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3 years ago

PLEASE EXTRA POINTS I REALLY NEED HELP!!! 1. A ski lift carries Carol up a slope at a rate of 5 mph.

Mathematics

1 answer:

gtnhenbr [62]3 years ago

4 0

Hi sorry for the late response, I know the assignment was due at 5pm today but anyway here is the answer.

System:

d= 5(0.75-t)

d= 20t

20t = 3.75 -5t

Define Variables:

d = how far Carol Skied

t = time it took Carol to go up/down

Solve:

20t = 3.75 -5t

20t + 5t = 3.75 -5t + 5t

25t = 3.75

25t/25 = 3.75/25

t = 0.15

Now we plug in the time into the Distances:

20t = 3.75 - 5t

20(0.15) = 3.75 - 5(0.15)

3 = 3.75 - 0.75

3 = 3

Solution as Sentence:

Carol Skied 3 miles

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Answer:

$(\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}$

Step-by-step explanation:

Given

$(\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})$

Required

Simplify

For clarity, group the expression in threes

$((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

Evaluate the first group [Divide 8 by 4]

$((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 9 by 3]

$((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 15 by 3]

$((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 16 by 2]

$((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$(\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

Evaluate the second group [Divide 35 and 25 by 5]

$(\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 49 by 7]

$(\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

[Divide 24 by 3]

$(\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$(\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

Merge the first and second group

$((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$(1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

$(\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))$

Evaluate the last group [Divide 99 by 9]

$(\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))$

[Divide 63 by 9]

$(\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))$

[Divide 64 and 80 by 8]

$(\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))$

[Divide 10 and 4 by 2]

$(\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))$

[Divide 100 by 5]

$(\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))$

$(\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))$

$(\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})$

$1*(\frac{11}{20})$

$\frac{11}{20}$

Hence;

$(\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}$

4 0

3 years ago