A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the caris 30 mph slower than twice the speed of the motorcycleIn two hours, the car is 20 miles ahead of the motorcycle. Find thespeed of both the car and the motorcycle, in miles per hour.
Answers
time is 2
distance of car is:
d_c = d_m + 20, d_m is distance of motorcycle.
speed is defined as:
s = d/t, distance over time.
hence:
d_c/2 = s_c = d_m/2 + 10
s_c = s_m + 10
from problem statement we know:
s_c = 2s_m - 30
so we have 2 simultaneous equations:
s_c = s_m + 10
s_c = 2s_m - 30
multiply second by -1 and sum them both:
s_c = s_m + 10
-s_c = -2s_m + 30
-------------------------
0 = -s_m + 40
s_m = 40
that is the speed of the motorcycle
s_c = s_m + 10
s_c = 40 + 10
s_c = 50
that is the speed of car, both speeds in miles per hour
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Owen’s grandmother put some money into his savings account on the day he was born. Today, Owen turns 18 years old, and he’s discovered that he has earned $225 in simple interest on his grandmother’s money. If the yearly interest rate was 5%, how much money did his grandmother deposit at the time of his birth?
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Simplify the expression in exponential notation. a a a
L{ sin(at) * [1/2 ( 1 - cos(2at)]}
1/2 L{sin(at)} - 1/2 L{cos(2at)*sin(at)}
1/2 * (a^2)/(s^2 + a^2) - 1/2 L{cos(2at)*sin(at)}
Answers
sin(at)*cos(2at)=1/2[sin(3at)-sin(at)]
The range of the graph is all real numbers.
The domain of the graph is all real numbers less than or equal to 0.
The range of the graph is all real numbers greater than or equal to 0.
Answers
Answer:
D
Step-by-step explanation:
only takes positive inputs and only outputs positive integers
Answers
Answers
Final Answer:
The largest scale map is indicated by the representative fraction 1:1. Option A is correct.
Explanation:
In cartography, the representative fraction (RF) of a map indicates the scale of the map, specifically the ratio between a distance on the map and the corresponding distance on the Earth's surface. A larger RF value means a larger scale map, which represents smaller areas with more detail.
Now, let's compare the given options:
1. 1:1 - This RF means that one unit on the map represents one unit on the ground, essentially a one-to-one scale. It doesn't get any larger than this, so this is the largest scale possible.
2. 1:0 - This doesn't make sense in cartography because you cannot represent the Earth's surface with zero on one side of the ratio. It's an invalid option.
3. 1:1,000,000 - This RF indicates that one unit on the map represents one million units on the ground. This is a much smaller scale compared to 1:1, so it represents a much larger area with less detail.
4. 1:24,000 - This RF means that one unit on the map represents 24,000 units on the ground. While this is a larger scale than 1:1,000,000, it is still smaller than 1:1, which is the largest scale.
In summary, the largest scale map is represented by 1:1. Option A is the answer.
Learn more about fraction
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Answer:
The representative fraction (RF) of a map indicates the scale of the map. In a representative fraction, the first number represents a unit of measurement on the map, and the second number represents the corresponding unit of measurement in the real world.
Among the options provided, a larger scale map would have a smaller second number because it means that one unit of measurement on the map represents a smaller unit of measurement in the real world. So, the largest scale map in the given options is:
1:24,000
In this case, 1 unit on the map represents 24,000 units in the real world, indicating a very detailed and large-scale representation of the area.
2) (0,4)
3) (1,-1)
4) (-3,3)
Answers
y+2x=1
3x=-3
x=-1
substitute to any equation
y-x=4
y+1=4
y=3