Please help me get this answer

Find the volume of the rectangle 4 2/3cm,9 1/8cm, 2cm

amm1812

Answer:

$\large\boxed{V=85\dfrac{1}{6}\ cm^3}$

Step-by-step explanation:

The formula of a volume of a rectangular prism:

$V=lwh$

l - length

w - width

h - height

We have

$l=4\dfrac{2}{3}\ cm=\dfrac{4\cdot3+2}{3}\ cm=\dfrac{14}{3}\ cm\\\\w=9\dfrac{1}{8}\ cm=\dfrac{9\cdot8+1}{8}\ cm=\dfrac{73}{8}\ cm\\\\h=2\ cm$

Substitute:

$V=\dfrac{14}{3}\cdot\dfrac{73}{8}\cdot2=\dfrac{7}{3}\cdot\dfrac{73}{2}\cdot1=\dfrac{511}{6}=85\dfrac{1}{6}\ cm^3$

6 0

2 years ago

What composition forms the equation p(x) when given the functions for h(x), f(x), k(x), and g(x)? PLEASE HELP!!!!! thank you!!!!

Flura [38]

Answer: Choice B. k(h(g(f(x))))

For choice B, the functions are k, h, g, f going from left to right.

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Explanation:

We have 4x involved, so we'll need f(x)

This 4x term is inside a cubic, so we'll need g(x) as well.

So far we have

g(x) = x^3

g( f(x) ) = ( f(x) )^3

g( f(x) ) = ( 4x )^3

Then note how we are dividing that result by 2. That's the same as applying the h(x) function

$h(x) = \frac{x}{2}\\\\h(g(f(x))) = \frac{g(f(x))}{2}\\\\h(g(f(x))) = \frac{(4x)^3}{2}\\\\$

And finally, we subtract 1 from this, but that's the same as using k(x)

$k(x) = x-1\\\\k(h(g(f(x)))) = h(g(f(x)))-1\\\\k(h(g(f(x)))) = \frac{(4x)^3}{2}-1\\\\$

This leads to the answer choice B.

To be honest, this notation is a mess considering how many function compositions are going on. It's very easy to get lost. I recommend carefully stepping through the problem and building it up in the way I've done above, or in a similar fashion. The idea is to start from the inside and work your way out. Keep in mind that PEMDAS plays a role.

6 0

2 years ago

Help anyone I have like 15 more minuets to finish

Naya [18.7K]

The answer is 45 it's the easiest

5 0

3 years ago

Exposure to ionizing radiation is known to increase the incidence of cancer. One thousand laboratory rats are exposed to identic

mojhsa [17]

Missing information :

The model was omitted from the question ; the possible model relating to the question was browsed online and could possibly be :

N(t) = 1.07t^2.3 for 0 ≤ t ≤ 10 months

Answer:

30.9 cases per month

Step-by-step explanation:

Given the model to determine the number of rats that have developed cancer after initial exposure ; N(t) = 1.07t^2.3

N(t) = 1.07t^2.3

Take the first derivative of N with respect to t to obtain the rate of change ;

N'(t) = (1.07)(2.3)t^2.3-1

N'(t) = (1.07)(2.3)t^1.3

The rate of growth of cancer cases at the 7th month can be calculated thus :

t = 7

N'(7) = (1.07)(2.3)t^1.3

N'(7) = 1.07 * 2.3 * 7^1.3

N'(7) = 1.07 * 2.3 * 12.549529

N'(7) = 30.884

The rate of growth of cancer at the 7th month is 30.9 cases per month.

7 0

3 years ago

Given the graph of g(x), describe the transformation of the parent function

Citrus2011 [14]

Answer:

The table is attached in the figure.

g(x) = f(4x) ⇒⇒⇒ differentiating both sides with respect to x

∴ g'(x) = \frac{d}{dx} [f(x)] * \frac{d}{dx} [4x]=4*f'(x) ⇒⇒⇒⇒⇒⇒ chain role

To find g '(0.1)

Substitute with x = 0.1

from table:

f'(0.1) = 1 ⇒ from the table

∴ g'(0.1) = 4 * [ f'(0.1) ] = 4 * 1 = 4

Step-by-step explanation:

7 0

2 years ago