Mathematics
Grade10
Easy

Question

When a watermelon is launched into the air, it forms a parabola y equals negative 4 x squared plus 240 x plus 4000 comma and the line equation of the watermelon launcher to the land is  y=300 x.
How far does the watermelon is launched?

  1. 7500 units
  2. 6000 units
  3. 5000 units
  4. 9000 units

hintHint:

simply equate the equation, and get the value of x
and put the value of x in the given equation

The correct answer is: 7500 units


    7500 comma space i s space t h e space c o r r e c t space c h o i c e
p a r a b o l a comma space space y space equals space minus 4 x squared plus 240 x plus 4000 space space left parenthesis g i v e n space i n space t h e space q u e s t i o n right parenthesis
t h e space l i n e space e q u a t i o n space o f space t h e space w a t e r m e l o n space l a u n c h e r space t o space t h e space l a n d space i s space space y equals 300 space x
p u t space t h e space v a l u e space o f space y space comma space i n space t h e space p a r a b o l a
space y space equals space minus 4 x squared plus 240 x plus 4000
s o comma space 300 x space equals negative 4 x squared plus 240 x plus 4000
space 4 x squared minus 240 x minus 4000 space plus space 300 x space equals space 0
4 x squared plus 60 x minus 4000 equals 0
4 left parenthesis x squared plus 15 x minus 1000 right parenthesis equals 0
x squared plus 15 x minus 1000 equals 0
x squared plus left parenthesis 40 minus 25 right parenthesis x minus 1000 equals 0
x squared space plus 40 x space minus space 25 x minus 1000 equals 0
x left parenthesis x plus 40 right parenthesis minus 25 left parenthesis x plus 40 right parenthesis equals 0
left parenthesis x plus 40 right parenthesis left parenthesis x minus 25 right parenthesis equals 0
x space equals negative 40 comma space i t space i s space u n d e f i n e d
a n d space x space equals space 25
e q u a t i o n space o f space t h e space w a t e r m e l o n space l a u n c h e r space t o space t h e space l a n d space i s space space y equals 300 space x space left parenthesis g i v e n right parenthesis
s o space y space equals space 300 x
y space equals space 300 cross times 25
y space equals space 7500 space u n i t s comma space i s space t h e space a n s w e r

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