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3 years ago

How do you solve to get y?

Mathematics

1 answer:

dmitriy555 [2]3 years ago

3 0

Answer:

y = 64

Step-by-step explanation:

Using the rule of logarithms

• $log_{b}$ x = n ⇔ x = $b^{n}$

Given

$log_{y}$ 4 = $\frac{1}3}$ , then

4 = $y^{\frac{1}{3} }$

Cube both sides

4³ = ( $y^{\frac{1}{3} }$ )³, hence

y = 64

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the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width

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Length and width of rectangle is 15 inches and 6 inches respectively

<h3>Solution:</h3>

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

The formula for area of rectangle is given as:

$\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}$

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

$\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}$

On solving the above expression for x we get

$\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}$

$\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}$

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