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3 years ago

Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown:

Mathematics

1 answer:

kipiarov [429]3 years ago

7 0

Answer:

15.59 feet

Step-by-step explanation:

We need to find BC and CD

First find BC

We can use the Pythagorean theorem

AB^2 + BC^2 = AC^2

11^2 + BC^2 = 13^2

121 + BC^2 =169

Subtract 121 from each side

121-121+BC^2 = 169-121

BC^2 = 48

Take the square of each side

sqrt(BC^2 ) = sqrt( 48)

BC = 6.92820323

then we need to find CD

We can use the Pythagorean theorem

CD^2 + DE^2 = CE^2

CD^2 + 5^2 = 10^2

CD^2 + 25 =100

Subtract 25 from each side

CD^2 + 25-25 =100-25

CD^2 = 75

Take the square of each side

sqrt(CD^2 ) = sqrt( 75)

BC = 8.660254038

BD = BC +CD

= 6.92820323 + 8.660254038

15.58845727

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If Ben invests $4500 at 4% interest per year, how much additional money must he invest at 5 1/2% annual interest to ensure that

pogonyaev

$Step \; 1: \; Assing \; variable \; for \; the \; unknown \; that \; we \; need \; to \; find.\\Let \; x \; be \; additional \; money \; invested$

$Step \; 2: \; Use \; the \; appropriate \; formula \; of \; simple \; interest \; set \; up \; an \; equation\\Interest \; earned \; each \; year = \; Amount \; invested \times annual \; rate \; of \; interest\\\\Amount \; invested \; in \; 4 \% \; rate \; of \; interest=\$4500\\Amount \; invested \; in \; 5\frac{1}{2}\% \; rate \; of \; interest= \$x\\Amount \; invested \; totally \; in \; 4\frac{1}{2}\% \; rate \; of \; interest = \$(4500+x)$

$Interest \; earned \; in \; 4\% \; interest \; rate\\ = \; 4500(4\%)=180\\Interest \; earned \; in \; 5\frac{1}{2}\% \; interest \; rate\\ = x(5\frac{1}{2}\%)=0.055x\\Interest \; earned \; totally \; in \; 4\frac{1}{2}\% \; interest \; rate = (4500+x)(4\frac{1}{2}\%)\\=0.045(4500+x)$

$\\\\So, \; the \; equation \; would \; be:\\180+0.055x=0.045(4500+x)$

$Step \; 1: \; Distribute \; 0.045 \; in \; the \; right \; side\\180+0.055x=202.5+0.045x\\\\Step \; 2: \; Subtract \; 0.045x \; and \; 180 \; on \; both \; sides \; to \; get \; x \; alone\\0.055x-0.045x=202.5-180\\\\Step \; 3: \; Combine \; Like \; Terms\\0.01x=22.5\\\\Step \; 4: Divide \; 0.01 \; on \; both \; sides\\\frac{0.01x}{0.01}=\frac{22.5}{0.01}\\\\Step \; 5: \; Simplifying \; fraction \; on \; both \; sides\\x=2250$

$\underline{Conclusion:}\\Ben \; should \; invest \; additional \; money \; of \; \$2250$

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