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3 years ago

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Mathematics

1 answer:

Westkost [7]3 years ago

8 0

Answer:

dy/dx = -b/a cot α

Step-by-step explanation:

x² / a² + y² / b² = 1

Take derivative with respect to x.

2x / a² + 2y / b² dy/dx = 0

2y / b² dy/dx = -2x / a²

dy/dx = -b²x / (a²y)

Substitute:

dy/dx = -b²a cos α / (a²b sin α)

dy/dx = -b cos α / (a sin α)

dy/dx = -b/a cot α

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You are planning to work in the summer (13 weeks). You

Llana [10]

Answer:

(a) Equations for both

$y = 500 + 12x$ --- lifeguard

$y = 15x$ --- camp counselor

(b) Total pay for 5 days

Lifeguard pays $800

Camp counselor pays $375

(c) Which pays more

Lifeguard job pays more

Step-by-step explanation:

Let

$x \to hours$

$y \to total\ pay$

Given

Lifeguard job

$Signing\ bonus = \$500$

$Rate = \$12/hr$

Camp counselor job

$Signing\ bonus =\$0$

$Rate = \$15/hr$

Solving (a): The equation for both

The total pay for each job is calculated as:

Total Pay = Signing Bonus + Rate * Hours

So, we have:

Lifeguard

$y = 500 + 12*x$

$y = 500 + 12x$

Camp counselor

$y = 0 + 15 * x$

$y = 15x$

Solving (b): Total pay for 5 days

First, we calculate the total hours worked in 5 days

$x = 5hrs/day * 5days$

$x = 25hrs$

So, the pay for each is:

$y = 500 + 12x$

$y =500 + 12*25$

$y =800$ --- Lifeguard

$y = 15x$

$y = 15 * 25$

$y = 375$ --- camp counselor

Solving (c): Which job pays more

By comparing the solution in (b)

$800 > 375$

Hence, lifeguard job pays more

6 0

3 years ago

Find parametric equations through point P=(2,2,7) in the direction of the vector v = (44, 14, -20)?

ycow [4]

9514 1404 393

Answer:

(x, y, z) = (2+44t, 2+14t, 7-20t)

Step-by-step explanation:

One way to write parametric equations for line L is ...

L = P + t·v

where P is the given point and v is the given direction vector. Using that form, we have ...

(x, y, z) = (2+44t, 2+14t, 7-20t)

If you like, you can remove a common factor of 2 from the coefficients of t.

(x, y, z) = (2+22t, 2+7t, 7-10t)

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Brilliant_brown [7]

Answer:

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3 years ago

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hammer [34]

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