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3 years ago

Find a cartesian equation for the curve. r = 9 sin(θ)

1 answer:

6 0

For this case we have the following equation:
r = 9 sin (θ)
In addition, we have the following change of variables:
y = r * sine (θ)
Rewriting the equation we have:
r = 9 sin (θ)
r = 9 (y / r)
r ^ 2 = 9y
On the other hand:
r ^ 2 = x ^ 2 + y ^ 2
Substituting values:
x ^ 2 + y ^ 2 = 9y
Rewriting:
x ^ 2 + y ^ 2 - 9y = 0
Completing squares:
x ^ 2 + y ^ 2 - 9y + (-9/2) ^ 2 = (-9/2) ^ 2
Rewriting:
x ^ 2 + 1/4 (2y-9) ^ 2 = 81/4
4x ^ 2 + (2y-9) ^ 2 = 81
Answer:
The Cartesian equation is:
4x ^ 2 + (2y-9) ^ 2 = 81

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Two paper drink cups are shaped like cones. The small cone can hold 6 oz of water. The large cone is 4/3 the height and 4/3 the

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2 years ago

The total resistance in a circuit with two parallel resistors is 2 ohms and R1 is 6 ohms. Using the equation for R2, in terms of

ivanzaharov [21]

<h2>Answer:</h2>

$R_2$ is 3 ohms

<h2>Step-by-step explanation:</h2>

In a circuit containing two resistors $R_1$ and $R_2$ connected together in parallel, the total resistance $R_T$ is given by;

$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$ ---------(i)

<em>Make </em> $R_2$ <em> subject of the formula;</em>

=> $\frac{1}{R_2} = \frac{1}{R_T} - \frac{1}{R_1}$

=> $\frac{1}{R_2} = \frac{R_1 - R_T}{R_TR_1}$

=> ${R_2} = \frac{R_TR_1}{R_1 - R_T}$ ---------------(ii)

From the question,

$R_1$ = 6Ω

$R_T$ = 2Ω

Substitute these values into equation (ii) as follows;

=> ${R_2} = \frac{2*6}{6 - 2}$

${R_2} = \frac{12}{4}$

$R_2$ = 3Ω

Therefore, the value of $R_2$ = 3 ohms or $R_2$ = 3Ω

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3 years ago

For a group of 100 people, compute(a) the expected number of days of the year that are birthdays of exactly 3 people.(b) the exp

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Answer:

Step-by-step explanation:

Leaving leap years, a year contains 365 days.

For a group of 100 people, each person is independent of the other and probability of any day being his birthday has a chance of

$\frac{1}{365}$

a) Probability that exactly 3 people have same birthday = $\frac{1}{365^3}$

Each day is independent of the other

And hence no of days having exactly 3 persons birthday out of 100 persons is binomial with n = 365 and p = $\frac{1}{365^3}$

Expected value of days = np = $\frac{1}{365^2}$

b) Distinct birthdays is binomail with p =1/365 and n = 365

Hence

expected value = np =1

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3 years ago

Don't really understand this math question yet

olga_2 [115]

Arranging the given distances from sea level on the number line, we have;

The error made by taking Egypt as being further from the sea level is assuming that the sea level is at the beginning (left) of the number line.

<h3>How can the number line be used to find the distance from the sea level?</h3>

The given elevation of the lowest points in the six countries are;

Country. Lowest point elevation (m)

China. →. -154

Egypt →. -133

Azerbaijan → -28

Serbia. →. 35

Israel. → -408

Laos. →. 70

Sorting the above countries from the country with the lowest point below sea level to the country with the highest point above sea level gives;

Israel → -408

China → -154

Egypt → -133

Azerbaijan → -28

Serbia. → 35

Laos. →. 70

On a number line, we have;

Israel < China < Egypt < Azerbaijan < Serbia < Laos

Relative to zero, which is the sea level, points -133 and -154 are located to the left of zero.

However, point -133 > -154, therefore, -154 < -133, the symbol < represents lesser (in this case 'lower') which indicates that China (point -154) is lower or further left from zero which is the sea level than Egypt (point -133).

The error is therefore mistaking the location of the sea level as being at the extreme left of the number line, rather than at the middle.

Learn more about the number line here:

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