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▹ Answer
<em>2c - 2b - a</em>
▹ Step-by-Step Explanation
(c + b + a) + (-2a - 3b + c)
<u>Remove the parentheses</u>
c + b + a + (-2a - 3b + c)
<u>Collect like terms</u>
2c + b + a - 2a - 3b
<u>Final Answer</u>
2c - 2b - a
Hope this helps!
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Q1: The answer is A. pyramid.
A pyramid has one polygon base. A prism has two polygon bases. A cone has one circular base. A cylinder has two circular bases.
Q6: The answer is false.
Surface area of a rectangular prism is:
A = 2(wl + hl + hw)
A1 = 2(4*5 + 6*5 + 6*4) = 2(20+30+24) = 2*74 = 148
A2 = 2(6*4 + 5*4 + 5*6) = 2(24+20+30) = 2*74 = 148
Q7. The answer is A. 6 feet
The volume of rectangular prism is:
V = w * l * h
w = ?
So, just replace the knowing facts:
288 = w * 8 * 6
288 = w * 48
w = 288/48 = 6
Q8: The answer is 216 ft³
The volume of the cube is:
V = a³
Since a = 6, then:
V = 6³ = 216
The tangent to through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces and at that point.
Let . Then is the level curve . Recall that the gradient vector is perpendicular to level curves; we have
so that the gradient of at (1, 1, 1) is
For the surface , we have
so that . We can obtain a vector normal to by taking the cross product of the partial derivatives of , and evaluating that product for :
Now take the cross product of the two normal vectors to and :
The direction of vector (24, 8, -8) is the direction of the tangent line to at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by . Then adding (1, 1, 1) shifts this line to the point of tangency on . So the tangent line has equation
With 5000 different trials with a 16.2% "success" rate, the "failed" simulations can be obtained by subtracting the number of simulations that succeeded by the original number of simulations. This is shown below:
No. of simulations that succeeded = 5000 * 0.162 = 810
No. of simulations that failed (had at least 1 missed free throw) = 5000 - 810 = 4190.