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3 years ago

Determine whether the function represents exponential growth, exponential decay, or neither. Explain.y = 161(0.725)t

1 answer:

6 0

If it looks like this
y = 161*(0.725)^t then it's a decay. Reason: the base is under 1. Try a couple of values for t say 0,1,2

y = 161 * (0.725)^0
y = 161

y = 161 * (0.725)^1
y = 161 * 0.725
y = 116.7

y = 161 * (0.725)^2
y = 161 * (0.5256
y = 84.63

You can see that the function is steadily getting smaller. Remember if the base is under 1 and more than 0 the function decays. If it is greater than 1 then the function grows.

Just to make sure we understand what I'm saying
0 < base < 1
y = a ( base)^power.

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There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)

Where:

$AC$ - The distance from A to C, measured in miles.

$AB$ - The distance from A to B, measured in miles.

$BC$ - The distance from B to C, measured in miles.

$\theta$ - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

$AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta$

$\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}$

$\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)$ (2)

If we know that $BC = 7\,mi$ , $AB = 8\,mi$ , $AC = 5\,mi$ , then the bearing from island B to island C:

$\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]$

$\theta \approx 38.213^{\circ}$

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0

2 years ago

Write two expressions that are equivalent to the expression below.<br> (9-0) + (9-c) + (9-c) + (9-C)

Nikolay [14]

Step-by-step explanation:

$4(9 - c) \\ 36 - 4c \\ an \: example \: of \: two \: equivalent \\ expression \: includes \: \\ the \: general \: experssion \: \\ and \: then \: the \: one \: that \: \\ the \: one \: that \: is \: factured$

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3 years ago

In science class, the students observed 24 of the 300 frogs from the local aquarium. If 6 of the frogs observed had spots, how m

Alona [7]

Answer:

225 frogs

Step-by-step explanation:

Total population of frogs = 300 frogs.

Observed population of frogs = 24

6 of the 24 observed frogs had spots

Which means , the number of frogs that did not have spots = 24 - 6 = 18 frogs.

We were told to find how many of the total population can be predicted to NOT have spots. We would form a proportion.

If 24 frogs = 18 frogs with no spots

300 frogs = Y

Cross multiply

24Y = 300 × 18

Y = (300 × 18) ÷ 24

Y = 5400 ÷ 24

Y = 225 frogs.

This means out of 300 frogs, 225 frogs do not have spots.

Therefore, the total population that can be predicted to NOT have spots is 225 frogs.

the total population can be predicted to NOT have spots

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2 years ago

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2 years ago

The cruising speed of a 747 airplane is approximately 9,944 inches per second. What is this speed to the nearest foot per second

sweet [91]

The answer is B. 829 feet per second.

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2 years ago

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