There are no algebraic methods for finding solutions to a general mix of exponential and polynomial terms. A graphing calculator can be helpful.
This equation has 3 real solutions, approximately ...
x ∈ {-0.802246431546, 1.51677641228, 7.17475582739}
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In the folder "iteration for solutions" is an equation for Newton's method iteration, essentially, ...
g(x) = x -f(x)/f'(x)
where f(x) is defined as shown in the picture.
Many graphing calculators can compute a numerical derivative, so you can essentially write the formula in this form without having to do the derivative-taking yourself. This calculator is nicely interactive, so the iteration result is produced at the same time the argument for g(x) is entered. Essentially, you write the answer by copying the answer using the 4-digit zero-crossing values shown on the graph as the iteration starting point.
Answer:

Step-by-step explanation:
We have the quadratic function:

And we want to determine its axis of symmetry.
Notice that this is in vertex form:

Where (<em>h, k</em>) is the vertex of the parabola.
From our function, we can see that <em>h</em> = 4 and <em>k</em> = -2.5. Hence, our vertex is the point (4, -2.5).
The axis of symmetry is equivalent to the <em>x-</em>coordinate of the vertex.
The <em>x-</em>coordinate of the vertex is 4.
Therefore, the axis of symmetry is <em>x</em> = 4.
Answer:
651 i think
Step-by-step explanation:
31/2 =15.5 so 15.5 times 42 = 651
a) The time taken by the rocket to reach the maximum height is 2.75 seconds.
b) The maximum height of the rocket will be 127 feet.
<h3>What is speed?</h3>
Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
- A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second.
- The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t²+88t+6.
a) The time taken by the rocket will be calculated as:-
We have a function h(t)=−16t²+88t+6. Now by taking the derivative of the function with respect to time and equating it to zero we will get the maximum time in which the rocket will reach the maximum height.
h(t) = -16t² + 88t + 6
h'(t) = 0
-32t + 88 = 0
32t = 88
t = 88 / 32 = 2.75 seconds
So the maximum time is 2.75 seconds.
b) Maximum height will be calculated as:-
Put the value of maximum time in the function h(t) = -16t² + 88t + 6 we will get the maximum height.
h(t) = -16t² + 88t + 6
h(2.75) = -16(2.75)² + ( 88 x 2.75 ) + 6
h(2.75) = 127 feet
Therefore the time taken by the rocket to reach the maximum height is 2.75 seconds and the maximum height of the rocket will be 127 feet.
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