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S_A_V [24]
3 years ago
5

What is the constant of proportionality for m=32•g

Mathematics
1 answer:
lina2011 [118]3 years ago
6 0

Answer:

∴ Constant of Proportionality is 32

Step-by-step explanation:

Here Given;

m=32\times g  (equation-1)

\frac{m}{g}=32  (equation-2) (divide with 'g' on both side)

We know,

The Constant of Proportionality equation is given;

y=k\times x  (equation-3)

Where 'k' is known as Constant of Proportionality.

Comparing equation-1 and equation-3;

y=m and x=g

Now equation-2 become;

k=\frac{y}{x}

Plug y=m and x=g in above equation;

\frac{m}{g}=k  (equation-4)

By comparing equation-2 and equation-4;

k=32

So Constant of Proportionality is 32

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x+55 + 90=180

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How many solutions does the equation have, x1 + x2 + x3 = 10 , where x1 , x2, and x3 are non-negative integers?
MAVERICK [17]

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1. When x_1=0, then there are such possible cases for x_2 and x_3:

  • x_2=0,\ x_3=10;
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In total 11 solutions for x_1=0.

2. For x_1=1, there are such possible cases for x_2 and x_3:

  • x_2=0,\ x_3=9;
  • x_2=1,\ x_3=8;
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  • x_2=5,\ x_3=4;
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In total 10 solutions for x_1=1.

3. This process gives you

  • for x_1=2 - 9 solutions;
  • for x_1=3 - 8 solutions;
  • for x_1=4 - 7 solutions;
  • for x_1=5 - 6 solutions;
  • for x_1=6 - 5 solutions;
  • for x_1=7 - 4 solutions;
  • for x_1=8 - 3 solutions;
  • for x_1=9 - 2 solutions;
  • for x_1=10 - 1 solution.

4. Add all numbers of solutions:

11+10+9+8+7+6+5+4+3+2+1=66.

Answer: there are 66 possible solutions (with non-negative integer variables)

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