20 points / WILL GIVE BRAINLIEST

Mathematics

1 answer:

valkas [14]2 years ago

6 0

Answer:

Total Volume = 15π + 18 π= 33π cubic mm

Step-by-step explanation:

What is the volume of the composite figure? Leave the answer in terms of π.

_33π mm3

We have a cone here conjoined to a semi-sphere.

Cone volume: C = (1/3)*(πr^2) * h

semi-sphere volume : V = (1/2)* (4/3) * (π * r^3)

r = 3 mm and h = 5mm

so C = (1/3)*(π (3)^2) * 5 = 15π cubic mm

V = (1/2)* (4/3) * (π * 3^3) = 18 π cubic mm

Total Volume = 15π + 18 π= 33π cubic mm

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Write an exponential equation in the form y = ab* whose graph passes through points (2, 18) and (5, 60.75).

DochEvi [55]

Let $y=ab^x,$ as described in the problem statement. Plugging in $x=2$ and $x=5$ gives us the equations $18=ab^2$ and $60.75=ab^5.$ Since $a,b$ are nonzero, we divide the second equation by the first to get $\frac{27}{8}=b^3,$ which means that $b=\frac{3}{2},$ after taking the cube root. Plugging this value for $b$ into the first equation, we now have $18=a(3/2)^2=\frac{9a}{4}.$ Solving gives $a=8,$ and our desired exponential equation is $\boxed{y=8\left(\frac{3}{2}\right)^x}.$