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3 years ago

When does the arrow hit the ground? From what height is the arrow shot?

Mathematics

1 answer:

mezya [45]3 years ago

3 0

Answer:

The arrow hits the ground after 2.25 seconds

the height the arrow is shot from is (0,18) or 18 units up

Step-by-step explanation:

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Can someone help me.

Helen [10]

The solutions of the equations for x are given as follows:

a. x = 36.

b. x = 15.

<h3>What is the solution for item a?</h3>

The equation for item a is given by:

x/3 - 5 = 7

Isolating x, we have that:

x/3 = 12

x = 3 x 12

x = 36.

<h3>What is the solution for item b?</h3>

The equation for item b is given by:

x/2 - 5 = 2.5

Isolating x, we have that:

x/2 = 7.5

x = 7.5 x 2

x = 15.

Hence the solutions are:

a. x = 36.

b. x = 15.

More can be learned about equations at brainly.com/question/25537936

#SPJ1

3 0

1 year ago

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

$V = \frac{1}{3}\pi r^{2}h$

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

$V = \frac{1}{3}\pi r^{2}h$

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

2 years ago

Helps asap an explaintion will help too so I can understand

Simora [160]

The last one, d, 2/3 < g < 2

4 0

3 years ago

16 points<br> 1) Write the following in standard form (answer). *<br> 4^5

m_a_m_a [10]

Answer:

1024

Step-by-step explanation:

You could put 4^5 into your calculator. It’s 4*4*4*4*4= 1024

3 0

3 years ago

Nick bought t candies and divided them equally between his y friends and me. Each of us got 7 candies.

inysia [295]

<h2>Hello!</h2><h2>Let me help you.</h2>

As I understand, you need to write an equation that relates $t \ and \ y$ . This problem will be solved using equations. The problem states:

<em>Nick bought t candies and divided them equally between his y friends and me. Each of us got 7 candies.</em>

<em />

From this statement, we know that:

t: Number of candies Nick bought.

y: Number of friends.

Since I am included in this problem, the number of people involved here can be expressed as:

$y+1$

Since each of us got 7 candies, then it is true that:

$\frac{t}{y+1}=7 \\ \\ t=7(y+1)$

<em>So t (number of candies) is a function of y(number of friends).</em>

6 0

2 years ago