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3 years ago

The ratio of two complementary angles is 5:4. Find the measure of both angles.

Mathematics

2 answers:

grandymaker [24]3 years ago

7 0

Answer:

50 degrees and 40 degrees

Step-by-step explanation:

50 degrees and 40 degrees

complimentary = add up to 90 degrees

5:4:9

50:40:90

Paha777 [63]3 years ago

6 0

Answer:

50° and 40°

Step-by-step explanation:

Complementary angles sum to 90°

sum the parts of the ratio, 5 + 5 = 9 parts

divide 90 by 9 for the value of one part of the ratio

90° ÷ 9 = 10° ← value of 1 part of the ratio, thus

5 parts = 5 × 10° = 50°

4 parts = 4 × 10° = 40°

The 2 angles are 50° and 40°

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Read 2 more answers

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Artyom0805 [142]

A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.
$\frac{dT}{dt} = \alpha(T -52)$

B) Find general solution by separating variables and integrating $\int\frac{dT}{T-52} = \alpha \int dt \\ ln (T-52) = \alpha t + C \\ T = C e^{\alpha t} +52$ :

C) Initial condition is t=0, T = 87
$87 = C +52 \\ C = 35$

D) Total time elapsed is 10 minutes, new temperature is 84
$84 = 35 e^{10\alpha} +52$
solve for alpha
$e^{10\alpha} =\frac{32}{35} \\ \alpha = \frac{ln(32/35)}{10} \\ \alpha = -.00896$

E) Temperature function is:
$T = 35 e^{-.00896 t} +52$
solving for t
$t = \frac{ln (\frac{T-52}{35})}{-.00896}$
Plug in T = 98.6
$t = -31.95$

This is approximately 32 minutes before he arrived or about 1:20 AM

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3 years ago