Carlos surveyed 50 students about their favourite subjects in school. He recorded his results. Favourite Subject Number of Students mathematics 18 science 15 neither mathematics nor 20 science Determine how many students like only mathematics. 3 15 30 18 12

Q: + + 1.3 3.5 5.7 + .. + ……. (2n-1)(2n+1)

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Q: 2 61-19]. and C 3 3 Given the matrices A = В: 9 3 5 the matrix X in the equation (A - 5B) X = C. X =…

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Q: What is the second derivative of ƒ(g) = 12g² + 15g² +26g³?

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Q: > Question 6 Let u and v be functions of and let u' and v' denote the derivatives of u ar (a) Dz…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: C) Find the arc length of the curve y-1-6x², 0≤x≤1

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Q: Find the volume of the solids generated by revolving the region bounded by the curves y = 7r² and y…

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Q: 2) evaluate the indefinite integral £x² 9+X² dx

A: We have to find solutions

Q: The Summation means that we take 2 the sum of 1²+3 as i goes from 6 to 8 { li i=6 (143) =…

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Q: A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29° and 53⁰ with…

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

Q: Find : dw/dk α w=2 sin m ka 2

A: To find dw/dk for the given w

Q: The set of all the solutions of the equation z³ = -27 in the complex plane is (a) (-3) (b)…

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

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Q: a f(x) = x² sec (ax)

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Q: a. Carbon-14 has half life of 5730 years. If initial mass of carbon-14 was 7 grams how much it will…

A: We need to find remains of carbon. As per Bartleby's guidelines we can solve one question from…

Q: Use the difference an+1 an to show that the sequence {n - 5"} is strictly increasing or strictly…

A: To find whether given sequence is strictly increasing or decreasing.

Q: The domain of the logarithmic function y = log4 (x + 3) is Ox>0, XER Ox-3, x=R Oxz-3,TER OX>0, XER

A: Let's find domain of given logarithmic function.

Q: Seatwork I eliminate the antitrany constants of the following. simplify your answers. En close your…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: x² - 4x-5 x-5 x² +6x + 8 x+2 13. What is the limx-5 14. What is the limx→-2 15. What is the limx-…

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Q: Find the area between the curve f(x) = x³ - 130 and the x-axis from x = 1 to x = 4. …….. The area is…

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Q: Given f(x, y) = 6x6 - 6x²y³ - 5y³, find fz(x, y) = fy(x, y) = fiz(x, y) = fay(x, y) =

A: Solution

Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. = If u(3, 6) = -7, us (3,- 6) =…

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Q: sin 4x Does it exist? '. 1. Calculate lim 2. Find lim x-2 x-2 x-2 3. Find the asymptotes of - and…

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Q: B. Use Green's theorem to evaluate f (x²y)dx + y²dy Where C is close path formed y = x and y = x³…

A: Above first question is solved. Solving more than one question is against the policy of bartleby.

Q: Rewrite the integral using substitution: o 12 /108 cos du 36 1,³6 cos u du 1/12 1/108 108 cos 108…

A: Given: I=∫13x2cos4x3dx   ...1   As we know that; ∫a·fxdx=a·∫fxdx, where a is constant.

Q: If y = -x-4/3, what is 4 321/3 -1/3 01- 45 3-76 4 32-7/3 dy 2

A: y=-x-43

Q: Please solve the last 2 parts as well please from the above equation

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

Q: 2. Which of the following definite integrals represents the area of the shaded region? A. S²(4-x²)…

A: To find the area bounded by the given curve, draw a strip as shown in the figure below:

Q: Indeterminate Form 4 7. lim 2 1–cosx x-0 4 1 8. lim x-2x²-4 x-2 9. limsin 3xcot 2x 10. limx²e 11.…

A: We have to determine the indeterminate forms.

Q: A box with an open top is to be constructed from a square piece of cardboard, 3 m wide, by cutting a…

A: 1) Given:

Q: Which of the following is a relative maximum of f? 1/5 5/6 A. (²2) ¹ c. - (²²) ³ √3 B. 0 D. 2 Which…

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Q: The boundary of a lamina consists of the semicircles y = √1-x² and y = √25 - x² together with the…

A: Solution

Q: Find the value of the Sum Σxi' if x₁ = 8₁ x₂ = −3₁ X3 = 4₁x₁4 = - 1=1

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Q: Find the horizontal and vertical asymptotes of f(x). f(x) = 6x x+4 .….. Find the horizontal…

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Q: (A) Find equations of the tangent and the normal lines to the curve x-4t-3, y-3t-6 at the…

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Q: 4. Classify the following differential equations according to whether they are linear or nonlinear.…

A: For (A), The above differential equation is linear. For (B), It is the same as dydt+1=0. So, the…

Q: Find an example of a subring of Z[x] which is not an ideal of Z[x].

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Q: 4. Let (x) - 6x² + 13x+7 3x + 2 What is the equation of the oblique asymptote of f(x)? From what…

A: Solution

Q: Which of the following phrases describes an empty set? Common factors of 5 and 9. O Multiples of 2…

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Q: Eliminate the arbitrary constants of the following. Simplify your answers.  9. y = e^2x (c1cosx +…

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Q: The graph of one complete period of a sine curve is given. y 1 4 4 -3 7814 X

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Q: A tank of capacity 300 liters originally contains 80 litres of brine with 1/8 kg of salt. A mixture…

A: Given data :-  Capacity of tank = 300 liters Rate of mixture poured into tank =4 L/min Rate of…

Q: Question 13 If f(x) = √ and g(x) = x¹, what is the derivative of (fog)(x) with respect to x? O 1…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

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Q: f(x) = 4e³x9e²x

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Q: -∞. Find (A) the leading term of the polynomial, (B) the limit as x approaches ∞o, and (C) the limit…

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Q: 1 1- Q2: Evaluate f ¹-² y² (x² + y²) dx dy the product

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Q: Suppose that f(x, y) = √√4² - x² - y² on the domain D = =4 Q Then the double integral of f(x, y)…

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Q: fidencos 3 Evaluate If (n²7y) dv kabrood if G. As the solid bounded by is the parabolic cylinder…

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Q: Which of the following definite integrals represents the area of the shaded region? A. S²x² dx B.…

A: