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maksim [4K]
3 years ago
7

How to find out the value of the lettered sides

Mathematics
2 answers:
Serggg [28]3 years ago
6 0

Answer:

<h2>a = 9.2</h2><h2>b = 8.65</h2><h2 />

Step-by-step explanation:

<u>First</u><u> </u><u>Question</u>

To find a we use sine

sin ∅ = opposite / hypotenuse

a is the opposite

12.8 is the hypotenuse

sin 46 = a / 12.8

a = 12.8 sin 46

<h3>a = 9.2</h3>

<u>Sec</u><u>ond</u><u> question</u>

To find b we use cosine

cos∅ = adjacent / hypotenuse

b is the adjacent

16.8 is the hypotenuse

cos 59 = b / 16.8

b = 16.8 cos 59

<h3>b = 8.65</h3>

Hope this helps you

umka2103 [35]3 years ago
3 0

Step-by-step explanation:

  • a

sin 46°= a/12.8

a = sin46° * 12.8 = 9.20

  • b

cos59°=b/16.8

b = cos59°*16.8 = 8.65

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<span> -14x + 11y = 23
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7x = 37 + 58.2
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x = 95.2/7
x = 13.6

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-14(13.6) + 11(19.4) = 23
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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}

4 0
3 years ago
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