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Natali [406]
3 years ago
14

find the volume of the composite figure ( also I'm not going to redo this question becuase, u should be able to zoom in) Ok, ple

ase help me answer 1-6 DUE ON MONDAY! Also I have to do the review!

Mathematics
2 answers:
cricket20 [7]3 years ago
5 0
This is all very simple math, divide the figures into 2 or more separate blocks. Next adjust the measurements, then calculate the volume of both boxes (LxWxH) and add them together to get the answer. 
Zepler [3.9K]3 years ago
5 0
I can answer only from 1 to 4 since idk how to do number 5 and the picture is missing part of number 6.
1) would be 12 since the bottom block would be 4*2*1 (8) and then 2*2*1 would be 4. 4+8= 12 cubic inch.

2) You did it correctly!

3) 6*3*1=18 and 7*1*3=21 21+18 is 39 cubic inch.

4) 6*4*12= 288 and 8*4*4= 128 128+288= 416 cubic ft
I am like 98% I did it correctly but sometimes I have a mistake so... yeah hope it helps!
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Given:

Sample Mean <span>= 30<span>
Sample size </span><span><span><span>= 1000</span></span><span>
</span></span></span>Population Standard deviation or <span><span><span>σ<span>=2</span></span><span>
</span></span>Confidence interval </span><span>= 95%</span>

to compute for the confidence interval

Population Mean or <span>μ<span><span>= sample mean ± (</span>z×<span>SE</span>)</span></span>

<span><span>where:</span></span>

<span><span>SE</span>→</span> Standard Error

<span><span>SE</span>=<span>σ<span>√n</span>= 30</span></span>√1000=0.9486

Critical Value of z for 95% confidence interval <span>=1.96</span>

<span>μ<span>=30±<span>(1.96×0.9486)</span></span><span>
</span></span><span>μ<span>=30±1.8594</span></span>

Upper Limit

<span>μ <span>= 30 + 1.8594 = 31.8594</span></span>

Lower Limit

<span>μ <span>= 30 − 1.8594 = <span>28.1406</span></span></span>

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<span><span><span>answer: 28.1406<u<31.8594</span></span></span>

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A circle is growing so that the radius is increasing at the rate of 3 cm/min. How fast is the area of the circle changing at the
Naya [18.7K]

Answer:

The area is growing at a rate of \frac{dA}{dt} =226.2 \,\frac{cm^2}{min}

Step-by-step explanation:

<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>

We identify that the info given on the increasing rate of the circle's radius is 3 \frac{cm}{min} and we identify such as the following differential rate:

\frac{dr}{dt} = 3\,\frac{cm}{min}

Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find  \frac{dA}{dt}.

So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):

A=\pi\,r^2

We now apply the derivative operator with respect to time (\frac{d}{dt}) to this equation, and use chain rule as we find the quadratic form of the radius:

\frac{d}{dt} [A=\pi\,r^2]\\\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}

Now we replace the known values of the rate at which the radius is growing ( \frac{dr}{dt} = 3\,\frac{cm}{min}), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :

\frac{dA}{dt} =\pi\,*2*r*\frac{dr}{dt}\\\frac{dA}{dt} =\pi\,*2*(12\,cm)*(3\,\frac{cm}{min}) \\\frac{dA}{dt} =226.19467 \,\frac{cm^2}{min}\\

which we can round to one decimal place as:

\frac{dA}{dt} =226.2 \,\frac{cm^2}{min}

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