<img src="https://tex.z-dn.net/?f=y%20%3C%20x%20-%203" id="TexFormula1" title="y < x - 3" alt="y < x

A projectile is an object launched into space, and moving under the influence of gravity and momentum. The stone here is an example. Thus, the time taken for the stone to reach the ground is 10 seconds.

On launching of the stone into space, it behaves as a projectile. Thus moving under the influence of gravity and its momentum. Its momentum is the product of its mass and velocity.

The height h, is given as:

h = 16 $t^{2}$ + 32t + 240

Differentiating the expression with respect to t, we have;

32t + 32 = 0

t = -1 seconds

Substitute the value of time, t, in the equation for the height;

h = 16 - 32 + 240

= 224

h = 224 m

Total height, S = 240 + 224

= 464

S = 464 m

The total height covered by the stone is 464 m.

From the second equation of free fall,

S = Ut + $\frac{1}{2}$ g $t^{2}$

S = $\frac{1}{2}$ g $t^{2}$

464 = $\frac{1}{2}$ *9.8* $t^{2}$

$t^{2}$ = $\frac{928}{9.8}$

= 94.694

t = $\sqrt{94.694}$

= 9.7311

t ≅ 10 seconds

The time taken for the stone to hit the ground is 10 seconds.

Thus option A is the required answer.

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7 0

2 years ago

Graphing Exponential Function in Exercise ,sketch the graph of the function.See example 3 and 4.

9966 [12]

Answer:

The graph is attached below.

Step-by-step explanation:

Considering the exponential function

$y=3^{-2x}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{bx}=\left(a^b\right)^x$

$3^{-2x}=\left(3^2\right)^{-x}$

$=\left(3^2\right)^{-x}$

$=9^{-x}$

The graph is also attached below.

Keywords: exponential function, graph

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7 0

3 years ago

Please please i need help i will mark u brill

zvonat [6]

Answer:

106 - 8h = 34

Whenever a math question says "when h = 9," they mean you substitute this number where h is in the equation.

106 - 8(9) = 34

106 - 72 = 34

34 = 34

This means the fact that h = 9 is a solution for h.

I hope this helps! I would really appreciate it if you would please mark me brainliest! Have a blessed day!

6 0

3 years ago

A cosmetics company that makes small cylindrical bars of soap wraps the bars in plastic prior to shipping. Find the surface area

Lelu [443]

We would have two circles of 5cm diameter each, and a rectangle of the length pi*diameter and 2cm, so lets add them:
total = 2circles + rectangle
total = 2(2*pi*(5/2)^2) + pi*diameter*heigth
= 4*pi*(2.5)^2 + pi*5*2
= 109.9
that is the surface area of a bar soap 109.9 cm^2

3 0

3 years ago

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