A box without a top is to be made from a rectangular piece of cardboard, with dimensions 4 in. by 8 in., by cutting out square c
orners with side length x and folding up the sides.
Write an equation for the volume V of the box in terms of x.
Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Write an equation for the volume V of the box in terms of x.
Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
1 answer:
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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