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3 years ago

What is the value of 9C4

Mathematics

1 answer:

Liula [17]3 years ago

6 0

Answer:

Step-by-step explanation:

Recall the formula nCr=n! {(n-r)!r!}

Here, n=9, r= 4

9C4=9! / {(9-4)! 4!

=9! / (5! 4)

= 362880 / (120* 24)

=126

Awnser is 126

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Solve Using Dirac Deltla/discontinuous forcing

Jet001 [13]

Let $A(t)$ denote the amount of salt in the tank at time $t$ . We're told that $A(0)=0$ .

For $0\le t\le15$ , the salt flows in at a rate of (1/5 lb/gal)*(5 gal/min) = 1 lb/min. When the regulating mechanism fails, 20 lbs of salt is dumped and no more salt flows for $t>15$ . We can capture this in terms of the unit step function $u(t)$ and Dirac delta function $\delta(t)$ as

$\text{rate in}=u(t)-u(t-15)+20\delta(t-15)$

(in lb/min)

The salt from the mixed solution flows out at a rate of

$\text{rate out}=\left(\dfrac{A(t)\,\mathrm{lb}}{50+(5-5)t\,\mathrm{gal}}\right)\left(5\dfrac{\rm gal}{\rm min}\right)=\dfrac A{10}\dfrac{\rm lb}{\rm min}$

Then the amount of salt in the tank at time $t$ changes according to

$\dfrac{\mathrm dA}{\mathrm dt}=u(t)-u(t-15)+20\delta(t-15)-\dfrac A{10}$

Let $\hat A(s)$ denote the Laplace transform of $A(t)$ , $\hat A(s)=\mathcal L_s\{A(t)\}$ . Take the transform of both sides to get

$s\hat A(s)-A(0)=\dfrac1s-\dfrac{e^{-15s}}s+20e^{-15s}-\dfrac1{10}\hat A(s)$

Solve for $\hat A(s)$ , then take the inverse of both sides.

$\hat A(s)=\dfrac{\frac{10-10e^{-15s}}{s^2}+\frac{200e^{-15s}}s}{10s+1}$

$\implies\boxed{A(t)=10-10e^{-t/10}+\left(30e^{3/2-t/10}-10\right)u(t-15)}$

7 0

4 years ago

In the right triangle above, a = 2.7 and b = 4.3. Find the value of c, rounded to the nearest tenth.

stiks02 [169]

It’s A your welcome

6 0

3 years ago

Read 2 more answers

How to solve for y??????

tia_tia [17]

What he said above yeah y

8 0

3 years ago

Mrs. Salinas bought 10 pounds of a mixture made of M&Ms and peanuts. M&Ms sell for $3 pound. Peanuts sell for $2 pound.

jek_recluse [69]

Answer:

Mrs. Salinas buys 4 ounces M&Ms and 6 ounces Peanuts.

Step-by-step explanation:

Given,

Total weight of the mixture = 10 pounds.

Total money Mrs. Salinas paid = $24.

We have to find out the weight of each M&Ms and peanuts.

Solution,

Let the weight of M&Ms be x.

And the weight of peanuts be y.

Since total weight of the mixture is 10 pounds.

So, we can frame it in equation as;

$x+y=10\ \ \ \ \ equation\ 1$

Again, Total money paid by Mrs. Salinas is the sum of weight of M&Ms multiplied by price for each ounce and weight of peanuts multiplied by price for each ounce.

So, we can frame it in equation as;

$3x+2y=24\ \ \ equation\ 2$

Now, multiplying equation 1 by 2, we get;

$2(x+y)=10\times2\\\\2x+2y=20\ \ \ \ \ equation\ 3$

Now subtract equation 3 from equation 2, we get;

$(3x+2y)-(2x+2y)=24-20\\\\3x+2y-2x-2y=4\\\\x=4$

On substituting the value of x in equation 1, we get;

$x+y=10\\\\4+y=10\\\\y=10-4\\\\y=6$

Hence Mrs. Salinas buys 4 ounces M&Ms and 6 ounces Peanuts.

5 0

3 years ago

what is the degree of the polynomial ? what is the leading coefficient ? describe the end behavior of each function. f(x)=x^4-2x

Verizon [17]

Answer:

4th degree polynomial with leading coefficient of 1.

As x goes to negative or positive infinity, y goes to positive infinity in both cases.

Step-by-step explanation:

The degree of a polynomial is the highest exponent on the variable. Here it is 4.

The leading coefficient is the coefficient on the the term with the highest degree, Here there is none so it is 1.

The end behavior is how x and y behave at negative and positive infinity. When graphed, this equation has a W shape. This means at each end y goes to positive infinity.

3 0

4 years ago