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Dovator [93]
3 years ago
13

I need help solving number 11 please.

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
3 0

set up the triangle with the information given. then just solve for x.

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Find a point on the curve x^3+y^3=11xy other than the origin at which the tangent line is horizontal.
attashe74 [19]

Compute the derivative dy/dx using the power, product, and chain rules. Given

x³ + y³ = 11xy

differentiate both sides with respect to x to get

3x² + 3y² dy/dx = 11y + 11x dy/dx

Solve for dy/dx :

(3y² - 11x) dy/dx = 11y - 3x²

dy/dx = (11y - 3x²)/(3y² - 11x)

The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when

11y - 3x² = 0

or

y = 3/11 x²

(provided that 3y² - 11x ≠ 0)

Substitute y into into the original equation:

x³ + (3/11 x²)³ = 11x (3/11 x²)

x³ + (3/11)³ x⁶ = 3x³

(3/11)³ x⁶ - 2x³ = 0

x³ ((3/11)³ x³ - 2) = 0

One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with

(3/11)³ x³ - 2 = 0

(3/11 x)³ - 2 = 0

(3/11 x)³ = 2

3/11 x = ³√2

x = (11•³√2)/3

Solving for y gives

y = 3/11 x²

y = 3/11 ((11•³√2)/3)²

y = (11•³√4)/3

So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).

3 0
2 years ago
How much chocolate will each person get if 3 people share 1/2 pound of chocolate equally?
eimsori [14]
1/6 pound of chocolate for each person ( 1/2 / 3 ).
3 0
3 years ago
30 treadmills to 36 elliptical machines the ratio in simplest form
Goshia [24]
30 treadmills : 36 ellipticals
this could be written in a few ways, but i am going to write it as a fraction. since treadmills come first, you put 30/36.

now that you have your fraction you have to find the GCF (greatest common factor) of the two numbers. the GCF is 6, so you have to divide 30 treadmills by 6, and 36 ellipticals by 6.
30/6=5
36/6=6

5/6 or 5:6 is the simplified ratio of treadmills to ellipticals



comment for any questions!!
4 0
3 years ago
The price for the items ordered at lunch was $23.45. How much would the price be after tax and tip if the tax rate is 8% and you
kiruha [24]
Cost of items = $23.45

Tax = 8% of $23.45 = 0.08*23.45 = $1.88
Tip = 20% of $23.45 = 0.2*23.45 = $4.69

Total cost = 23.45 + 1.88 + 4.69 = 30.02

Answer: $30.02

8 0
3 years ago
A small bar of gold measures 20 mm by 150 mm by 2 mm. One cubic milimeter of gold weighs about 0.0005 ounces. Find the volume in
Kay [80]

Answer:

= 3oz

Step-by-step explanation:

v = 20mm ×150mm ×2mm = 6000 mm^3

so, the weight is

6000 mm^3 × 0 .0005oz/1mm^3 = 3oz

6 0
2 years ago
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