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trapecia [35]
3 years ago
12

Find the measure of ∠P.

Mathematics
1 answer:
saveliy_v [14]3 years ago
7 0
180-28-67=85. Angle P is 85 degrees
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Please someone help me. It's about proving related to transformation of trigonometric ratios. Thank you!!​
kvasek [131]

Answer:

see explanation

Step-by-step explanation:

Using sum to product identities

cos x - cos y = - 2sin(\frac{x+y}{2} )sin(\frac{x-y}{2} ) = 2sin(\frac{x+y}{2} )sin(\frac{y-x}{2} )

cos x + cos y = 2cos(\frac{x+y}{2} )cos(\frac{x-y}{2} )

Note that

sin10° = sin(90 - 10)° = cos80°

Thus

\frac{2sin(\frac{10+80}{2})sin(\frac{80-10}{2})  }{2cos(\frac{10+80}{2})cos(\frac{80-10}{2})  } ← cancel 2 from numerator/ denominator

= \frac{sin45}{cos45} × \frac{sin35}{cos35}

= tan45° × tan35° { tan45° = 1 ]

= 1 × tan35°

= tan35° ← as required

5 0
3 years ago
Read 2 more answers
A scientist counts 25 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 25
Ksju [112]
y = 25\cdot~3^x\\ \\ 1170 = 25\cdot~3^x\\ \\ \frac{1170}{25} = 3^x\\ \\ \frac{243}{5} = 3^x\\ \\ log\ \frac{243}{5} = log~3^x\\ \\ log~243-log~5=x~log~3\\ \\ 
 log~3^5-log~5=x~log~3\\ \\ 5~log~3-log~5 = x~log~3\\ \\ 5(0,48)-0,70= 0,48x\\ \\ 2,4-0,7 = 0,48x\\ \\ 1,7=0,48x\\ \\ x=\frac{1,7}{0,48}\\ \\ \large{\boxed{x=3,54\ h}}
6 0
4 years ago
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Find the exact area of the shaded region. A. 16π−8 cm² B. 42.3 cm² C. 92.5 cm² D. 84.6 cm2
Anika [276]

Answer:

A = (16π - 8) cm^2

Step-by-step explanation:

The shaded area is trhe area of the circle minus rthe area of the truiangle,.

A = πr^2 - bh/2

A = π(4 cm)^2 - (4 cm)(4 cm)/2

A = 16π cm^2 - 8 cm^2

A = (16π - 8) cm^2

5 0
3 years ago
Can someone help me drag this please correct answers only
jeka57 [31]
180- 44= 136 = x
90-57=33 = y
107 - 27 = 80 = x
P = 57
8 0
3 years ago
Read 2 more answers
Write the three numbers less then 40 that have 2 and 5 as factors
ozzi
No. which have factors 2 & 5 have 2 & 5 as their prime factor
therefore, No. are :
2*5 = 10
2*5*2 = 20
2*5*3 = 30
3 0
3 years ago
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