How to find the angle of a right triangle given 1 side and no angles?

Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions th

trasher [3.6K]

Answer:

(a) 100 fishes

(b) t = 10: 483 fishes

t = 20: 999 fishes

t = 30: 1168 fishes

(c)

$P(\infty) = 1200$

Step-by-step explanation:

Given

$P(t) =\frac{d}{1+ke^-{ct}}$

$d = 1200\\k = 11\\c=0.2$

Solving (a): Fishes at t = 0

This gives:

$P(0) =\frac{1200}{1+11*e^-{0.2*0}}$

$P(0) =\frac{1200}{1+11*e^-{0}}$

$P(0) =\frac{1200}{1+11*1}$

$P(0) =\frac{1200}{1+11}$

$P(0) =\frac{1200}{12}$

$P(0) = 100$

Solving (a): Fishes at t = 10, 20, 30

$t = 10$

$P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483$

$t = 20$

$P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999$

$t = 30$

$P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168$

Solving (c): $\lim_{t \to \infty} P(t)$

In (b) above.

Notice that as t increases from 10 to 20 to 30, the values of $e^{-ct}$ decreases

This implies that:

${t \to \infty} = {e^{-ct} \to 0}$

So:

The value of P(t) for large values is:

$P(\infty) = \frac{1200}{1 + 11 * 0}$

$P(\infty) = \frac{1200}{1 + 0}$

$P(\infty) = \frac{1200}{1}$

$P(\infty) = 1200$

5 0

3 years ago

How much fabric is needed to make curtains for a 5foot tall 3 foot wide window?

SpyIntel [72]

Area = 5(3) = 15 feet

3 0

3 years ago

Someone help me pleaseeeee

Dafna11 [192]

In an isosceles triangle, there are two sides that are congruent.

In this case, AB and BC are congruent.

Knowing this, we know that AB = BC

Since we know the values of AB and BC, we can put them into the equation:

3x - 4 = 5x - 10

Subtract 3x from both sides:

-4 = 2x - 10

Add 10 to both sides to isolate 'x':

6 = 2x

Divide both sides by 2:

x = 3

Now that we know the value of the variable, we just have to input it into AB's equation:

3x - 4 = 3(3) - 4

3(3) - 4 = 9 - 4

9 - 4 = 5

AB = 5

Good luck!

5 0

3 years ago

How do i solve this?

Alina [70]

Answer:

m∠R = 60°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Trigonometry

[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] sinθ = opposite over hypotenuse

Step-by-step explanation:

Step 1: Identify

Angle θ = ∠R

Opposite Leg of ∠R = 10√3

Hypotenuse = 20

Step 2: Solve

Substitute in variables [sine]: $\displaystyle sin(R^\circ) = \frac{10\sqrt{3}}{20}$
[Equality Property] Trig inverse: $\displaystyle R^\circ = sin^{-1}(\frac{10\sqrt{3}}{20})$
Evaluate trig: $\displaystyle R = 60^\circ$

8 0

3 years ago

The length of a rectangle is 7 centimeters greater than the width. The perimeter is 54 centimeters. What is the length and width

Hatshy [7]

When I put it in, I got 378

7 0

3 years ago