Pls help with steps also

Part (i)

We're told that which means angle DAB is 60 degrees. This angle is cut into two equal halves of 30 degrees each (for angles DAP and PAB) due to segment AP being a bisector of angle DAB.

Since ABCD is a parallelogram, the adjacent angles A and B are supplementary. A = 60 leads to...

A+B = 180

B = 180 - A

B = 180-60

B = 120

Angle ABC is 120 degrees which splits in half to get 60. The angles PBA and PBC are 60 degrees each.

Focus on triangle PAB. We found A = 30 and B = 60 earlier. That must mean:

P+A+B = 180

P+30+60 = 180

P+90 = 180

P = 180-90

P = 90

Triangle PAB is a right triangle with angle P being the 90 degree angle. This is another way of saying angle APB is 90 degrees.

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Part (ii)

From the previous part, we know that angles DAP and PAB are 30 degrees each. The alternate interior angles DPA and PAB are equal because we have a parallelogram, so angle DPA is also 30 degrees.

For triangle DPA, the base angles A and P are congruent (30 degrees each). This leads immediately to the fact triangle DPA is isosceles. The congruent sides are opposite the congruent base angles.

Therefore, AD = DP

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Also from part (i), we found that angles PBA and PBC were 60 degrees each.

Since we have a parallelogram, the alternate interior angles PBA and BPC are congruent, meaning that angle BPC is also 60.

For triangle PBC, we have the interior angles of:

P+B+C = 180

60+60+x = 180

120+x = 180

x = 180-120

x = 60

Each interior angle of triangle PBC is 60 degrees. Triangle PBC is equilateral. By definition, equilateral triangles have all sides the same length.

Therefore, PB = PC = BC.

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Part (iii)

ABCD is a parallelogram with congruent opposite sides.

Let AD = BC = x

From part (ii), we found that AD and DP were the same length. So DP = x as well.

Also from part (ii), we found that BC = PC, so PC = x

We can then say:

DC = DP + PC

DC = x + x

DC = 2x

DC = 2*AD

the reporter's right

step-by-step explanation:

1/4 = .25 / 25%

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).