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Ket [755]
2 years ago
8

A) The cosine rule can be used to find the value of x in the triangle below.

Mathematics
1 answer:
BartSMP [9]2 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

(a)

(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )

x² = 12² + 15² - (2 × 12 × 15 × cos71°)

(b)

x² = 144 + 225 - 360cos71°

   = 369 - 360cos71° ( take square root of both sides )

x = \sqrt{369-360cos71}

  ≈ 16 cm ( to the nearest integer )

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Answer:

The equation of the line is,

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Step-by-step explanation:

First, you have to write it in a form of y = mx + b :

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y = 3 -  \frac{2}{5} x

y =   - \frac{2}{3} x + 5

When both lines are parallel to each other, they will have to same gradient value. So the equation of the line is y = (-2/5)x + b. Next, you have to find the value of b by substutituting (-10,3) into the equation :

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let \: x =  - 10,y = 3

3 =  -  \frac{2}{5} ( - 10) + b

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Answer:

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Step-by-step explanation:

Given equation that shows the amount of the substance after t years,

A=A_0 e^{kt}

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Taking ln both sides,

\ln(0.5) = \ln(e^{19k})

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0.78 A_0=A_0 e^{-0.03648t}

0.78 = e^{-0.03648t}

Again taking ln both sides,

\ln(0.78) = -0.03648t

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