Solve for x 2(X-5) +6=7(X-1)-2 (x -6)
1 answer:
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This will be a 4th degree polynomial. Our root of x = 7 in factorization form is (x-7). Our root of x = -11 in factorization form is (x+11) and the last one is a complex number. According to the conjugate root theorem, if we have 2+8i, we also HAVE to have 2-8i. In factorization form that first one is (x-(2+8i)) which simplifies to (x-2-8i). Its conjugate in factorization form is (x-2+8i). Now we will FOIL all that out. Let's start with the (x-2-8i)(x-2+8i). That multiplies out to 
. We have to combine like terms here to shorten that a bit. 
. i^2 is equal to -1, and -1(64) = -64. Now we have 
. That is 
. Now let's FOIL in another factorization. 
. That comes out to 
. One more term to go! 
. That, finally, is 
.
Answer:
1a) 230 feet
1b) 3.75s
1c) t=7.54s
2) t=2s
3) t=2.32s
Step-by-step explanation:
The equation that models Brett's last home run is
We need to complete the square to obtain the function in the vertex form:
1a) The vertex is (3.75,230).The maximum value is the y-coordinate of the vertex, which is 230 feet.
1b) The time it takes to reach the maximum value is the x-coordinate of the vertex. It reach the maximum heigth after t=3.75 seconds
1c) To find the time the ball hit the ground, we equate the h(t)=0 and solve for t.
The time is positive, so the ball hit the ground after 7.54 seconds.
Question 2)
The function that models the amusement ride is
We want to find the time it takes for the riders to reach the maximum height.
This time is given by:
Comparing to
we have a=-16, b=64, c=60.
We substitute to obtain:
Hence it took 2 seconds to rech the maximum height.
Question 3)
The equation that models the height f the catridge is
To find the time that the catridge will land, we equate the function to zero and solve for t.
This is a quadratic equation with =-16, b=35, an c=5
The solution is given by:
We substitute the values to get:
This gives:
This simplifies to:
The time it takes to land must be positive thefore t=2.32 seconds