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3 years ago

Angle 5 and 6 are supplements and angle 5 is 24 more than half the measure of angle 6. find the measure of each angle.

Mathematics

1 answer:

brilliants [131]3 years ago

3 0

Supplementary angles equal 10 degrees.

Let angle 6 = X

Angle 5 is 24 more than half of angle 6, which can be written as 1/2X +24

So now we have X + 1/2x +24 = 180

Combine the like terms ( X +1/2X = 1.5X)

1.5x + 24 = 180

Subtract 24 from each side:

1.5x = 156

Divide both sides by 1.5:

x = 156 / 1.5

X = 104

Angle 6 = 104 degrees.

Angle 5 = 180 - 104 = 76 degrees

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In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled a

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Answer:

The answer is " $\bold{T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5}$ "

Step-by-step explanation:

Given value:

Temp-maximum= $18^{\circ}$

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It is halfway between 10 am and 10 pm to 4 am.

The sinus and cosine roles could be used throughout the year to predict fluctuations in climate models. Its type of formula that can be used to model such information is:

$T = A \cos B(t-C) + D,$ where parameters are A, B , C, D, T is the ° C temperature and t is the time (1-24)

$A = amplitude = \frac{(T_{max} - T_{min})}{2}\\\\$

$= \frac{(3 - 18)}{2}\\\\= - \frac{15}{2}\\\\ = -7.5$

$B = \frac{2 \pi}{24}\\\\$

$= \frac{\pi}{12}$

$C = \text{ units translated to the right}= 4$

$D = y_{min} + amplitude = units \ translated \ up\\\\$

D = 7.5 + 3 = 10.5

Its trigonometric function equation that model temperature T hours after midnight in Johannesburg t.

$T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5$

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i usually always use this to help me to keep it in order

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(X1,Y1)(X2,Y2)

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use this and your garanteed to get the right answer everytime

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