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andrew11 [14]
3 years ago
5

I sphere has a diameter of 24 units what is the volume in cubic units

Mathematics
1 answer:
Stolb23 [73]3 years ago
6 0
The formula to find the volume of a sphere is:
4π(r³/3)=V
The radius is half of the diameter.
24÷2=12
4π(12³/3)=V
12.5663706(576)=V
7238.22947=V
So, the volume of the sphere is 7,238.22947 units³.
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A particle is projected with a velocity of <img src="https://tex.z-dn.net/?f=40ms%5E-%5E1" id="TexFormula1" title="40ms^-^1" alt
Katena32 [7]

Answer:

2\sqrt{55}\text{ m/s or }\approx 14.8\text{m/s}

Step-by-step explanation:

The vertical component of the initial launch can be found using basic trigonometry. In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. Let the vertical component at launch be y. The magnitude of 40\text{ m/s} will be the hypotenuse, and the relevant angle is the angle to the horizontal at launch. Since we're given that the angle of elevation is 60^{\circ}, we have:

\sin 60^{\circ}=\frac{y}{40},\\y=40\sin 60^{\circ},\\y=20\sqrt{3}(Recall that \sin 60^{\circ}=\frac{\sqrt{3}}{2})

Now that we've found the vertical component of the velocity and launch, we can use kinematics equation v_f^2=v_i^2+2a\Delta y to solve this problem, where v_f/v_i is final and initial velocity, respectively, a is acceleration, and \Delta y is distance travelled. The only acceleration is acceleration due to gravity, which is approximately 9.8\:\mathrm{m/s^2}. However, since the projectile is moving up and gravity is pulling down, acceleration should be negative, represent the direction of the acceleration.

What we know:

  • v_i=20\sqrt{3}\text{ m/s}
  • a=-9.8\:\mathrm{m/s^2}
  • \Delta y =50\text{ m}

Solving for v_f:

v_f^2=(20\sqrt{3})^2+2(-9.8)(50),\\v_f^2=1200-980,\\v_f^2=220,\\v_f=\sqrt{220}=\boxed{2\sqrt{55}\text{ m/s}}

3 0
3 years ago
How might snakes running out of food affect other organisms such as hawks? please help
marissa [1.9K]

Answer:

The population of Hawks and other species would likely start to edge off.

Step-by-step explanation:

Commonly, a Food Chain is dependent on all the parts of it sataying at a perfect point. If the food that the Snakes eat starts to run out, more of them will die off. With less Snakes, the Hawks will then have less food, and that continues throughout the chain. The same thing would happen if there was too much food, except instead of the populations of species dying off, the Snake population would spike.

3 0
2 years ago
PLEASE HELP ME I ONLY HAVE 20 MINUTES!!!!
Over [174]

h(x) = 40x - 16x^2\\h(x) = 15\\40x - 16x^2 = 15\\-16x^2 + 40x - 15 = 0\\

Using the quadratic formula we get

x_1 = 0.5\\x_2 = 2.04

Therefore the tennis ball is at least 15 feet above the ground from 0.5 seconds to 2.04 seconds

7 0
2 years ago
Select the correct answer.
gizmo_the_mogwai [7]

Answer:

Factors are (x-1), (x+1), and (x+2).

Step-by-step explanation:

g(x)=x^{3}+2x^{2} -x-2\\g(x)=(x - 1) (x + 1) (x + 2)

7 0
2 years ago
What is the average speed in kilometers per hour if you travel 194 kilometers in 4.1 hours?
Sedaia [141]

Answer:

47.32 kilometers per hour

Step-by-step explanation:

194 (kilometers) / 4.1 ( hours)

194/4.1 = 47.32 kilometers per hour.

5 0
3 years ago
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