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user100 [1]
3 years ago
15

It has been observed that a particular nail's growth is

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
8 0
NOTE: I have made this explaination long so that you understand it as some people view my answers too short or without enough info. feedback would be nice.

If The growth is directly proportional this means that the graph will be linear.

For simplicity and since the question does not specify, we will make one time unit one week.

Our base function is "F(t) = mt + b"  with F(t) being the length of nail with respect to time.
[This is just mx + b]

so F(t)  = mt + b

We will assume that when t = 0, we have 3mm of nail. So...

F(0)  = 3
3  = m(0) + b
b = 3

F(t)  = mt + 3
To find slope we can sub when F(t) is 1

F(1)  = 3.5
3.5  = m + 3
m = 0.5 = \frac{1}{2}

Our Equation is:

"F(t)  = \frac{1}{2} t + 3

Use a graphing calculator, an online grapher, or pen and paper for your graph.

Brainest answer is appreciated.






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Subject to some of (3/5 + 1/5i) and (4/5 - 2/5i) from (9/5 - 1/5i). the result is what
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The correct answer is: 2/5.

Explanation:

First you have to add the following expressions:

(\frac{3}{5}+\frac{1}{5}i)+(\frac{4}{5}-\frac{2}{5}i) \\ (\frac{3}{5}+ \frac{4}{5})+(\frac{1}{5}i-\frac{2}{5}i) \\= \frac{7}{5}-\frac{1}{5}i

Now subtract the above expression from (\frac{9}{5}-\frac{1}{5}i):

(\frac{9}{5}- \frac{1}{5}i) - (\frac{7}{5} -\frac{1}{5}i) \\ (\frac{9}{5} -\frac{7}{5}) + (\frac{1}{5}i -\frac{1}{5}i) \\ \frac{2}{5} \\


Hence the correct answer is 2/5.


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Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the ques
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<h2>a. What is your equation?</h2>

This is a problem of projectile motion. A projectile is an object you throw with an initial velocity and whose trajectory is determined by the effect of gravitational acceleration. The general equation in this case is described as:

h(t)=-\frac{1}{2}gt^2+v_{0}t+h_{0}

Where:

h(t): \ height \ at \ any \ time \\ \\ g: \ acceleration \ due \ to \ gravity \ 9.8m/s^2 \ or \ 32.16ft/s^2 \\ \\ v_{0}= \ Initial \ velocity

So:

v_{0}=64ft/s \\ \\ h_{0}=3ft

Finally, the equation is:

h(t)=-\frac{1}{2}(32.16)t^2+(64)t+3 \\ \\ \boxed{h(t)=-16.08t^2+64t+3}

<h2>b. How long will it take the rocket to reach its maximum height?</h2>

The rocket will reach the maximum height at the vertex of the parabola described by the equation h(t)=-16.08t^2+64t+3. Therefore, our goal is to find t at this point. In math, a parabola is described by the quadratic function:

f(x)=ax^2+bx+c

So the x-coordinate of the vertex can be calculated as:

x=-\frac{b}{2a}

From our equation:

a=-16.08 \\ \\ b=64 \\ \\ c=3

So:

t=-\frac{64}{2(-16.08)} \\ \\ \boxed{t=1.99s}

So the rocket will take its maximum value after 1.99 seconds.

<h2>c. What is the maximum height the rocket will reach?</h2>

From the previous solution, we know that after 1.99 seconds, the rocket will reach its maximum, so it is obvious that the maximum height is given by h(1.99). Thus, we can find this as follows:

H_{max}=h(1.99)=-16.08(1.99)^2+64(1.99)+3 \\ \\ \boxed{H_{max}=66.68ft}

So the maximum height the rocket will reach is 66.68ft

<h2>d. How long is the rocket in the air?</h2>

The rocket is in the air until it hits the ground. This can be found setting h(t)=0, so:

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We can't have negative value of time, so the only correct option is t_{1}=4.0264 and rounding to the nearest hundredth we have definitively:

\boxed{t=4.03s}

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