a farmer leans a 12-ft ladder against a barn. The base of the ladder is 3 ft from the barn. To the nearest tenth, how high on th
e barn does the ladder reach?
1 answer:
Answer:
11.6 ft
Step-by-step explanation:
I attached a diagram for you to easily visualize this problem.
To solve this problem, you would use the pythagorean theorem. The 12-ft ladder is the hypotenuse and the 3 ft from the barn is one of the side legs. You want to find the length of the "other side leg", or the height of the barn.
Substitute 3, 12, and x into the pythagorean theorem like so.
a^2 + b^2 = c^2
3^2 + x^2 = 12^2
Evaluate the exponents.
9 + x^2 = 144
Subtract 9 from both sides.
x^2 = 135
Square root both sides.
x = 11.618
Round this to the nearest tenth: 11.6 feet.
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The vertex-form equation is
y = a(x+1)² -16
Putting in the y-intercept values, we have
-15 = a(0+1)² -16
1 = a . . . . . . . . . . . add 16
Then the x-intercepts can be found where y=0.
0 = (x+1)² -16
16 = (x+1)²
±4 = x+1
x = -1 ± 4 = {-5, 3}
y = a(x+1)² -16
Putting in the y-intercept values, we have
-15 = a(0+1)² -16
1 = a . . . . . . . . . . . add 16
Then the x-intercepts can be found where y=0.
0 = (x+1)² -16
16 = (x+1)²
±4 = x+1
x = -1 ± 4 = {-5, 3}
Answer with Step-by-step explanation:
So in this sequence,
1st term = 7
2nd term = 10
3rd term = 13
4th term = 16
10th term = 34
In this sequence,
1st term = -1
2nd term = 3
3rd term = 7
4th term = 11
10th term =35
Answer:
They should walk on a bearing of 59.4 degrees
Step-by-step explanation:
Given
Required
The bearing back to the base
The given question is illustrated with the attached image.
To do this, we simply calculate the measure of angle a using:
Take arctan of both sides
