If x varies inversely at the cube root of y and x=1 when y =8 find y when x=3
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Answer:
Exactly 12 years it will take for these trees to be the same height
Step-by-step explanation:
Slope intercept form: An equation of line is in the form of where m is the slope or unit rate and b is the y-intercepts.
Let x represents the time in years and y represents the height of the tree.
Use conversion:
1 ft = 12 inches
As per the given statement:
Type A is 8 feet tall and grows at a rate of 3 inches per year.
⇒unit rate per year = 3 inches = ft
Then, we have;
......[1]
Similarly for;
Type B is 7 feet tall and grows at a rate of 4 inches per year.
⇒unit rate per year = 4 inches = ft
then;
.....[2]
To find after how many years it will take for these trees to be the same height.
Since, trees to be the same height;
⇒equate [1] and [2], to solve for x;
Subtract 7 from both sides we get;
Simplify:
Subtract from both sides we get;
Simplify:
Multiply both sides by 12 we get;
x = 12
Therefore, exactly it will take for these trees to be the same height is, 12 years