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astraxan [27]
3 years ago
9

Which of the following tables represents the rule, y equals seven less than four times a number

Mathematics
1 answer:
zaharov [31]3 years ago
8 0

Answer:

89.9403 ...

Step-by-step explanation:

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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
Simpifly (-5x2 - 3x - 7) + (-2x3 + 6x2 - 8)
ioda

Answer:

-2x³ + x² - 3x - 15

Step-by-step explanation:

Simply combine like terms together:

-5x² - 3x - 7 - 2x³ + 6x² - 8

-2x³ + (-5x² + 6x²) - 3x + (-7 - 8)

-2x³ + x² - 3x + (-7 - 8)

-2x³ + x² - 3x - 15

5 0
3 years ago
Read 2 more answers
The ratio of bous to girls in the school is 1 to 4. If there are 20 girls, how many boys are there?
anyanavicka [17]

if there's 1 boy to every 4 girls, there's going to be 5 boys for every 20 girls

6 0
3 years ago
Read 2 more answers
in a bag of marbles 1/2 of the marbles have a star on them if 8 marbles have a Star how many total marbles are in the bag​
Step2247 [10]

Answer:

Step-by-step explanation:

8x1/2

8/1 x 1/2

8/2

4

The answer is 4

8 0
3 years ago
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Write the fact family for these factors: 8, 64
natka813 [3]

Answer:

8*64=512

64*8=512

512/64=8

64/512=8

3 0
3 years ago
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