Answer:
Step-by-step explanation:
Area of a circle is ...
A = πr² . . . r is the radius
Area of a sphere is ...
A = 4πr²
Lateral area of a cylinder is ...
A = πdh = 2πrh . . . h is the height
Volume of a cylinder is ...
V = πr²h
Volume of a sphere is ...
V = (4/3)πr³
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The area of the composite figure is the sum of the areas ...
total area = base circle area + cylinder lateral area + 1/2 sphere area
= πr² + 2πrh + (1/2)4πr² = (πr)(r +2h +2r)
= πr(3r +2h)
For the given dimensions, r=3 in, h = 13 in, this is ...
total area = π(3 in)((3·3 +2·13) in) = 105π in²
___
The volume of the composite figure is the sum of the volumes ...
total volume = cylinder volume + 1/2 sphere volume
= πr²h + (1/2)(4/3)πr³ = πr²(h + 2/3r)
= π(3 in)²((13 +2/3·3) in) = 135π in³
<span>(5x+10)/(x²-x-6)
1) 5x+10 = 5(x+2)
2) x² - x - 6 = (x+2)(x-3) 6 = -3*2, -1=-3+2
</span>(5x+10)/(x²-x-6) = 5(x+2)/5(x+2)
As we can see greatest common factor is <span>C. x + 2.</span>
Answer:
45 m
Step-by-step explanation:
<h3>Given</h3>
<u>Function to produce the stone's height</u>
Maximum value the given function can get is at (x - 1) = 0 ⇒ x = 1
because the -5(x - 1)² can get maximum value of zero as the square of any number is zero or positive
<u>So maximum height is </u>
The answer to this question is true
Answer:
Answered
Step-by-step explanation:
It is a combbinatorics problem. let's think as we need to do 8 partitions
of these 13 to separate the postcards of different types. So The number of
partitions of n=13 into r=8 terms counting 0's as terms as C(n+r-1,r-1).
(a)
Here n=13 and r=8, put it in the above formula so we get C(13+8-1,8-1)= C(20,7)= 77520 selections.
b).
Here, either (i) we can choose none of type I or (ii) we choose one of type I
Case(i): r=7, n=12 (Here we have only 7 types to choose from)
Case(ii): r=7, n=11 (Here we have only 11 cards to choose and only 7 types to choose them from)
Case (i) + Case(ii) = ,C(12+7-1,7-1) + C(11+7-1,7-1) = C(18,6) + (17,6) = 18564+12376 = 30940 selections.