Determine whether the equation represents a direct variation. If it does, find the constant of variation. 4y=3x+5

Two cities are building bicycle paths. Charles City has built 5km of bicycle paths by the end of the first month, and the total

sergey [27]

Answer:

Month 4

Step-by-step explanation:

To solve this problem we must propose an equation that models the number of kilometers of bicycle trails made monthly in Charles City and in Tinsel Town

For Charles City we know that the number of kilometers built in the first month is 5, and it doubles every month. Then we have an exponential equation, in base 2, whose initial value is 5.

This equation has the following form:

$y = C_1 (2^{x-1})$

Where:

$C_1$ is the number of kilometers built in month 1

x is the number of months: {1, 2, 3, 4, 5 ... x}

x = 1 represents month 1.

So:

$Charles\ City\ (km) = 5(2^{x-1})$

For Tinsel Town we know that the number of kilometers built in the first month is 21 and increases at a fixed rate of 5 kilometers per month. This can be modeled by a linear equation.

$Tinsel\ Town\ (km) = 21 + 5(x-1)$

Where x is the number of months. x: {1, 2, 3, 4, 5 ...}

We want to know at the end of what month the total length of the cycle lanes in Charles City first exceeds the length in Tinsel Town

Then we equal both equations and clear x.

$5 (2^{x-1}) = 21 + 5(x-1)\\\\5 (2^{x-1}) - (21 + 5(x-1)) = 0$

Clearing x from this equation is very difficult, so to find x, we iterate until we get the value of x that causes the equation to approach 0.

For x = 3

$5(2^{3-1}) - (21 +5(3-1)) = 0\\\\20- 31= -11$

For x = 4

$5(2^{4-1}) - (21 +5(4-1)) = 0\\\\40 - 36 = 4$

The value must be between x = 3 and x = 4

For x = 3.8

$5 (2^{3.8-1}) - (21 +5(3.8-1)) = 0\\\\34.82 - 35 = 0.18$

Then x ≈ 3.8 months.

Finally we have that By the end of the fourth month the total length of the cycle lanes in Charles City exceeds the length in Tinsel Town

6 0

3 years ago

Mrs. Bolch has been in martial arts for 85% of her life. She’s almost 35. How long has she been in martial arts (round to neares

Lady bird [3.3K]

Answer:

Step-by-step explanation:

30 years

7 0

2 years ago

Read 2 more answers

Find the measure of angle A

Sladkaya [172]

Answer:

40°

X=11

I can't give you a very good explanation because I'm

only a freshman lol, I only studied so far in this stuff so I think ill stick to questions like this that give me side lengths and require an angle.

Anyways, hope this helped!

4 0

3 years ago

Explain how you could use the construction tool or a compass and straightedge to create a line segment that is twice as long.

ycow [4]

Answer: Use a compass to measure the length of AB. Draw an arc from point B (or point A) with that distance. Extend line AB through that arc and label the intersection as point C. AC is twice the length of AB.

3 0

3 years ago

What property does the statement show? (4x8)x3=(8x4)x3

8090 [49]

Why not? Because every math system you've ever worked with has obeyed these properties! You have never dealt with a system where a×b did not in fact equal b×a, for instance, or where (a×b)×c did not equal a×(b×c). Which is why the properties probably seem somewhat pointless to you. Don't worry about their "relevance" for now; just make sure you can keep the properties straight so you can pass the next test. The lesson below explains how I kept track of the properties.

6 0

2 years ago

Determine whether the equation represents a direct variation. If it​ does, find the constant of variation. 4y=3x+5

Determine whether the equation represents a direct variation. If it does, find the constant of variation. 4y=3x+5