Eh so im confused on this question ill give brainliest.
2 answers:
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Answer:
y = 6x + 9
Step-by-step explanation:
The equation of a line in slope- interceot form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 2x + 12y = - 1 into this form
Subtract 2x from both sides
12y = - 2x - 1 ( divide all terms by 12 )
y = - x -
← in slope- intercept form
with slope m = -
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= 6
Note the line passes through (0, 9) on the y- axis ⇒ c = 9
y = 6x + 9 ← equation of perpendicular line
Answer:
Santos should run approximately 36.145 meters along the shore
Step-by-step explanation:
The given parameters are;
The distance along the shore of the child = 50 meters
The distance from the shore of the child = 60 meters
The rate at which Santos can run = 4 m/s
The rate he can swim = 0.9 m/s
Let 'x' represent the distance he runs along the shore
We have;
The time he spends running on the shore, t₁ = x/4
The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9
The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9
To find the maximum, we have;
dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0
1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0
Simplifying using a graphing calculator gives;
1519·x² - 151900·x + 3505900 = 0
x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)
x ≈ 63.86 m or x ≈ 36.145 m
We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same
Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child
