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telo118 [61]
3 years ago
11

Find p small and blue

Mathematics
1 answer:
Inga [223]3 years ago
8 0

Answer:

P(Small and Blue) = 3/40

Step-by-step explanation:

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I’ve been at these questions all day. Please help
Phantasy [73]

Answer:

தமிழ்நாட்டில் உள்ள நெல் வகைகளை குறிப்பிட்டு எழுதுக

7 0
3 years ago
Read 2 more answers
Find dy/dx when r=2 2cos(theta) , then find slope of tengent line at point(4, 2pi)
Korolek [52]

The slope of tangent line at point(4, 2pi) is undefined.

For given question,

We have been given a polar equation r = 2 + 2cos(θ)

We need find dy/dx as well as the slope of tangent line at point(4, 2π).

We know that, for polar equation we use,

x = r cos(θ)   and  y = r sin(θ)

plug the given value of r into these equations we get:

⇒ x = r cos(θ)

⇒ x = (2 + 2cos(θ) ) ×  cos(θ)

⇒ x = 2(cos(θ) + cos²(θ))

⇒ x = 2cos(θ) + 2cos²(θ)

Similarly,

⇒ y = r sin(θ)

⇒ y = (2 + 2cos(θ) ) ×  sin(θ)

⇒ y =  2(sin(θ) + sin(θ)cos(θ))

⇒ y =  2sin(θ) + 2sin(θ)cos(θ)

Now we find derivative of x and y with respect to theta.

\Rightarrow \frac{dx}{d\theta} =-2sin(\theta)+2(-2cos(\theta)sin(\theta))\\\\\Rightarrow  \frac{dx}{d\theta} =-2sin(\theta)-2sin(2\theta)          .............(1)

Similarly,

\Rightarrow \frac{dy}{d\theta}=2cos(\theta)+2(cos^2(\theta)-sin^2(\theta))\\\\\Rightarrow \frac{dy}{d\theta}=2cos(\theta)+2(cos(2\theta))          ..............(2)

Now we find dy/dx

⇒ dy/dx = (dy/dθ) / (dx/dθ)

From (1) and (2),

\Rightarrow \frac{dy}{dx} =\frac{2cos(\theta)+2cos(2\theta)}{-2sin(\theta)-2sin(2\theta)} \\\\\Rightarrow \frac{dy}{dx} =\frac{2(cos(\theta)+cos(2\theta))}{-2(sin(\theta)+sin(2\theta))}\\\\\Rightarrow \frac{dy}{dx} =-\frac{cos(\theta)+cos(2\theta)}{sin(\theta)+sin(2\theta)}

We know that The slope of tangent line is given by dy/dx.

So, the slope is: m =-\frac{cos(\theta)+cos(2\theta)}{sin(\theta)+sin(2\theta)}

Now we need to find the slope of tangent line at point(4, 2pi)

Substitute θ = 2π in above slope formula.

\Rightarrow m =-\frac{cos(2\pi)+cos(2\times 2\pi)}{sin(2\pi)+sin(2\times 2\pi)}\\\\\Rightarrow m=-\frac{1+cos(4\pi)}{0+sin(4\pi)}\\\\\Rightarrow m=-\frac{1+cos(4\pi)}{sin(4\pi)}

⇒ m = ∞

The slope of tangent line at point(4, 2pi) is not defined.

This means, the tangent line must be parallel to Y-axis.

Therefore, the slope of tangent line at point(4, 2pi) is undefined.

Learn more about the slope here:

brainly.com/question/10785137

#SPJ4

8 0
2 years ago
In the figure, find the value of x that makes a ∥ b. A. 50° B. 65° C. 75° D. 95°
Anon25 [30]

Answer:

B

Step-by-step explanation:

Because alternate interior angles are congruent in parallel lines, the angle next to the 25° in the right triangle is 85 - 25 = 60° which makes the other angle in the right triangle 180 - 90 - 60 = 30°. Since they form a straight angle, we can write x + 30 + 85 = 180 → x + 115 = 180 → x = 65°.

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3 years ago
Pouvez vous maider pour la questuon deux merci
Vanyuwa [196]

quelle est ta question?


6 0
3 years ago
We’ve seen that natural numbers are closed under addition. Determine the closure of natural numbers under the other three operat
Butoxors [25]
The natural numbers are the counting numbers.
The set of natural numbers consists of 1, 2, 3, 4, 5, ...
Zero is not part of the natural numbers.

You need to know what it means for natural numbers to be closed under addition. That means that if you add any two natural numbers, you get a natural number. Natural numbers are closed under addition since the sum of any two natural numbers is a natural number. You cannot find any pair of natural numbers whose sum is not a natural number. 5 + 6 = 11; 10 + 12 = 22; 40 + 50 = 90. Al the numbers above are natural numbers.

Now think of multiplication. If you multiply any two natural numbers, will the answer always be a natural number? The answer is yes. That means that natural numbers are closed under multiplication. For example, 4 * 2 = 8; 10 * 20 = 200; 15 * 3 = 45. All numbers above are natural numbers.

What about subtraction? If you subtract a natural number from another natural number, will the difference always be a natural number?
Look at 8 - 18 = -10. The difference, -10, is not a natural number, so the natural numbers are not closed under subtraction.

Finally, think of division. If you divide a natural number by another natural number, the quotient may or may not be a natural number.
For example, 24/6 = 4. Here the quotient is a natural number,
but 4/24 = 1/4. 1/4 is not a natural number,
so with division, you may not get a natural number, so the natural numbers are not closed under division.
6 0
3 years ago
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