\(\displaystyle \dfrac{dy}{dx} = 5x\)

\(\displaystyle dy = 5x\, dx\)

\(\displaystyle \int dy = \int 5x\, dx\)

\(\displaystyle y = \dfrac{5x^{2}}{2} + C\)

What is the particular solution if f(2) = 2?

\(\displaystyle 2 = \dfrac{5(2)^{2}}{2} + C\)

\(\displaystyle 2 = \dfrac{20}{2} + C\)

\(\displaystyle \dfrac{2}{10} = C\)

\(\displaystyle \dfrac{1}{5} = C\)

\(\displaystyle y = \dfrac{5x^{2}}{2} + \dfrac{1}{5}\)

What is the particular solution if f(2) = 3?

\(\displaystyle 3 = \dfrac{5(2)^{2}}{2} + C\)...

Finding the General and Particular Solution]]>

Solution:

Sally = 3x

John = x

3x + 8 = 2(x + 8)

Correct set up?

2. Kim is 6 years more than twice Timothy's age. Two years ago, Kim was three times as old as Timothy. How old was Kim 2 years ago?

Solution:

Kim = 6 + 2x

Timothy = x

(6 + 2x) - 2 = 3(x - 6)

Correct set up?

3. Leah is 2 less than 3 times Rachel's age. Three years from now, Leah will be 7 more than twice...

Age Word Problems 3]]>

Solution:

Becca = 2x

Susan = x

Greg = x + 9

2x - 3 = 3x - 9

Correct set up?

2. Lauren is 3 less than twice Andrew's age. Four years from now, Sam will be 2 more than twice Andrew's age. Five years ago, Sam was three times Andrew's age. How old was Lauren 5 years ago?

What is the set up?

3. Gabby is 1 year more than twice Larry's age...

Age Word Problems 4]]>

1. Devon owns a house cleaning company and has to give price quotes to potential customers. He figures out his price by assuming a $25 base charge and then adding $8 for each bathroom and $4 for each other room. If he uses P to represent the price, B for bathroom, and R for other rooms, create a formula describing the situation.

2. Given f(x) = 2x^2 − 3x + 7, find f(2.5)

3. Solve 5x + 8 < 3(x + 2)

4. Simplify (x^6)(x^5)

5. The area of a circle is 100π. Find the...

Algebra Practice Test 1]]>

Solution:

Let x + 750 = Increase of Rita's monthly expenses.

My set up:

(4 people)/(3 people) = 750/x

Is this the correct equation set up?]]>

Solution:

John = 2(x + 5)

Peter = x + 5

Alice = x

2(x + 5) + 5 = 3x

Is this the correct equation set up?

John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now?

Solution:

John' father = 5(2x)

John = 2x

Alice = x

[5(2x) + 2x + x]...

Age Word Problems 2]]>

Solution:

Let J = John's age now.

J - 5 = (1/2)(J + 8)

Is this the correct equation set up?

2. Ten years from now, Orlando will be three times older than he is today. What is his current age?

Solution:

Let x = Orlando's current age.

10 + x = 3x

Is this the correct equation set up?

3. In 20 years, Kayleen will be four times older than she is today. What is her current age?

Solution:

Let K =...

Age Word Problems 1]]>

Solution:

x = sqrt{y}k

K is the constant of proportionality.

128 = sqrt{16}k

128 = 4k

128/4 = k

32 = k

x = sqrt{y}k

x = sqrt{36}•32

x = 6 • 32

x = 192

Find y when x = 48.

x = sqrt{y}k

48 = sqrt{y}32

48/32 = sqrt{y}

(48/32)^2 = [sqrt{y}]^2

2.25 = y]]>

Solution:

Let D = difference in price per ounce

D = 2.94 ÷ 14 - 3.60 ÷ 20

D = 0.21 - 0.18

D = 0.03 or 3 cents]]>

How do you think gravity has effect on bones and also weight of human body?]]>

While many found joy and happiness solving different mathematical theories such as calculus, algebra and the rest, others felt that maths is a difficult subject many should be afraid to study. So, what's your take? Did you miss the course you wanted...

Did you find mathematics difficult?]]>

Any idea on how such chemical reactions are chained for this event?]]>