Answer:
The capacity of the mug is 1,527.43 cm^3
Step-by-step explanation:
In this question, we are asked to calculate the capacity of the hemisphere. This is same as calculating the volume of the hemisphere.
A hemisphere is a sharpe which is half a sphere. Meaning to get a hemisphere, we shall be diving a sphere into 2.
Mathematically, the volume of a hemisphere V = 2/3 * π * r^3
Since D = 18cm , r = D/2 = 18cm/2 = 9 cm
The volume V is thus = 2/3 * 22/7 * 9^3
V = 1,527.428 cm^ 3
To the nearest hundredth,
V = 1,527.43 cm^3
Answer:
<h2>
50+50i</h2>
Step-by-step explanation:
Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.
Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)
On expansion
(3 - i)(3 + i)
= 9+3i-3i-i²
= 9-(-1)
= 9+1
(3 - i)(3 + i) = 10
For the expression (2 + i)(1 - i), we have;
(2 + i)(1 - i)
= 2-2i+i-i²
= 2-i+1
= 3-i
Multiplying 3-i with the last expression (1 + 2i)
(2 + i)(1 - i)(1 + 2i)
= (3-i)(1+2i)
= 3+6i-i-2i²
= 3+5i-2(-1)
= 3+5i+2
= 5+5i
Finally, [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]
= 10(5+5i)
= 50+50i
Hence, (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i
Answer:
Step-by-step explanation:
Base is an equilateral triangle
slant hight= 12 in
side of base= 5 in
so, perimeter of base = 3(5)=15 in
lateral area = 1/2 pl =1/2 (15)(12) in
=90 in²
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hope it helps..
have a great day!!
<span>Point slope form is (y - y1) = m(x - x1), where m is a slope of 2, and x1 = 0 and y1 = 0 are our point at the origin. Therefore, we can plug in these values to get the point slope equation for our line:
(y – 0) = 2*(x - 0)</span>
Answer:
13646514108
Step-by-step explanation:
Used calculator.
