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bezimeni [28]
3 years ago
15

Please help :c How do I convert 19.3g/mL to lb/in^3? (manually) I tried to so 19.3g (453.592lb)/1g but I'm not sure how to chang

e it into in^3 :
Mathematics
1 answer:
Alecsey [184]3 years ago
3 0
1 pound = 453.59237 grams
1 cubic inch = 16.387064 milliliters

19.3 grams * 1 pound / 453.59 grams = <span> <span> <span> 0.0425494389 </span> </span> </span> pounds

1 cubic inch * 16.387
<span> <span> 0.0425494389 * 16.387 =  </span></span><span><span><span>0.6972576553 pounds / cubic inch
</span> </span></span>

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Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=12. y=
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Y = 20x + 7 for instance
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Fully simplify 14xy^4(-14y)​
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Evaluate log^8x-4log^8x​
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2 years ago
The deer population in a certain state park doubles every year. In the year 2010, there were 30 deer in the park. Which function
Gala2k [10]

Answer:

y = 30(2)^x

Step-by-step explanation:

Initial deer population = 30 (in 2010)

Every year, deer population doubles ; this means there is an 100% increase in the population every year ;

Hence, using the exponential growth relation :

Final = initial * (1 + rate)^year

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7 0
2 years ago
For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;
Dmitrij [34]

Answer:

a.

x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

ax+by=c

Suppose integers x0 and yo satisfy the equation; that is,

ax_0+by_0 = c

what other values

x = x_0+h and y=y_0+k

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

as+bt=gcd(a,b)

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

a(sk) + b(tk) = gcd(a,b)k = c

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

a(x_1-x) + b(y_1-y)=0

Therefore,

a(x_1-x) = b(y-y_1)

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

y = y_1+r(\frac{a}{gcd(a, b)})  for some integer r. Substituting into the equation

a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba

or

x = x_1-r(\frac{b}{gcd(a, b)} )

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

15 = 6*2+3\\6=3*2+0

Therefore gcd(6,15) = 3. Since 3|12, the equation has integral solutions.

We then find a way of representing 3 as a linear combination of 6 and 15, using the Euclidean algorithm computation and the equalities, we have,

3 = 15-6*2

Because 4 multiplies 3 to give 12, we multiply by 4

12 = 15*4-6*8

So one solution is

x=-8 & y = 4

All other solutions will have the form

x=-8+\frac{15r}{3} = -8+5r\\y=4-\frac{6r}{3} =4-2r

where r ∈ Ζ

Hence by putting r values, we get many (x, y)

3 0
3 years ago
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