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3 years ago

NEED HELP! I ALREADY DID HALF, BUT STILL CONFUSED!

Mathematics

1 answer:

Anna35 [415]3 years ago

8 0

Answer:

Step-by-step explanation:

Triangle BCZ is a right angle triangle. Triangle BCU is also a right angle triangle. Side BU is common to both triangles.

To determine m∠ZBC, we would apply the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan B = 8/6 = 1.33

m∠ZBC = Tan^-1(1.33) = 53.06

m∠UBC = m∠ZBC/2 = 26.53

To determine CU, we would apply

the tangent trigonometric ratio.

Therefore,

Tan 26.53 = CU/6

CU = 6Tan26.53

CU = 6 × 0.4992

CU = 2.9952

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Step-by-step explanation:

Let’s say that x is number of trees at the begging of the first year, we know that for four years the number of trees were incised by 1/4 of the number of trees of the preceding year, so at the end of the first year the number of trees was $x+\frac{1}{4} x=\frac{5}{4} x$ , and for the next three years we have that

Start End

Second year $\frac{5}{4}x$ -------------- $\frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x$

Third year $(\frac{5}{4} )^{2}x$ ------------- $(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x$

Fourth year $(\frac{5}{4})^{3}x$ -------------- $(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.$

So the formula to calculate the number of trees in the fourth year is

$(\frac{5}{4} )^{4} x,$ we know that all of the trees thrived and there were 6250 at the end of 4 year period, then

$6250=(\frac{5}{4} )^{4}x$ ⇒ $x=\frac{6250*4^{4} }{5^{4} }= \frac{10*5^{4}*4^{4} }{5^{4} }=2560.$

Therefore the number of trees at the begging of the 4-year period was 2560.

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