HELP I WILL MARK BRAINLIEST!!!

The tables show proportional relationships. Find the constant of

SpyIntel [72]

Answer:

If the ratio of one variable to the other is constant, then the two variables have a proportional relationship,

If x and y have a proportional relationship, the constant of proportionality is the ratio of y to x.

In this section, you will learn, how to find the constant of proportionality from a table which contains the values of x and y.

Step-by-step explanation:

I hope that helps, I'm so sorry if it doesn't

7 0

3 years ago

(6x-5y+4)dy+(y-2x-1)dx=0

Len [333]

(6x - 5y + 4) dy + (y - 2x - 1) dx = 0

(6x - 5y + 4) dy = (2x - y + 1) dx

dy/dx = (2x - y + 1) / (6x - 5y + 4)

Let X = x - a and Y = y - b. We want to find constants a and b such that

dY/dX = (a rational function)

where the numerator and denominator on the right side are free of constant terms. Substituting x and y in the equation, we have

dY/dX = (2 (X + a) - (Y + b) + 1) / (6 (X + a) - 5 (Y + b) + 4)

dY/dX = (2X - Y + 2a - b + 1) / (6X - 5Y + 6a - 5b + 4)

Then we solve for a and b in the system,

2a - b + 1 = 0

6a - 5b + 4 = 0

==> a = -1/4 and b = 1/2

With these constants, the equation reduces to

dY/dX = (2X - Y) / (6X - 5Y)

Now substitute Y = VX and dY/dX = X dV/dX + V :

X dV/dX + V = (2X - VX) / (6X - 5VX)

The equation becomes separable after some simplification:

X dV/dX + V = (2 - V) / (6 - 5V)

X dV/dX = (2 - V) / (6 - 5V) - V

X dV/dX = (2 - V - (6 - 5V)) / (6 - 5V)

X dV/dX = (4V - 4) / (6 - 5V)

- (5V - 6) / (4V - 4) dV = 1/X dX

Integrate both sides:

-5/4 V + 1/4 ln|4V - 4| = ln|X| + C

Extract a constant from the logarithm on the left:

-5/4 V + 1/4 (ln(4) + ln|V - 1|) = ln|X| + C

-5/4 V + 1/4 ln|V - 1| = ln|X| + C

-5V + ln|V - 1| = 4 ln|X| + C

Get this back in terms of Y :

-5Y/X + ln|Y/X - 1| = 4 ln|X| + C

Now get the solution in terms of y and x :

-5 (y - 1/2)/(x + 1/4) + ln|(y - 1/2)/(x + 1/4) - 1| = 4 ln|x + 1/4| + C

With some manipulation of constants and logarithms, and a bit of algebra, we can rewrite this solution as

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|x + 1/4| + 4 ln(4) + C

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| - ln|4x + 1| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| = 5 ln|4x + 1| + C

8 0

3 years ago

Calculate each mountain path grade to the nearest .

nordsb [41]

I’m not exactly sure how to calculate the grade, but this is what I’ve done below. Hope it helps!

5 0

3 years ago

ANSWER ASAP !!!!!!!!!!

tekilochka [14]

Option C is correct or y=3/4x-5. Use the given functions to set up and simplify y=mx+b
to find the equation.

6 0

3 years ago

An HMO pamphlet contains the following recommended weight for women: "Give yourself 100 pounds for the first 5 feet plus 5 pound

fenix001 [56]

Answer: 5 feet and 7 inches

Step-by-step explanation:

"Give yourself 100 pounds for the first 5 feet plus 5 pounds for every inch over 5 feet tall"

100 pounds for 5 feet + 5 pounds/inch [over 5 feet]

We can separate 135 pounds into two parts: the first 100 pounds and the other 35 pounds: 135 = 100 + 35

100 = 5 feet

35 pounds/5 pounds/inch = 7 inches

So, the height is 5 feet and 7 inches

7 0

3 years ago