I cant get this question right :(
You can estimate the height, h , in meters of a toy rocket at any time, t in seconds during its flight. Use the formula h= -5t squared + 23t +10. Write the formula in factored form. Then calculate the height of the rocket 3s after it is launched.
You can estimate the height, h , in meters of a toy rocket at any time, t in seconds during its flight. Use the formula h= -5t squared + 23t +10. Write the formula in factored form. Then calculate the height of the rocket 3s after it is launched.
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ok so first part of the question is telling you to factorise the equation that you're already given:
h= -5t^2 +23t +10
h= (-5t - 2)x(t-5)
you can take aout a factor of -1:
h= -(5t -2)x(t-5)
Because mathematicians are lazy, they don't put the 'x' for multiplicatin and just assume that you'll know the brackets are to be multiplied by each other:
h= -(5t -2)x(t-5)
Now this is true - you can expand the brackets and see that you'll get back to the original equation. But how did I get the answer? Well, you know that you'll need brackets with 't' in one and '-5t' in the other because when you multiply these, you get -5x^2 which is in the equation. The other terms, well it's kinda like trial and error - but with a lot of practice you'll just know what numbers should go in.
Now, you've got the equation for h, so if you substitute t=3 (time in seconds which the question is asking you to find the height at), you'd get the height in metres:
h= -( (5x3) +2) (3-5)
h = - (15 +2) x -2
h= -17 x -2
h= 34 m
Hope that makes sense :)
h= -5t^2 +23t +10
h= (-5t - 2)x(t-5)
you can take aout a factor of -1:
h= -(5t -2)x(t-5)
Because mathematicians are lazy, they don't put the 'x' for multiplicatin and just assume that you'll know the brackets are to be multiplied by each other:
h= -(5t -2)x(t-5)
Now this is true - you can expand the brackets and see that you'll get back to the original equation. But how did I get the answer? Well, you know that you'll need brackets with 't' in one and '-5t' in the other because when you multiply these, you get -5x^2 which is in the equation. The other terms, well it's kinda like trial and error - but with a lot of practice you'll just know what numbers should go in.
Now, you've got the equation for h, so if you substitute t=3 (time in seconds which the question is asking you to find the height at), you'd get the height in metres:
h= -( (5x3) +2) (3-5)
h = - (15 +2) x -2
h= -17 x -2
h= 34 m
Hope that makes sense :)
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h=-5t^2+23t+10
factor this out
multiply-5t^2*10 and find the products that add up to 23t
-5t^2+25t-2t+10
find the common factors of each pair.. put the factor outside the bracket and divide each term inside the bracket by the factor
5t(-5t^2/5t +25t/5t) +2(-2t/2 +10/2)
5t(-t+5)+2(-t+5)
do the same as above here except that the common facot is (-t+5) or -(t-5)
-(t-5)(5t+2)
h=-(t-5)(5t+2)
therefore... h=-(3-5)(5(3)+2)
h= -(-2)(17)
h=34m
factor this out
multiply-5t^2*10 and find the products that add up to 23t
-5t^2+25t-2t+10
find the common factors of each pair.. put the factor outside the bracket and divide each term inside the bracket by the factor
5t(-5t^2/5t +25t/5t) +2(-2t/2 +10/2)
5t(-t+5)+2(-t+5)
do the same as above here except that the common facot is (-t+5) or -(t-5)
-(t-5)(5t+2)
h=-(t-5)(5t+2)
therefore... h=-(3-5)(5(3)+2)
h= -(-2)(17)
h=34m