Write the equation of the trigonometric graph.

The scale on a map is 1: 75 000. (a) Calculate the ACTUAL distance, in km, between two places which are 16 cm apart on the map.

finlep [7]

Answer:

a. 1 200 000 km

b. 0.000 773 cm

c. 67 500 000 000 km²

d. 0.000 000 016 cm²

Step-by-step explanation:

a. Calculate the ACTUAL distance, in km, between two places which are 16 cm apart on the map.

Since the scale is 1 : 75000 that is 1 cm : 75000 km, we want to find the actual distance of 16 cm on the map. Let x be the actual distance in km.

So, 1 cm : 75000 km = 16 cm : x km

So, 1 cm/75000 km = 16 cm/x km

Thus x km = 16 cm × 75000 km/1 cm = 1 200 000 km

(b) Calculate length of a road on the map which is 0.58 km.

Let y be the length of road on the map. So, using our scale

1 cm : 75000 km = y cm : 0.58 km

So, 1 cm/75000 km = y cm/0.58 km

Thus y cm = 0.58 km × 1 cm/75000 km = 0.000 773 cm

(c) Calculate, in km², the ACTUAL area of a lake which is 12 cm2 on the map.

Since the scale is 1 : 75000 , the scale for the area would be the square of this. So, 1² : 75000² = 1 : 5 625 000 000 which is 1 cm² : 5 625 000 000 km²

Let z be the actual area of the lake.

So, 1 cm² : 5 625 000 000 km² = 12 cm² : z km²

So, 1 cm²/5 625 000 000 km² = 12 cm²/z km²

Thus z km² = 12 cm² × 5 625 000 000 km²/1 cm² = 67 500 000 000 km²

(d) Calculate the area of a play field on the map which has has an actual area of 90 km².

Let a represent the area of the play field on the map. Using our scale for the area,

1 cm² : 5 625 000 000 km² = a cm² : 90 km²

So, a cm² = 90 km² × 1/5 625 000 000 km² = 0.000 000 016 cm²

4 0

2 years ago

Which statement is true about this argument? premises: if an angle measure is greater than 90°, then the angle is an obtuse angl

vazorg [7]

Answer: option d. the argument is valid by the law of detachment.

The law of detachment consists in make a conlcusion in this way:

Premise 1) a => b
Premise 2) a is true

Conclusion: Then, b is true

Note: the order of the premises 1 and 2 does not modifiy the argument.

IN this case:

Premise 1) angle > 90 => obtuse

Premise 2) angle = 102 [i.e. it is true that angle > 90]]

Conclusion: it is true that angle is obtuse

3 0

3 years ago

Read 2 more answers

It takes a bear 9 more days to eat a barrel of honey alone than it takes the bear and a second bear to eat the barrel of honey t

Rudik [331]

Answer:

it takes the bears 12 days to eat honey together.

Step-by-step explanation:

1/x+9+1/x+16=1/x

(solve this using cross multiplication)

= x^2 = 144

x=12

8 0

2 years ago

Calculate the x and y-intercept for the line: y=-2x+8

Kryger [21]

x-intercept, y = 0:
-2x + 8 =0
-2x = -8
x= -8/-2 = 4

y-intercept, x =0
y = 8

3 0

3 years ago

Mary eats 5 bananas and an additional 2 bananas when she works out for 2 hours. Represent the number of bananas that she eats wh

ElenaW [278]

For this item, we let x be the number of hours she works out and y be the total number of bananas that she will be eating after the workout. The expression that best described the given above is,
y = 5 + 2x
5 is given as the y-intercept because of the initial condition.

8 0

3 years ago