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Grace [21]
3 years ago
10

"a frog is sitting on a stump 12 feet above the ground. it hops off the stump and lands on the ground 6 feet away. during its​ l

eap, its height h is given by the equation h equals negative 0.5 x squared plus x plus 12 where x is the distance in feet from the base of the​ stump, and h is height in feet. how far was the frog from the base of the stump when it was 0.5 feet above the​ ground?"
Mathematics
1 answer:
CaHeK987 [17]3 years ago
3 0

Solution:

Given equation: h = -0.5x² + x + 12

h = 0.5

-0.5x² + x + 12 = 0.5

-0.5x² + x + 11.5 = 0

Find the roots of quadratic equation.

x = ((-b )+- √(b² - 4ac))/2a

= ((-1 )+- √(1² - 4*(-0.5)*(11.5)))/2(1)

= -3.9, 5.9

The distance will not be negative.

Hence, the distance is 5.9.




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To get G^-1 all we need to do is flip the points around Example for (5,3) make it (3,5)
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The sum of squares of three consecutive numbers is 77 find the numbers​
ollegr [7]

Answer:

4,5,6 are the three consecutive numbers. 16, 25 and 36 are their squares.

Step-by-step explanation:

Let the three consecutive numbers be x, (x+1), (x+2)

Now, the squares of these three numbers are  x^{2} ,(x+1)^{2} ,(x+2)^{2}

Sum = 77

∴by the problem ,

x^{2} +(x+1)^{2}+(x+2)^{2}  = 77\\x^{2} +(x^{2} +2x+1)+(x^{2}+4x +4) = 77\\x^{2} +x^{2} +2x+1+x^{2} +4x +4 = 77\\3x^{2} +6x+5 = 77\\3x^{2} +6x = 77-5\\3x^{2} + 6x = 72\\3x^{2} +6x-72= 0\\

{Taking 3 common }

x^{2} +2x- 24 = 0\\

{By factorization}

x^{2} +2x- 24 =0\\ x^{2} +6x-4x-24=0\\x(x+6)-4(x+6)=0\\(x+6)(x-4)=0\\

Therfore,

x= -6,4\\

<em>X can't be negetive </em>

∴ x =4\\x+1=5\\x+2=6

The squares of the three consecutive numbers are 16, 25, 36

The three consecutive numbers whose sum is 77 are 4, 5, 6

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