Find the value of x in each of the given figures.

Mathematics

1 answer:

Kaylis [27]3 years ago

8 0

Answer:

Step-by-step explanation:

1) Given figure is a parallelogram

Area = 144 cm²

base * altitude = 144

16 * x = 144

x =144/16

x = 9 cm

2)2) Trapezium

Area = $\frac{a+b}{2}*h$ ; {a and b are parallel sides of trapezium}

( 37 +27 /2) * x = 480 cm²

64/2 * h = 480

32 * h = 480

h = 480/32

h = 15 cm

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$\text{Consider the function}\\
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h(t)=\cot(t) \text{ on the interval }\left [ \frac{\pi}{4}, \ \frac{3\pi}{4} \right ]\\
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\text{we know that the average rate of change of a funtion f(x) over the }\\
\text{interval [a, b] is given by}\\
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f_{avg}=\frac{f(b)-f(a)}{b-a}\\
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\text{so using this, the average rate of change of the given function is}$

$h_{avg}=\frac{h\left ( \frac{3\pi}{4} \right )-h\left ( \frac{\pi}{4} \right )}{\frac{3\pi}{4}-\frac{\pi}{4}}\\
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=\frac{\cot \left ( \frac{3\pi}{4} \right )-\cot \left ( \frac{\pi}{4} \right )}{\frac{3\pi-\pi}{4}}\\
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=\frac{(-1)-(1)}{\frac{2\pi}{4}}\\
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=\frac{-2}{\frac{\pi}{2}}\\
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\text{Average rate of change of function}=\frac{-4}{\pi}$