Identify the constant of proportionality in the graph.
2 answers:
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<h3>Answer: roughly 12.6274 meters</h3>
The more accurate value is 12.6274169979696, though it's not fully exact.
Round this however you need to.
The exact distance 32*sin(45) - 10 meters.
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Explanation:
Refer to the diagram below.
I'll use point A in place of point O since the letter 'oh' is very similar looking to the number zero.
Plot point A at the origin (0,0). While at point A, look directly north. Then turn 30 degrees eastward to look at the bearing 030°. Next, move 20 meters along that bearing direction to arrive at point R. Segment AR is 20 meters long.
In the diagram, note how angle RAB is 30 degrees. The side opposite this is BR = m.
We can use the sine ratio to say that
sin(angle) = opposite/hypotenuse
sin(A) = BR/AR
sin(30) = m/20
m = 20*sin(30)
m = 10
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While still at point A, look directly north and turn 135 degrees clockwise (ie toward the east) and move 32 meters along that bearing. You'll arrive at point S as the diagram shows.
Notice how
angle RAB + angle RAC + angle CAS = 30+60+45 = 135
The remaining angle DAS is 180-135 = 45 degrees.
When focusing on triangle DAS, we can say
sin(A) = DS/AS
sin(45) = n/32
n = 32*sin(45)
n = 22.6274169979696
This value is approximate.
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Subtract the values of m and n
n - m = 32*sin(45) - 10 = exact distance
n - m = 22.6274169979696 - 10
n - m = 12.6274169979696
n - m = 12.6274 = approximate distance
Round it however you need to. I'm choosing to round to four decimal places.
So we see that point S is roughly 12.6274 meters east of point R.
If your teacher wants the exact distance, then stick with 32*sin(45)-10.
Answer:
- 7-5 => 2
- -7+5 => -2
- -7-5 => -12
- 7-(-5) => 12
Step-by-step explanation:
Lets solve the expressions one by one
<u>1. 7-5</u>
we can see that it is simple subtraction. A smaller number is being subtracted from a large number.
So the answer is 2
<u>2. -7+5</u>
There are two numbers with different signs. When there is a number with plus and a number with minus both quantities are subtracted but the larger quantity determines the sign of the answer.
In this case, 7 is larger and has negative sign, the answer will be -2
<u>3. -7-5</u>
When there are two numbers with minus sign they are added but the answer has the minus sign with it.
So the answer will be: -12
<u>4. 7-(-5)</u>
When minus is multiplied with minus it converts to positive
So
Hence,
- 7-5 => 2
- -7+5 => -2
- -7-5 => -12
- 7-(-5) => 12
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Answer:
(a) x: Ferris wheel once; y: roller coaster once
Step-by-step explanation:
The coefficients of x and y are both 1 in the equation representing the statement ...
"if he rides them each once, it takes 14 minutes total."
That tells you that x and y represent the times for one ride.
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The coefficient of x is 6 in the equation representing the statement ...
"he rides the Ferris wheel 6 times ..."
This tells you the variable x represents the Ferris wheel ride time. It is further confirmation that x represents the time for one ride.
