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4 years ago

Fill in the missing value to make the equations true.

Mathematics

1 answer:

Furkat [3]4 years ago

7 0

Answer:

a) 7/4 b) 5 c) 2

Step-by-step explanation:

Logrithmic Rule for a and b

Let a, M, N be positive real numbers.

logaM - logaN = loga(M/N)

log9(7) - log9(4) = log9 (7/4)

logaM + logaN = logaMN

log2 (x) + log2(9) = log2(45)

x9=45

(x9)/9 = 45/9

x = 5

Change of base formula.

logb(x)=logd(b)/logd(x)

x log6(5) = log6(25) divide each term by log6(5)

x log6(5) / log6(5) = log6(25) / log6(5) Cancel common factor log6(5)

x = log6(25) / log6(5)

x = log6(5^2) / log6(5)

Expand log6(5^2) by moving 2 outside the logarithm.

x = 2log6(5) / log6(5) cancel the like term log6(5)

x = 2

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17. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find

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Answer:

$r = 3.74cm$

Step-by-step explanation:

Given

Hemisphere

$Radius = 7cm$

Cone

$Height = 49m$

Required

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First, we calculate the volume (V1) of the hemisphere.

$V_1 = \frac{2}{3}\pi r^3$

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So, we have:

$\frac{686}{3}\pi = \frac{1}{3}\pi r^2h$

$686 = r^2h$

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$686 = r^2 * 49$

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$r^2 = \frac{686}{49}$

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