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lozanna [386]
3 years ago
7

Please help this question.

Mathematics
1 answer:
sergejj [24]3 years ago
3 0

Answer:

a). 59.049°C

b). 2.1179 seconds

Step-by-step explanation:

Expression representing the final temperature after decrease in temperature of the metal from 100°C to T°C is,

T = 100(0.9)^{x}

where x = duration of cooling

a). Temperature when x = 5 seconds

T = 100(0.9)⁵

  = 59.049

  ≈ 59.049°C

b). If the temperature of the metal decreases from 100°C to 80°C

Which means for T = 80°C we have to calculate the duration of cooling 'x' seconds

80 = 100(0.9)^{x}

0.8 = (0.9)^{x}

By taking log on both the sides

log(0.8) =log[(0.9)^{x}]

-0.09691 = x[log(0.9)]

-0.09691 = -0.045757x

x = \frac{0.09691}{0.045757}

x = 2.1179

x ≈ 2.1179 seconds

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netineya [11]

Answer:

(a)\ Area = 195\pi

(b)\ Volume = 700\pi

Step-by-step explanation:

Given

h = 12

d_1 = 10 --- lower diameter

d_2 = 20 --- upper diameter

Solving (a): The curved surface area

This is calculated as:

Area = \pi l(r_1 + r_2)

Where

r_1 = 0.5 * d_1 = 0.5 * 10 = 5 --- lower radius

r_2 = 0.5 * d_2 = 0.5 * 20 = 10 --- upper radius

And

l = \sqrt{h^2 + (r_1 - r_2)^2 ---- l represents the slant height of the frustrum

l = \sqrt{12^2 + (5 - 10)^2

l = \sqrt{12^2 + (-5)^2

l = \sqrt{144 + 25

l = \sqrt{169

l = 13

So, we have:

Area = \pi l(r_1 + r_2)

Area = \pi * 13(5 + 10)

Area = \pi * 13(15)

Area = 195\pi

Solving (b): The volume

This is calculated as:

Volume = \frac{1}{3}\pi * h * (r_1^2 + r_2^2 + (r_1 * r_2))

This gives:

Volume = \frac{1}{3}\pi * 12 * (5^2 + 10^2 + (5 * 10))

Volume = \frac{1}{3}\pi * 12 * (25 + 100 + (50))

Volume = \frac{1}{3}\pi * 12 * (175)

Volume = \pi *4 * 175

Volume = 700\pi

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3 years ago
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Answer:

x = 24

Step-by-step explanation:

a^2 + b^2 = c^2

7^2 + b^2 = 25^2

49 + b^2 = 625

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b^2 = 576

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b = 24, or x = 24

<em><u>Hope this helped! Have a nice day! Plz mark as brainliest!!!</u></em>

<em><u>-XxDeathshotxX</u></em>

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Answer:

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Step-by-step explanation:

<u>64% of 1600</u>

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