The equation represents height as a function of time.
The bullet was in the air for 75 seconds.
The equation is given as:
The time spent in the air is the time it takes the bullet to land on the ground.
When the bullet is on the ground, the height is:
So, we have:
Factor out t
Split
or
represents when the shot is fired.
So, we solve for t in
Collect like terms
Divide both sides by 16
Hence, the bullet was in the air for 75 seconds
Read more about height and time at:
Answer:
Step-by-step explanation:
To begin simplifying this, we can first divide the coefficients, giving us:
We know that when dividing exponents, this means we need to subtract the exponent on the denominator from the numerator. This gives us:
Now, simplifying this gets:
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
<h3>How to estimate a definite integral by numerical methods</h3>In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:
∫ f(x) dx = F(b) - F(a) (1)
The steps of Euler's method are summarized below:
The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
To learn more on Euler's method: brainly.com/question/16807646
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