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2 years ago

One term of (x+y)^m is 31,824x^18y^11 What is the value of m ?

Mathematics

1 answer:

alisha [4.7K]2 years ago

7 0

Answer: The value of m is 29.

Step-by-step explanation:

Given that, One term of $(x+y)^m$ is $31,824x^{18}y^{11}$ ...(i)

We know that that (r+1)th term in $(a+b)^n$ is given by :-

$T_{r+1}=^nC_ra^{n-r}b^r$ ...(ii)

On comparing (i) with (ii) , we get

$a= x \text{ and } b= y \\n-r =18 \text{ and } r=11\\n=m$

i.e.

$m-r=18\Rightarow\ m-11=18\\\\\Rightarrow\ m=18+11=29$

Hence, the value of m is 29.

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Let x represent the amount of frozen yogurt (in hundreds of gallons) sold by the G&T restaurant on any day during the summer

musickatia [10]

Answer:

a) The probability of selling less than 100 gallons (x≤1) is P=0.16.

b) The mean number of gallons is M=80 gallons.

Step-by-step explanation:

The probability of selling x, in hundred of gallons, on any day during the summer is y(x)=0.32x, in a range for x from [0;2.5].

The probability of selling less than 100 gallons (x≤1) is then:

$P(x\leq1)=\int_0^{100}0.32x\cdot dx\\\\P(x\leq1)=0.16(x_b^2-x_a^2)\\\\P(x\leq1)=0.16(1^2-0^2)=0.16$

The mean number of gallons can be calculated as:

$M=\int_0^{2.5}(y(x)/x)\cdot dx=\int_0^{2.5}(0.32)\cdot dx\\\\M=0.32(x_b-x_a)=0.32(2.5-0)=0.32*2.5=0.8$

3 0

2 years ago

An elevator starts on the 100th floor. It descends 4 floors every 10 seconds. At what floor will the elevator be 60 seconds afte

Artyom0805 [142]

So is 4 floors / 10 seconds
If you have 60 seconds you can multiple 10 by 6 because 10×6=60
so you also have to multiple 4 by 6
4×6=24
and because it's descending it's 100-24= 76

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2 years ago

Read 2 more answers

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.