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3 years ago

Y4 = 2x − 1 is this a straight line?

Mathematics

1 answer:

Alchen [17]3 years ago

3 0

Answer:

yes

Step-by-step explanation:

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Hi! I need help with the attached question in calc. Thank you:)

Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

$\displaystyle V=\pi \int_a^b [R(y)]^2\, dy$

So:

$\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy$

Simplify:

$\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy$

Integrate:

$\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]$

Evaluate (I ignored the 0):

$\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi$

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

$\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi$

We acquire the exact same answer.

8 0

3 years ago

If you have a GCF of x is that a root?

Mekhanik [1.2K]

Answer:

No,

Step-by-step explanation:

No, GCF is not a root, it is the coefficient of x.

3 0

2 years ago

Your teacher writes the fact below on the board.Using only mental math, will the answer be less than or greater than 5? How do y

Levart [38]

Answer:

Less than 5

Step-by-step explanation:

The eason behind the answer being less than 5 is because if you multiply something by a fraction that is less than a whole number, then you will get less than the original number you multiplied the fraction with.

Hope this helps :)

4 0

2 years ago

Suppose that the probability that a person is killed by lightning, in a year is, independently of other people, 1/(500 million).

Katen [24]

Answer:

a) $P(X \geq 3) = 1- P(X$

The individual pprobabilities are:

$P(X=0)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.548812$

$P(X=1)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.329287$

$P(X=2)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.098786$

And if we replace we got:

$P(X \geq 3) = 1- [0.548812+0.329287+0.098786]=0.023115$

b) $P(X \geq 3) = 1- P(X$

And we can calculate this with the following excel formula:

$=1-BINOM.DIST(2;300000000;(1/500000000);TRUE)$

And we got:

$P(X\geq 3) = 0.023115$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=300000000, p=\frac{1}{500000000})$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

(a) Write down the exact expression for the probability P(3 or more people will be killed by lightning in the U.S. next year). Evaluate this expression to 6 decimal places.

For this case we want this probability, we are going to use the complement rule:

$P(X \geq 3) = 1- P(X$

The individual probabilities are:

$P(X=0)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.548812$

$P(X=1)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.329287$

$P(X=2)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.098786$

And if we replace we got:

$P(X \geq 3) = 1- [0.548812+0.329287+0.098786]=0.023115$

(b) Write down a relevant approximate expression for the probability from (a). Justify briefly the approximation. Evaluate this expression to 6 decimal places.

For this case we want this probability, we are going to use the complement rule:

$P(X \geq 3) = 1- P(X$

And we can calculate this with the following excel formula:

$=1-BINOM.DIST(2;300000000;(1/500000000);TRUE)$

And we got:

$P(X\geq 3) = 0.023115$

7 0

3 years ago

Please help me on this question I really don't understand it

Aleonysh [2.5K]

Itz c the answer is c

4 0

3 years ago