Archive for the ‘Applied Mathematics’ Category

Problem 721

Evaluate

lim_{x\rightarrow 0}\frac{x+7}{x^{2}+9x+14}

 

Solution:-

 

Evaluate x = 0

lim_{x\rightarrow 0}\frac{x+7}{x^{2}+9x+14} = \frac{0+7}{0^{2}+9\ast 0+14}

=\frac{7}{14}

=\frac{1}{2}

 

 

logarithmic basic formulas/Ruels

Logarithm product rule

log_{a}(x ∙ y) = log_{a}(x) + log_{a}(y)

Logarithm quotient rule

log_{a}(\frac{x}{y}) = log_{a}(x) - log_{a}(y)

Logarithm power rule

log_{a}(x^{y}) = y ∙ log_{a}(x)

Logarithm base switch rule

log_{a}(c) = \frac{1}{log_{c}(a))}

 

 

Convert from square yards to square feet

One square yard equals 9 ft ^{2}. Use this information to convert 25.5 yd ^{2} to square feet.

 

Solution

 

Convert from square yards to square feet by multiplying the number of square yards by 9.

Multiply

25.5 yd ^{2} = 25.5 * 9 ft ^{2}

= 229.5 ft^{2}

Convert from square feet to square yards

One square yard equals ft ^{2}. Use this information to converts 153 ft ^{2}to square yards.

 

Solution

 

To convert from square feet to square yards, divide the number of square feet by the number of square feet per square yard.

There are 9 square feet for every square yard.

From the previous step, it is known that 9 ft ^{2}= 1 yd ^{2}. Now to convert square feet to square yards, divide the number of square feet by 9.

153ft ^{2} = \frac{153}{9}yd^{2}

=17yd ^{2}

Therefore, 153 ft ^{2} = 17yd ^{2}