What is the radius of a hemisphere with a volume of 165\text{ cm}^3,165 cm 3 , to the nearest tenth of a centimeter?

4.3cm

Step-by-step explanation:

the radius of the hemisphere can be determined its volume

volume of a hemisphere = (2/3) x (n) x (r^3)

n = 22/7

r = radius

(2/3) x (22/7) x( r^3) = 165 cm^3

44/21 x r^3 = 165

divide both sides of the equation by 21/44

165 x 21/44

r^3 = 78.75

find the cube root

r = 4.2863 cm

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

the 100th terms, 8 is greater than 6, so add 1 to 2. this give 4.3cm

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

32

step-by-step explanation: