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3 years ago

Please help me ASAP thank you

Mathematics

1 answer:

DaniilM [7]3 years ago

6 0

Answer:

x=17°

Step-by-step explanation:

163+x=180 (L.P)

x=180-163

x=17°

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A van starts off 191 miles directly north from the city of Morristown. It travels due east at a speed of 25 miles per hour. Afte

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Distance between the van and Morristown is changing at the rate of 13.22 miles per hour.

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From the figure attached,

Van starts from C (City of Morristown), reaches the point A 191 miles due North and then it travels with a speed of 25 miles per hour due East from A towards B.

We have to calculate the rate of change of distance BC, when the van reaches point B which is 119 miles away from A.

By Pythagoras theorem in the triangle ABC,

$BC^{2}=AB^{2}+AC^{2}$

Distance AC is constant equal to 191 mi.

By differentiating the equation with respect to time 't'

$2BC.\frac{d(BC)}{dt}=0+2AB.\frac{d(AB)}{dt}$

$BC.\frac{d(BC)}{dt}=AB.\frac{d(AB)}{dt}$

Since BC² = (119)²+ (191)²

BC = √50642 = 225.04 miles

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$(225.03).\frac{d(BC)}{dt}=119\times 25$ [Since $\frac{d(AB)}{dt}=25$ miles per hour]

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4 0

3 years ago

The current population of a small town is 2463 people. It is believed that town's population is tripling every 12 years. Approxi

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{Answer:

3893 residents.

Step-by-step explanation:

Equation for population growth:

The equation for the size of a population, considering that it doubles every n years, is given by:

$A(t) = A(0)(3)^{(\frac{t}{n})}$

In which A(0) is the initial population.

The current population of a small town is 2463 people. It is believed that town's population is tripling every 12 years.

This means that $A(0) = 2463, n = 12$ . So

$A(t) = A(0)(3)^{(\frac{t}{n})}$

$A(t) = 2463(3)^{(\frac{t}{12})}$

Approximate the population of the town 5 years from now.

This is A(5). So

$A(t) = 2463(3)^{(\frac{t}{12})}$

$A(5) = 2463(3)^{(\frac{5}{12})} = 3892.8$

Rounding to the nearest whole number, 3893 residents.

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