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Mathematics

1 answer:

olchik [2.2K]3 years ago

3 0

- 2x and 70 are equal, because they are vertical angles.

- 110 and 3x + 5 are equal, becasue they are vertical angles.

- so, the answer would be A.

-- this is because vertical angles are not supplementary so would not be equal to 180°

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An airplane is flying at a speed of 500 mi/h at an altitude of one mile. The plane passes directly above a radar station at time

d1i1m1o1n [39]

Answer:

a) $s=\sqrt{1+d^2}$

b)d(t)=500t

c) $s(t) =\sqrt{1+250000t^2}$

Step-by-step explanation:

d = Horizontal distance

s = the distance between the plane and the radar station

The horizontal distance (d), the one mile altitude, and s form a right triangle.

So, use Pythagoras theorem

$Hypotenuse^2=Perpendicular^2+Base^2$

$s^2=1^2+d^2$

a) $s=\sqrt{1+d^2}$

(b) Express d as a function of the time t (in hours) that the plane has flown.

$distance = speed \times time$

d(t)=500t

$s(t) =\sqrt{1+d^2}$

using b

$s(t) =\sqrt{1+(500t)^2}\\s(t) =\sqrt{1+250000t^2}$

6 0

3 years ago

You decide to put $5000 in a savings account to save $6000 down payment on a new car. If the account has an interest rate of 7%

bezimeni [28]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&\$6000\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}$

$\bf 6000=5000\left(1+\frac{0.07}{12}\right)^{12\cdot t}\implies \cfrac{6000}{5000}\approx (1.0058)^{12t}\implies \cfrac{6}{5}\approx(1.0058)^{12t} \\\\\\ \log\left( \cfrac{6}{5} \right)\approx \log[(1.0058)^{12t}]\implies \log\left( \cfrac{6}{5} \right)\approx 12t\log(1.0058) \\\\\\ \cfrac{\log\left( \frac{6}{5} \right)}{12\log(1.0058)}\approx t\implies 2.63\approx t\impliedby \textit{about 2 years, 7 months and 16 days}$