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IrinaK [193]
2 years ago
5

Pleaseeeeeeeeeee help.

Mathematics
1 answer:
Sauron [17]2 years ago
6 0

Answer:

The total distance Remy will swim is approximately 236 meters

Step-by-step explanation:

From the given diagram, of triangle ΔCAB, we have that the path Remy is to swim are;

1) Length of segment C to A

2) Length of segment A to B

3) Length of segment B to C

The length of the perpendicular at point D on segment AB to C = 60 meters

Therefore, DC = 60 m

By trigonometric ratios, we have;

tan (\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length}

cos(\theta) = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}

We are given the values of the trigonometric ratios of the following angles;

tan(27°) = 0.51

tan(43°) = 0.93

cos(27°) = 0.89

cos(43°) = 0.73

∴ tan(43°) = AD/DC = 0.93

Where the lengths of AC, AD, DB, DC and BC

AD = DC × tan(43°)

∴ AD = 60 × 0.93 ≈ 55.8

Similarly, we have;

tan(27°) = DB/DC

∴ DB = DC × tan(27°)

DB = 60 × 0.51 ≈ 30.6

From cos(\theta) = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}, we have;

cos(43°) = DC/AC

AC = DC/(cos(43°))

∴ AC = 60/0.73 ≈ 82.2

Similarly, we have;

cos(27°) = DC/BC

BC = DC/(cos(27°))

∴ BC = 60/0.89 ≈ 67.4

The total distance Remy will swim = AC + AD + DB + BC

∴ The total distance Remy will swim = 82.2 + 55.8 + 30.6 + 67.4 = 236

The total distance Remy will swim = 236 meters

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Trava [24]

Answer:

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(b)\log_5(\dfrac{625}{25})=2

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Step-by-step explanation:

Let as consider the given equations are \log_3(\dfrac{81}{3})=?,\log_5(\dfrac{625}{25})=?,\log_2(\dfrac{64}{8})=?,\log_4(\dfrac{64}{16})=?,\log_6(36^4)=?,\log(100^3)=?.

(a)

\log_3(\dfrac{81}{3})=\log_3(27)

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(b)

\log_5(\dfrac{625}{25})=\log_5(25)

\log_5(\dfrac{625}{25})=\log_5(5^2)

\log_5(\dfrac{625}{25})=2        [\because \log_aa^x=x]

(c)

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\log_2(\dfrac{64}{8})=\log_2(2^3)

\log_2(\dfrac{64}{8})=3        [\because \log_aa^x=x]

(d)

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\log_4(\dfrac{64}{16})=1        [\because \log_aa^x=x]

(e)

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\log_6(36^4)=8            [\because \log_aa^x=x]

(f)

\log(100^3)=\log((10^2)^3)

\log(100^3)=\log(10^6)

\log(100^3)=6            [\because \log10^x=x]

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