Answer:
Equation of the tangent to the curve
y = 240x - 215994
Equation of the normal
y = (-1/240)x + 9.75 = - 0.00417x + 9.75
Step-by-step explanation:
y = (6 + 4x)² = 36 + 48x + 16x² = 16x² + 48x + 36
dy/dx = 32x + 48
At the point (6,900),
dy/dx = 32(6) + 48 = 240
Equation of the tangent at point (a,b) is
(y - b) = m(x - a)
a = 6, b = 900, m = 240
y - 6 = 240(x - 900)
In the y = mx + b form,
y - 6 = 240x - 216000
y = 240x - 215994
The slope of the normal line = -(1/slope of the tangent line) (since they're both perpenducular to each other)
Slope of the normal line = -1/240
Equation of normal
y - 6 = (-1/240)(x - 900)
y - 6 = (-x/240) + 3.75
y = (-1/240)x + 9.75
y = - 0.00417x + 9.75
Using a proportional relationship, the amounts are given as follows:
<h3>What is a proportional relationship?</h3>
A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For this problem, we have that:
- The input variable is the number of tennis players.
- The output variable is the number of soccer players.
From the first row of the table, the constant is given as follows:
k = 35/15 = 7/3.
Hence the relationship is:
y = 7/3x.
For the second row of the table, we have that x = 3, hence:
y = 7/3 x 3 = 7.
For the third row of the table, we have that y = 84, hence:
84 = 7/3x
x = 84 x 3/7
x = 36.
Then the amounts are given as follows:
More can be learned about proportional relationships at brainly.com/question/10424180
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Answer:
Step-by-step explanation:
x < 12
Answer: x=1
Step-by-step explanation:
Hi there!
To solve this problem, you need to use the distributive property. You distribute the 4 inside the parenthesis as well as the 5.
Hope this helps!
