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3 years ago

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(a) find parametric equations for the line that passes through the point (−2, 5) and is parallel to the vector <3, −8>. (e

nter your answer as a comma-separated list of equations where x and y are in terms of the parameter t.)

1 answer:

Fittoniya [83]3 years ago

6 0

= <-2 +3t, 5 -8t>

Multiply the direction vector by the parameter and add it to the given point.

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3 years ago

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Answer: $\bold{(1)\ \dfrac{19,683}{64}\qquad (2)\ 16}$

<u>Step-by-step explanation:</u>

(1) (12, 18, 27, ...)

The common ratio is:

$r=\dfrac{a_{n+1}}{a_n}\quad r =\dfrac{18}{12}=\boxed{\dfrac{3}{2}}\quad \rightarrow \quad r=\dfrac{27}{18}=\boxed{\dfrac{3}{2}}$

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$a_n=a_o(r)^{n-1}\\\\Given:a_o=12,\ r=\dfrac{3}{2}\\\\\\Equation:\\a_n =12\bigg(\dfrac{3}{2}\bigg)^{n-1}\\\\\\\\9th\ term:\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{9-1}\\\\\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{8}\\\\\\.\quad =\large\boxed{\dfrac{19643}{64}}$

$(2)\qquad \bigg(\dfrac{1}{16},\dfrac{1}{8},\dfrac{1}{4},\dfrac{1}{2}\bigg)\\\\\\\text{The common ratio is}:\\\\r=\dfrac{a_{n+1}}{a_n}\quad r=\dfrac{\frac{1}{8}}{\frac{1}{16}}=\boxed{2}\quad \rightarrow \quad r=\dfrac{\frac{1}{4}}{\frac{1}{8}}=\boxed{2}$

The equation is:

$a_n=a_o(r)^{n-1}\\\\Given:a_o=\dfrac{1}{16},\ r=2\\\\\\Equation:\\a_n =\dfrac{1}{16}(2)^{n-1}\\\\\\\\9th\ term:\\a_9=\dfrac{1}{16}(2)^{9-1}\\\\\\a_9=\dfrac{1}{16}(2)^{8}\\\\\\.\quad =\large\boxed{16}$

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3 years ago

to communication companies offer calling plans with company X it cost $0.35 to connect and then $0.05 for each minute with compa

Mama L [17]

Answer:

X Company charges $(0.2+0.01n)\times 10^2 \ cents$ more than Company Y

Step-by-step explanation:

Given:

Cost of X company = $\$ 0.35+(\$0.05\times 1 \ minute)$

Cost of Y Company = $\$ 0.15+(\$0.04\times 1 \ minute)$

for n minutes

Cost of X company for n minutes = $\$ 0.35+(\$0.05\times n \ minute)$

Cost of Y Company for n minutes = $\$ 0.15+(\$0.04\times n \ minute)$

Difference for n minutes we get by Subtracting Cost of Y Company for n minutes by Cost of X company for n minutes

Difference for n minutes = $(\$ 0.2+\$ 0.01n)$ = $(0.2+0.01n)\times 10^2 \ cents$

X Company charges $(0.2+0.01n)\times 10^2 \ cents$ more than Company Y

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FromTheMoon [43]

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