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bagirrra123 [75]
3 years ago
15

A cone has radius 3 and height 4. Your classmate calculates its surface area as shown:

Mathematics
1 answer:
I am Lyosha [343]3 years ago
4 0

Answer:

Lateral surface area of cone = π(3)(5)

Lateral surface area of cone = 47.1 unit² (Approx.)

Step-by-step explanation:

Given:

Radius of cone = 3 unit

Height of cone = 4 unit

Find:

Lateral surface area of cone

Computation:

Slant height of cone = √Radius² + Height²

Slant height of cone = √3² + 4²

Slant height of cone = √9 + 16

Slant height of cone = √25

Slant height of cone = 5 unit

Lateral surface area of cone = πrl

Lateral surface area of cone = π(3)(5)

Lateral surface area of cone = (3.14)(15)

Lateral surface area of cone = 47.1 unit² (Approx.)

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<u>Solution:</u>

Given function is:

f(x) = 2x - 1

We have to find the average rate of change from x = -1 to x = 2

<em><u>The average rate of change is given as:</u></em>

\text {Average rate of change}=\frac{f(b)-f(a)}{b-a}

<em><u>The average rate of change from x = -1 to x = 2 is given by formula:</u></em>

\text {Average rate of change}=\frac{f(2)-f(-1)}{2-(-1)}\\\\\text {Average rate of change}=\frac{f(2)-f(-1)}{3}

<em><u>Find f(2) and f( - 1)</u></em>

<em><u>Substitute x = 2 in given function</u></em>

f(2) = 2(2) - 1 = 4 - 1 = 3

<em><u>Substitute x = -1 in given function</u></em>

f( - 1) = 2(-1) - 1 = -2 - 1 = -3

<em><u>Substitute the values in above formula,</u></em>

\text {Average rate of change}=\frac{3-(-3)}{3}=\frac{6}{3}=2

Thus average rate of change from x = -1 to x = 2 is 2

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So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is \frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }

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On cross-multiplication we get,

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On cross multiplication ,we get

\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}

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