) intercept. ( constant )

- The gradient m can be determined by the given points that lie on the graph:

                         m = ( f(t2) - f(t1) ) / ( t2 - t1 )

                         m = ( 6 - 18 ) / ( 15 - 3 )

                         m = -12 / 12 = -1

- The constant c can be evaluated by using any one point and m substituted back into the linear expression as follows:

                          f(t) = -t + c

                          18 = -(3) + c

                           c = 21

- The function f(t) is as follows:

                            f(t) = -t + 21

- The general expression for an exponential function can be written as:

                           g(t) = a*e^(b*t)

Where, a and b are constants to be evaluated.

- We will develop two expressions for g(t) using two given points that lie on the curve as follows:

                           18 = a*e^(3*b)

                           6 = a*e^(15*b)

- Divide the two expressions we have:

                           3 = e^( 3b - 15b )

                           Ln(3) = -12*b

                           b = - Ln(3) / 12

- Then the expression 1 becomes:

                          18 = a*e^( - Ln(3)*3 / 12)

                          18 = 3*a*e^(-1/4)

                           6 = a / e^(0.25)

                           a = 6*e^( 1 / 4 )

- The function g(t) can be expressed as:

                          g(t) = 18*e^( - t / 12 + 1/4 )

3 0
3 years ago
The perimeter of a college athletic field is 96 meters and the length is 16 m more than the width. Find the length and width.
Andre45 [30]
In order to figure this out, you are going to do the math backwards. If the perimeter of the entire field is 96 meters, you will want to remove 16, which will give you 80 meters. You will then divide this by 2, giving you 40 meters. The width of the field will be 40 meters. That means that the length of the field is going to be 56 meters.
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3 years ago
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KonstantinChe [14]

Answer:

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2 years ago
Gail bought 1180 buttons to put on the shirts she she makes. She uses 6 buttons for each shirt. How shirts can Gail make with th
stepladder [879]
To answer this question, we need o divide.

Since she has 1180 buttons, we can divide that number by the amount of buttons it takes to make a shirt, 6.

1180/6=196

Hope this helps!
8 0
3 years ago
Read 2 more answers
The polygons are similar. Find the missing side length.
zloy xaker [14]

Answer:

44

Step-by-step explanation:

Since triangles are similar, so their corresponding sides would be in proportion.

Therefore,

\frac{24}{32}  =  \frac{33}{?}  \\  \\  \\ ? =  \frac{32 \times 33}{24}  \\  \\ ? =  \frac{4\times 33}{3} \\  \\ ? =  4\times 11 \\  \\  ? =  44 \: units

6 0
2 years ago
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