A small lake is stocked with a certain species of fish. The fish population is modeled by the function 10 P= 1 4e-0.4t where P is the number of fish in thousands and t is measured in years since the lake was stocked. (a) Find the fish population after 4 years. (Round your answer to the nearest whole fish.) fish (b) After how many years will the fish population reach 5000 fish? (Round your answer to two decimal places.) yr

Q: Suppose x=4tan(theta) and the angle theta is in the first quadrant. Write algebraic expressions for ...

A: Given that

Q: proof trigonometry identities cot(x)+tan(x)+sec(x)csc(x)=2sec(x)csc(x)

A: To prove: The identity cot(x) + tan(x) + sec(x) csc(x) = 2sec(x) csc(x).

Q: photo attached, the answer is NOT (5/<sqrt>26)

A: It is given that

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A: Given,

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A: Left side is more complicated side. So we 'll start with left side. Plug sin3x=(3sinx-4sin^3x) and c...

Q: proof trigonometry identities tan^4(x)-1/(sec^2(x)(tan(x)-1))=tan(x)+1

A: Given that

Q: photo attached

A: To convert  an ordered pair from polar to rectangular coordinate, use the relationship x=_______ and...

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A: Use the double angle formula as follows.

Q: I don't understand this homework question.

A: Given: -

Q: photo attached

A: The given trigonometric values are,

Q: Solve e2x +4 ex- 21- 0

A: Given:

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A: Given,

Q: proof trigonometry identities sec^2(x)csc^2(x)=sec^2(x)+csc^2(x)

A: We need to proof trigonometry identitiessec^2(x)csc^2(x)=sec^2(x)+csc^2(x).

Q: sin2 x cos2 4. sin x- cos4 x X - - 1 4

A: To prove that the left-hand side is equals to the right-hand side.

Q: Photo attached

A: From the given statement, x = 6 cost and y = 6 sint.

Q: Solve for 0 if 0° < 0 < 360°. (Enter your answers as a comma-separated list.) 3 sin 0 cos 0 = V3

A: Given,

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A: Sum of all angles of a triangle = 180 degree or pi radian.Answer: B=pi/6

Q: Complete the half-angle identity. sin 스 =

A: To express sin(x/2) in terms of trigonometric ratios of x.

Q: Photo attached

A: Area formula of parallelogram is ab*sin(C)Plug a,b,C in it.a=11,b=14, C=120

Q: Can you help me with this?

A: To find the height (h) from the given figure.

Q: Photo attached

A: Given that:In a triangle side b = 4.8 m, c = 6.3 m and angle A = 112ᵒ.

Q: Find the indicated angle or side. Give an exact answer.Find the measure of angle A in degrees.

A: Given a triangle with sides as follows:

Q: How do you get the equation of the line in general form?

A: Equation of line in general form is: Ax+By+C=0Since line is parallel to line with equation: 3x-5y-6=...

Q: Use an Addition or Subtraction Formula to simplify the equation. sin(3θ) cos(θ) − cos(3θ) sin(θ) = 0

A: Given,

Q: what is the equivalent algebraic expression for the composition: sin(arccsc(x))

A: Given trigonometric composition equation

Q: Number 29

A:

Q: photo attached

A: Given,

Q: if cosx=tany,cosy=tanz,cosz=tanx ,then find sinx

A: Given,

Q: 8. 12 cos2 + 17 sin x - 18 = 0

A: Find the value of x.

Q: Photo attached

A: The parametric equations is given by,

Q: with x in QIV and find the following. 8 Let cos x = cot 2x

A: Since x is in 4th quadrant, there sin x will be negative. sinx =-sqrt(15)/8 when cos x= 7/8 (given)

Q: find x ,x+2tanx=90degree

A: Start by converting degrees on the right side to equivalent radian angle:

Q: Tdentiles rval [0, 2T). 2. -2 sin2 x = 3 sin x + 1 ** A/ X * cALM

A: Factor the expression first. 

Q: can you explain step by step how to find x?

A: Given the triangle,CD=x unitLet, AD=y unit

Q: what is the equivalent algebraic expression for the composition: tan(arcsin(x))

A: The given expression is,

Q: proof trigonometry identities cot(x)+tan(x)+sec(x)+csc(x)=2sec(x)csc(x)

A: We are going to prove:

Q: A rectangular strip of paper of width 4 inches is folded on the dashed line. See the diagram. Certai...

A: Let us name the figure as shown below:

Q: photo attached

A: The given equation in the cartesian coordinates is:            x2 + y2 = 16

Q: if sin x= 5/8, x in quadrant I, then (dont solve or x) sin (2x)= cos(2x)= Tan(2x)=

A:

Q: find x,sin(2cos-1(cot(2tan-1x)))=0

A: Given: -

Q: plot the point in the complex plane corresponding to the number (square root 3)-i. also determine th...

A: From given, real number is, 

Q: Find a possible formula for the trigonometric function graphed below. Use x as the independent varia...

A: Let us take the original function f(x) = cos x The graph of the function cos x is shown below:

Q: 01 4. sin e= sin 0 - cos 0 sin

A: We will start with right side. Plug cos^2 theta= 1-sin^2 theta [ by Pythagorean identity]

Q: The question says: "Find sin(x/2), cos(x/2), and tan(x/2) from the given information: cosx= -4/5, 18...

A: It is given that,

Q: Suppose you are solving a trigonometric equation for solutions over the interval [0,2π)​, and your w...

A: Given that the solution of trigonometry equation over the interval [0, 2pi) is

Q: How to come to the solutions

A: The given equation is,

Q: For each of the following, ∆ABC has sides a, b, c opposite angles A, B, C, respectively. Find the re...

A: Draw the rough diagram as shown below.

Q: Prove that the following identity is true. tan A = sin A sec A We begin by writing the left side of ...

A: Here we have to prove

Q: 3. 1+ tanx tan 2x = sec 2x s*

A: The given identity

Q: Photo attached

A: We need law of cosine formula to find b. b=27.4