All categories

2 years ago

The slope of the tangent line for the curve r=2 cos(3 theta) where theta = pi/6 is.

Mathematics

1 answer:

Phantasy [73]2 years ago

7 0

as you already know, the slope of the tangent line is simply the derivative of the function, so

$r=2cos(3\theta )\implies \cfrac{dr}{d\theta }=2\stackrel{chain~rule}{\left[ -sin(3\theta )\cdot 3 \right]} \\\\\\ \left. \cfrac{dr}{d\theta }=-6sin(3\theta ) \right|_{\theta =\frac{\pi }{6}}\implies -6sin\left( 3\cdot \frac{\pi }{6} \right)\implies -6sin\left( \frac{\pi }{2} \right)\implies -6$

You might be interested in

Help me pls will give brainliest

Kobotan [32]

Answer:

x = 10

Step-by-step explanation:

Assuming you require the value of x

AB is a straight angle, thus the 3 given angles sum to 180°, that is

3x + 94 + x + 30 + 2x - 4 = 180, that is

6x + 120 = 180 ( subtract 120 from both sides )

6x = 60 ( divide both sides by 6 )

x = 10

4 0

3 years ago

Read 2 more answers

N is an integer s=1/2 n(n+1) prove that 8s + 1 is an odd square number

pychu [463]

$s=\frac{1}{2}n(n+1) \\ \\
8s+1=8 \times \frac{1}{2}n(n+1)+1=4n(n+1)+1=4n^2+4n+1=(2n+1)^2$

n is an integer, so 2n+1 is also an integer. 8s+1 is equal to the square of 2n+1, so it's a square number.

2n+1 is an odd integer for any value of n. The square of an odd integer is always an odd integer. Therefore 8s+1=(2n+1)² is odd.

8s+1 is an odd square number.

7 0

3 years ago

A box contains 3 coins, one fair, one weighted with a 2 3 chance of coming up heads, and one weighted with a 2 3 chance of comin

ddd [48]

Answer:

The probability that we have a fair coin is 0.2717

Step-by-step explanation:

Let Ci be the event that the coin i is used for while we let i = 1,2,3 (representing the three coin)

We also let H be the event that the coin which is flipped lands (which is head)

Therefore, the problem arise:

That: P(H/C1) = 1/2.............fair coin

p(H/C2) = 2/3..........Chance of head

p(H/C3) = 2/3............Chance of tail

Now, noting that the coin was picked at random,

We have, : p(Ci) = P(C1) = P(C2) = P(C3) = 1/3

We can then say that or calculate thus:

P( C2 | H ) = P (H ∩ C2) ÷ P(H)

Where P (H ∩ C2) means the probability of event intersection

= P(H ∩ C2) ÷ P(H ∩ C1) + P(H ∩ C2) + P(H ∩ C3)

= P(H | C2) P(C2) ÷ P(H | C1) P(C1) + P(H | C2) P(C2) + P(H | C3) P(C3)

= (1 / 2) (1 / 3) ÷ (1/2)(1/3) + (2/3)(1/3) + (2/3) (1/3)

0.5 × 0.3 ÷ (0.5 × 0.3) + (0.67 × 0.3) + (0.67 × 0.3)

0.15 ÷ 0.15 + 0.201 + 0.201

=0.15 / 0.552

= 0.2717

7 0

3 years ago

Nicole bought a meal in a town with a 9% sales tax. She tips 20% on the bill, and then adds the sales tax. What is the total cos

zloy xaker [14]

Answer:

The total cost of the meal is $19.35.

Step-by-step explanation:

As Nicole ordered a $ 15 menu, and on that price she paid a tip of 20% and the town in which she bought it had a sales tax of 9%, the total cost of the meal is determined by performing the following calculation:

1- Menu $ 15

2- Tip $ 3 (15 x 0.2)

3- Sales tax $ 1.35 (15 x 0.09)

Thus, adding the three expenses, the total cost of the food for Nicole is $ 19.35 (15 + 3 + 1.35).

6 0

2 years ago

In a certain country, the true probability of a baby being a girl is 0.469. Among the next seven randomly selected births in th

-BARSIC- [3]

Answer:

The probability is 0.995 ( approx ).

Step-by-step explanation:

Let X represents the event of baby girl,

The probability of a baby being a girl is, p = 0.469,

So, the probability of a baby who is not a girl is, q = 1 - 0.469 = 0.531,

Also, the total number of experiment, n = 7

Thus, by the binomial distribution formula,

$P(x)=^nC_x(p)^x q^{n-x}$

Where, $^nC_x=\frac{n!}{x!(n-x)!}$

The probability that all babies are girl or there is no baby boy,

$P(X=7)=^7C_7(0.469)^7(0.531)^{7-7}$

$=0.00499125661758$

Hence, the probability that at least one of them is a boy = 1 - P(X=7)

= 1 - 0.00499125661758

= 0.995008743382

≈ 0.995

8 0

3 years ago