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Ad libitum [116K]

2 years ago

12

A gym membership costs $25 to join, plus a $12 monthly fee. If Adam has spent $133 on his gym membership this year, for how many

months has he been a member?

1 answer:

max2010maxim [7]2 years ago

3 0

Answer:

133= 12x +25 (subtract 25 from both sides to isolate the x-term)

108= 12x (divide by 12 on both sides to get x alone)

x= 9 months

Step-by-step explanation:

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Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular soluti

Vikki [24]

Answer:

General Solution is $y=x^{3}+cx^{2}$ and the particular solution is $y=x^{3}-\frac{1}{2}x^{2}$

Step-by-step explanation:

$x\frac{\mathrm{dy} }{\mathrm{d} x}=x^{3}+3y\\\\Rearranging \\\\x\frac{\mathrm{dy} }{\mathrm{d} x}-3y=x^{3}\\\\\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{3y}{x}=x^{2}$

This is a linear diffrential equation of type

$\frac{\mathrm{d} y}{\mathrm{d} x}+p(x)y=q(x)$ ..................(i)

here $p(x)=\frac{-2}{x}$

$q(x)=x^{2}$

The solution of equation i is given by

$y\times e^{\int p(x)dx}=\int e^{\int p(x)dx}\times q(x)dx$

we have $e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}$

Thus the solution becomes

$\tfrac{y}{x^{2}}=\int \frac{1}{x^{2}}\times x^{2}dx\\\\\tfrac{y}{x^{2}}=\int 1dx\\\\\tfrac{y}{x^{2}}=x+c$ $y=x^{3}+cx^{2$

This is the general solution now to find the particular solution we put value of x=2 for which y=6

we have $6=8+4c$

Thus solving for c we get c = -1/2

Thus particular solution becomes

$y=x^{3}-\frac{1}{2}x^{2}$

5 0

3 years ago

If the product of two integers is positive, their signs are positive or negative

worty [1.4K]

Answer:

It could be both 2 positives, or 2 negatives.

Step-by-step explanation:

This is because a negative times a negative is a positive, and a positive times a positive is a positive.

7 0

3 years ago

Could someone help and explain their answer? (NO LINKS!)<br> Thanks!

Nonamiya [84]

Answer:

5

Step-by-step explanation:

To find the prime factorization of a number, start by dividing the number by each prime number that you can divide by as many times as possible, starting with the smallest prime number and moving up. Then move on to the next prime number. The last division must give a quotient of 1. Then the prime factorization is the product of all the prime factors you divided the number by.

Here's how you use this method with 180.

Here are the first 10 prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Start by trying to divide by 2. 180 is divisible by 2.

180/2 = 90 90 is divisible by 2.

90/2 = 45 45 is not divisible by 2, so now try 3.

45/3 = 15 15 is divisible by 3.

15/3 = 5 5 is prime, so it is divisible by 5.

5/5 = 1 The divisors in bold are the prime factors of 180.

180 = 2 × 2 × 3 × 3 × 5

180 = 2² × 3² × 5

Answer: 5

3 0

2 years ago

Read 2 more answers

43: PLEASE HELP Write the equation 22x-2y-10 in slope-intercept form

Gnoma [55]

Answer:

y= 11x -5

Step-by-step explanation:

I believe you rearrange it to get y on one side of the equation so,

2y= 22x-10

and then divide 2 on both sides to get,

y=11x-5

7 0

3 years ago

√(4x-9) + 1 =2√x <br>Find the value of X

Natasha_Volkova [10]

There are no values for x that make the equation true

7 0

3 years ago