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Natalija [7]
3 years ago
13

Show that the curve x = 6 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations.

Mathematics
1 answer:
Arlecino [84]3 years ago
7 0
We can write
  cos(t) = x/6
so
  y = 5(±√(1 -(x/6)^2)*x/6
Then
  y' = (±5/6)*(√(1 -(x/6)^2) + x/(2√(1 -(x/6)^2)*(-2(x/6))
The limit as x → 0 is ±5/6

The equations of the two tangents are
  y = (5/6)x
  y = (-5/6)x

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(x + 2) = 3
-2 -2
0 1
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How many different menus showing 10 main courses can a restaurant make if it has 15 main courses from which to choose? 360,360 3
PtichkaEL [24]

Answer:

3003

Step-by-step explanation:

The number of differents menus containing 10 main courses that the restaurant can make if it has 15 main courses from which to chose is calculated through the combination: 15C10. The formula of the combination is: nCr = n! / ((r!) x(n - r)!) 

Where r=10 and n=15

Substituting the values to the equation: 15C10 = 15! / (10!)x(10 - 5)! = 3003

Then there are 3003 different menus that a restaurant can makeif it has 15 main courses from which to choose.

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A machine in an office can shred 65 sheets of paper every 5 seconds. How many sheets of paper can the machine shred in 60 second
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780 sheets

Step-by-step explanation:

we know that

A machine can shred 65 sheets of paper every 5 seconds

so

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Evaluate x(y+3)/(3+y)z for x=12, y=1, and z=6.<br><br> A) 2<br><br> B) 5<br><br> C) 8<br><br> D) 6
fgiga [73]

Answer:

2

Step-by-step explanation:

We take the equation

x(y+3)/(3+y)z

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12(1+3)/(3+1)6

Now we can solve the equation.

When solved, it equals 2.

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What is the answer I need help?
Bad White [126]

Answer:

8 1/8 units^3

Step-by-step explanation:

This figure is a rectangular prism, and the volume of a rectangular prism is given by the formula:

lwh

But since we have the area of the base snd the height of the figure, there is also one formula that we can use to find the volume:

bh

Which means area of base times the height.

USE THE FORMULA bh:

16 1/4 x 1/2

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= 65/8

SIMPLIFIED: 8 1/8

Volume is measured in cubic units

SO YOUR ANSWER IS 8 1/8 units^3

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3 years ago
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