Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle
Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.
The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.
Answer:
Option D
Step-by-step explanation:
Answer:
The average value of the function on the given interval 6.5.
Step-by-step explanation:
Consider the given function is
![f(x)=\dfrac{2x-1}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B2x-1%7D%7B2%7D)
We need to find the average value of the function on the given interval [1,13].
![f(x)=\dfrac{2x}{2}-\dfrac{1}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B2x%7D%7B2%7D-%5Cdfrac%7B1%7D%7B2%7D)
![f(x)=x-0.5](https://tex.z-dn.net/?f=f%28x%29%3Dx-0.5)
The average value of the function f(x) on [a,b] is
![Average=\dfrac{1}{b-a}\int\limits^b_a {f(x)} \, dx](https://tex.z-dn.net/?f=Average%3D%5Cdfrac%7B1%7D%7Bb-a%7D%5Cint%5Climits%5Eb_a%20%7Bf%28x%29%7D%20%5C%2C%20dx)
Average value of the function on the given interval [1,13] is
![Average=\dfrac{1}{13-1}\int\limits^{13}_{1} {x-0.5} \, dx](https://tex.z-dn.net/?f=Average%3D%5Cdfrac%7B1%7D%7B13-1%7D%5Cint%5Climits%5E%7B13%7D_%7B1%7D%20%7Bx-0.5%7D%20%5C%2C%20dx)
![Average=\dfrac{1}{12}[\dfrac{x^2}{2}-0.5x]^{13}_{1}](https://tex.z-dn.net/?f=Average%3D%5Cdfrac%7B1%7D%7B12%7D%5B%5Cdfrac%7Bx%5E2%7D%7B2%7D-0.5x%5D%5E%7B13%7D_%7B1%7D)
![Average=\dfrac{1}{12}[\dfrac{(13)^2}{2}-0.5(13)-(\dfrac{(1)^2}{2}-0.5(1))]](https://tex.z-dn.net/?f=Average%3D%5Cdfrac%7B1%7D%7B12%7D%5B%5Cdfrac%7B%2813%29%5E2%7D%7B2%7D-0.5%2813%29-%28%5Cdfrac%7B%281%29%5E2%7D%7B2%7D-0.5%281%29%29%5D)
![Average=\dfrac{1}{12}[78-0]](https://tex.z-dn.net/?f=Average%3D%5Cdfrac%7B1%7D%7B12%7D%5B78-0%5D)
![Average=6.5](https://tex.z-dn.net/?f=Average%3D6.5)
Therefore, the average value of the function on the given interval 6.5.
Answer:
Step-by-step explanation:
We are solving for the segment of AB. Note that it is a line segment, so there will be end points, those being A(-4, 5) & B(2, -5).
Use the following distance formula:
<em />
<em> </em>
![\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - x_{2})^2 }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D%20-%20x_%7B1%7D%29%5E%7B2%7D%20%2B%20%28y_%7B2%7D%20-%20x_%7B2%7D%29%5E2%20%7D)
Let:
Point B(2 , -5) = (x₁ , y₁)
Point A(-4 , 5) = (x₂ , y₂)
Plug in the corresponding numbers to the corresponding variables.
![\sqrt{(-4 - 2)^{2} + (5 - (-5))^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28-4%20-%202%29%5E%7B2%7D%20%2B%20%285%20-%20%28-5%29%29%5E%7B2%7D%20%7D)
Simplify. Remember to follow PEMDAS. First, solve the parenthesis, then the powers, then add, and then finally square root.
![d = \sqrt{(-6)^{2} + (5 + 5)^{2} } \\d = \sqrt{(-6 * -6) + (10)^2} \\d = \sqrt{(36) + (10 * 10)} \\d = \sqrt{36 + (100)} \\d = \sqrt{136}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28-6%29%5E%7B2%7D%20%2B%20%285%20%2B%205%29%5E%7B2%7D%20%20%7D%20%5C%5Cd%20%3D%20%5Csqrt%7B%28-6%20%2A%20-6%29%20%2B%20%2810%29%5E2%7D%20%5C%5Cd%20%3D%20%5Csqrt%7B%2836%29%20%2B%20%2810%20%2A%2010%29%7D%20%5C%5Cd%20%3D%20%5Csqrt%7B36%20%2B%20%28100%29%7D%20%5C%5Cd%20%3D%20%5Csqrt%7B136%7D)
Simplify:
![d = \sqrt{136} = \sqrt{2 * 2 * 2 * 17} = \sqrt[2]{17 * 2} = \sqrt[2]{34}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B136%7D%20%3D%20%5Csqrt%7B2%20%2A%202%20%2A%202%20%2A%2017%7D%20%20%3D%20%5Csqrt%5B2%5D%7B17%20%2A%202%7D%20%3D%20%5Csqrt%5B2%5D%7B34%7D)
is your answer.
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Ok so if they make 15 bears every 10 mins then they will make 90 bears in one hour.
15 x 6 = 90
If they work for 8 hours then they’ll make 720 bears in one work day.
90 x 8 = 720
Let x be the number of days...
720x = 5000
5000 / 720 = 6.9444444.....
Round up because they want the least number of work days
So the answer is 7 work days
Hope this helps! Any questions let me know :)