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Alecsey [184]
3 years ago
8

Fish enter a lake at a rate modeled by the function E given by ( ) 20 15sin 6 t E t          . Fish leave the lake at a

rate modeled by the function L given by 2 0.1 L( ) 4 2 t t   . Both E(t) and L(t) are measured in fish per hour, and t is measured in hours since midnight (t = 0). a) How many fish enter the lake over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5)? Give your answer to the nearest whole number.

Mathematics
1 answer:
liraira [26]3 years ago
5 0

Answer: The number of fish that enter the lake from midnight (t = 0) to 5 A.M. (t = 5) is 101 fish

Step-by-step explanation:

Given that

Fish enter a lake at a rate modeled by the function E given by E(t) = 20 + 15 sin(πt/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4 + 2^0.1t2. Both E(t) and L(t) are measured in fish per hour, and t is measured in hours since midnight (t = 0).

(a) How many fish enter the lake over the 5-hour period from midnight (t = 0) to 5 A.M. (t = 5)?

Please find the attached file for the solution

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marin [14]

Answer:

46.1 in

Step-by-step explanation:

Given data

Width= 30in

Height= 35in

To find the diagonal, we have to use the Pythagoras theorem

z^2= x^2+y^2

z^2= 30^2+ 35^2

z^2= 900+1225

z^2= 2125

z= √2125

z= 46.09

Hence the diagonal of the TV is 46.1 in

4 0
3 years ago
Noah is buying a pair of jeans and using a coupon for 10%off. The total price is $56.70 which includes $2.70 in sales tax. Noah’
lora16 [44]

Answer:

See below.

Step-by-step explanation:

So, we know that Noah's purchase can be modeled by the equation:

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Part 1)

The solution to the equation will be the value of x.

In this case, x will represent the original price of the jeans.

We know that Noah has a coupon for 10% off the <em>original price of the jeans</em>.

So, 0.1x will represent how much of the original price Noah gets a a discount on.

Therefore, (x - 0.1x) represents the total cost of the jeans <em>after</em> the coupon.

So, x is our original price of the jeans.

Part 2)

To verify that 70 is <em>not</em> a solution, we can simply substitute 70 for x and check whether or not the equation is true. So:

(70)-0.1(70)+2.7\stackrel{?}{=}56.70

Multiply:

70-7+2.7\stackrel{?}{=}56.7

Subtract:

63+2.7\stackrel{?}{=}56.7

Add:

65.7\neq56.7

However, we <em>can</em> verify that 60 <em>is</em> the solution by substituting. So, substitute 60 for every x:

(60)-0.1(60)+2.7\stackrel{?}{=}5.7

Multiply:

60-6+2.7\stackrel{?}{=}56.7

Subtract:

54+2.7\stackrel{?}{=}56.7

Add:

56.7\stackrel{\checkmark}{=}56.7

So, 60 is indeed the solution and is the value of x.

So, this means that $60 was the original price of the jeans.

8 0
3 years ago
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Kipish [7]

Answer:

egnue5neiybyejmkye dt

Step-by-step explanation:

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3 years ago
A geologist noticed that a land along a fault line moved 24.8 centimeters over the past 175 years . On average, how much did the
olasank [31]

Answer:

On average, the land moved 0,14 cm each year.

Step-by-step explanation:

To know how much did, on average, the land move,  we should divide the total number of cm over the total number of years:

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If we divide years over cm we will get x in years each cm, which is wrong.

Because the problem asks for the answer rounded to the hundredths place:

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Trigonometry help; how would I even do these?
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Answer:

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Cos(A) = 36/45

=0.8

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