9514 1404 393
Answer:
4 : 1
Step-by-step explanation:
Each segment joining midpoints is called a "midline." It is parallel to the segment not being joined, and is half its length. All the dimensions of the smaller triangle are half those of the larger triangle. (They are similar triangles.) The ratio of areas is the square of the ratio of side lengths:
2² : 1² = 4 : 1 . . . . . . ratio of triangle areas
Answer: the radius is 2.61 cm
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
From the information given,
Volume = 156 cm³
Height = 7.3 cm
Therefore,
156 = 3.14 × r² × 7.3
156 = 22.922r²
r² = 156/22.922 = 6.81
Taking square root of both sides of the equation, it becomes
r = 2.61 cm
B and C are absurd; if a series converges, it must have a sum, but if a series diverges, it cannot have a sum.
Now, notice that

That is, we can write the sum more compactly as

The series is geometric with common ratio

, so the series converges (and thereby has a sum), so the answer is D.
I think its D. 32.6 s/ft and appoximatley 0.03 ft/s
Use the rules of logarithms and the rules of exponents.
... ln(ab) = ln(a) + ln(b)
... e^ln(a) = a
... (a^b)·(a^c) = a^(b+c)
_____
1) Use the second rule and take the antilog.
... e^ln(x) = x = e^(5.6 + ln(7.5))
... x = (e^5.6)·(e^ln(7.5)) . . . . . . use the rule of exponents
... x = 7.5·e^5.6 . . . . . . . . . . . . use the second rule of logarithms
... x ≈ 2028.2 . . . . . . . . . . . . . use your calculator (could do this after the 1st step)
2) Similar to the previous problem, except base-10 logs are involved.
... x = 10^(5.6 -log(7.5)) . . . . . take the antilog. Could evaluate now.
... = (1/7.5)·10^5.6 . . . . . . . . . . of course, 10^(-log(7.5)) = 7.5^-1 = 1/7.5
... x ≈ 53,080.96