3) The Venn diagram below represents the modules students are taking. . S is the event students study Statistics . M is the event students study Mathematics F is the event students study Further Maths . F 15 0 24 32 18 S M a. How many students are there in total?

Q: Vector A) Prove that: V × (F×G) = (GV)F- (FV)G+ F(VG) - G(V-F). m) Find all of the second…

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Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

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Q: 1 Find the first five non-zero terms of the Taylor series for f(x) = - X Written compactly, this…

A: Taylor Series for f(x) centered at x=a is given by f(x) = f(a) + f'(a)1!(x-a) + f''(a)2!(x-a)2 +…

Q: V = πT -0.5x Sin 4x 4 +8x-cos2x 2 - X²-4 2²- 19.5x 1.478 -1-082

A: To determine the limit of the following equation.V=π-0.5×sin 4x4+8×-cos…

Q: Evaluate the six trigonometric functions (the unit circle). a) t= 5 corresponds to the point (x, y)…

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Q: A population of birds on an island is initially 380 birds, and it doubles (or grows by 100%) each…

A: It is given that initial population of birds on an island is 380. Each year population of birds gets…

Q: Step 1 of 4: Find lim f(x). x--3- Enable Zoom/Pan 10 10 -10 Keypad Keyboard Shortcuts Selecting a…

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Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A: There are three methods to find the volume of a solid generated by revolving a curve f(x) about a…

Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y - 2 = 0…

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Q: The law of Sines. b) Given: A= 36° a = 8 b=5 Find: B-? C-? c-?

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Q: A company produces a special new type of TV. The company has fixed costs of $480,000, and it costs…

A:

Q: 5. The Fourier transform of signal e²²¹ u(t-3) is . e-3(2-jw) a) 2-jw b) e-3(2+jw) 2+ jw c) e3(2-jw)…

A: NOTE: As per our guidelines, I have solved one question. If you want the answers of rest, kindly…

Q: For 2 and 3, find the Mac series of f(x) by any algebraic method using the above known expansions.…

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Q: 4. A population of squirrels is currently measured to be 500 squirrels a. Write a function P(t) to…

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Q: 1. What is the value of Sin 3? 4 TT 2. What is the value of Tan 3

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Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x - cos x (a) lim…

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Q: Determine the equation of the hyperbola with center (3, -3), a focus at (16, –3), and a co-vertex at…

A: To find out the equation of hyperbola.

Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: The equation of motion of a particle is s = t3 - 27t, where s is measured in meters and t is in…

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Q: Q2: The population of a state is known to grow at a rate proportional to the number of people…

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Q: Let g(x,y)=2xy with x=x(s, t)=s²+t² and y=y(s,t)=s/t. Calculate gs and gt. Express your final…

A: Differentiate

Q: [2 + m 3 1. Given A= 1 a. (AB)¹ - A 1 2 -1 -1 4 5+ ml and B = [-1-m 2 91 3 5+m 3 0+m 6 11 Find the…

A: According to Bartleby guidelines I can only answer the first question of the given three questions.

Q: 2. The graph of f(x) is shown to the right and has the following characteristics. 100 f(x) = x55x4 +…

A: We can solve this as follows:

Q: Convert the Polar coordinate to the Cartesian coordinate. 1. r= 1+2r cose 2. r=1-cos8

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Q: y = ln x and x - y -4 = 0

A: Explanation of the answer is as follows

Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A: We need to choose correct option.

Q: Q) find differential equation of the following equation 1) y' = y-x y+x

A: Solution of the above differential equation is

Q: 2- 3- Evaluate the integrals in Exercises [² dx L₁3 3 dx 3x - 2 dy 1- 2. S sec y tan y 2 + secy

A: We can answer all the three questions as below.

Q: 1-2x²=1+x+x²³ 2²-2²-1+2+ -2(-1) (2n + 1)! x²+1 sin x- ---- cos x=(-1). - (2n)! −2+4- 6! tan 'x-…

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Q: Let y = 3x² + 3x + 4. ind the differential dy when x = 4 and dx = 0.4 ind the differential dy when x…

A: Given query is to find differential at given point.

Q: 9 The slope of the function ƒ (x) = 8 - 2x is _____. -8 -2 2 8

A: here we have to find the slope of function  so we have to find dy/dx so differentiate the function

Q: Select all that apply. Solve this equation; domain 0° ≤ ≤ 360°; answer to the nearest whole degree.…

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Q: Solve the equation using Exponential Shift (D² - 2D + 2) y = 12x³e²x O y = e (c! COSx + c2 sinx) +…

A: Answer is given.

Q: In the 2000 U.S. Census, a small city had a population of 50,000. By the 2010, the population had…

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Q: Evaluate the difference quotient f(a+h)-f(a) for the function f(x) = x² + 4x - 5. h 2a +h+4 h+4 2a +…

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Q: Question 13 d²2 Which of the following satisfies the differential equation dx² A. y = e³x B.y = e-3x…

A: We need to choose correct option.

Q: Differentiate and simplify this function k (t) = e√t^2+t+1 - e-√t^2+t+1

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Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y ( ) = 0 O y =…

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Q: OA-3 Close Date: Wed, Jun 1, 2022, 11:59 PM Question 3 of 9 Meadow Company wants to invest its net…

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Q: Find the angle of intersection between the equations f(x) = 3x and g(x) = 4 - x 2 in the first…

A: Given f(x)=3x, g(x)=4-x2.

Q: x 0/x 6+29r² SS S 0 0 0 Evaluate the cylindrical coordinate integral The value is 247 960 (Type an…

A: This question can be solved using the concept of triple integrals.

Q: 1. Find the interest paid on a loan of $2000 for 1 year at a simple interest rate of 7% per year…

A: "According to the guidelines issued by the company we are supposed to answer only one question.…

Q: 5 Given h(x) = x³ + px² − x − 4, find a value for p so h(x) has an inflection point at x = -4.…

A: I am attaching image so that you understand each and every step.

Q: Question 1 CD Assume that "Foo is a function defined by Foo = x²-3x+1 288-1 For a ≤x≤3 Prove that…

A: Given: fx = x2-3x+12x-1---------------------------------To prove: Fx is bounded for 2≤x≤3.…

Q: Find the first five non-zero terms of the Taylor series for f(x) = 1 3 Jo.[ + + + Written compactly,…

A: Use taylor series formula for the function

Q: Vectors a, b, c are given below. Accurately draw the following vectors. a. u=3a-b+ 0.5€ b. v = ²6-2ä…

A: answer is in next step

Q: tid Q3. Evaluate the following integrals 1) cothx.csch2x. dx (50-3x - √x+1+73 44x

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Q: Q2: The population of a state is known to grow at a rate proportional to the number of people…

A: Given ,  The population of a certain state is known to grow at a rate proportional to the number of…

Q: A company produces a special new type of TV. The company has fixed costs of $480,000, and it costs…

A: