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olya-2409 [2.1K]

2 years ago

13

Angelo wants to buy a laptop and an android phone to be used in his online class. He paid a total of Php 24, 200.00 for both gad

gets. The price of the laptop is Php 3, 800.00 more than the price of the android phone.

1 answer:

katrin2010 [14]2 years ago

6 0

Answer:

laptop: 14000

phone: 10200

Step-by-step explanation:

laptop: x + 3800

phone: x

x + 3800 + x = 24200

2x + 3800 = 24200

2x = 20400

x = 10200

laptop: 10200 + 3800 = 14000

phone: 10200

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Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

A pet store has 15 birds and 75 fish.

Ludmilka [50]

Answer:

1/5

Step-by-step explanation:

6 0

1 year ago

Read 2 more answers

George tells you that when variables are in the denominator, the equation four over five plus three over x equals one over two b

jeka57 [31]

<span><span><u>Answer</u>
This explanation shows that the equation is solvable and there is not where in the steps we get a zero on the denominator.

</span><span><u>Explanation</u>
</span><span>The equation given in the statement is;
4/5+3/x=1/2
This equation can be solved as follows:
4/5+3/x=1/2
3/x=1/2-4/5=(5-8)/10
3/x= -3/10
Taking the reciprocal on both side of the equation;
x/3=-10/3
Multiplying by 3 both sides we get;
</span><span>x= -10
</span></span>

3 0

2 years ago

Read 2 more answers

Simplify 3.3l : 900ml

stich3 [128]

<span>3.3l : 900ml = 3300 ml / 900 ml = 33/9 </span>

3 0

2 years ago

The radius of a cylinder is 5" and the lateral area is 70 sq. in. Find the length of the altitude. 2.8" 7" 14"

algol13

The correct question is
<span>The radius of a cylinder is 5" and the lateral area is 70pi sq. in. Find the length of the altitude.
</span>
we know that

[surface lateral area]=(2*pi*r)*height
height= [surface lateral area]/(2*pi*r)
surface lateral area=70*pi in²
r=5 in
so
height= [70*pi]/(2*pi*5)------> 7 in

the answer is
7 in

5 0

2 years ago