Question 7 30 cm (b) Show that sin0 = P VZ4 0° 42 cm Figure 1 36 cm NOT TO SCALE Figure 1 shows the acute-angled triangle PQR with PQ = 30 cm, PR = 36 cm and QR = 42 cm. Angle A = 8°. (a) Find cos 8. Give your answer in the form where m and n are integers. You must show your working. R (c) Find the area of triangle PQR. Give your answer in the form k√6 where k is an integer.

Q: 2. Without graphing, Find the vertex and y-intercept of the quadratic function: f(x) = -4x² - 8x - 4…

A: To find the vertex and intercept of given quadratic function.

Q: What type of quadratic surface with equation x2 + 6y² – 4z² = 2. a. hyperbolic paraboloid b.…

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Q: Find the gradient of the function at the given point. w = x tan(y + 2), (2, 12, -7) Vw(2, 12, -7)=

A: To find the gradient of given function.

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Q: On which intervals is the graph of f(x)=2x4-12x² concave up? None of the choices. (1,+∞) only (-∞,…

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Q: Example 1 Find the function f(x) satisfying the given conditions: f'(x) = 2x + 4, f(1) = 3.

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Q: Use the 2 solutions Bernoulli's equation y y' + √y=0

A: Given differential equation y' + yx - y = 0

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A: Given differential equation ( tan( 8y ) - 4 )dx + ( 8xsec2( 8y ) + 1y )dy = 0 Mdx + Ndy = 0

Q: Differentiate the function. h(x) = 14 csch-¹ (x³) Give your answer in exact form. h'(x): = 42x²…

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Q: Let the graph below represent f(x) on the interval [−2, 2]. For which values of x is ƒ'(x) = 0? 3

A: We know that the function has derivative 0 at the bumps. So, from the given graph, f'(x)=0 will be…

Q: Consider the parallelepiped with adjacent edges Find the volume. V = i u = 5i + 4j + k v=i+j+ 7k w =…

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Q: 5. To find the -intercepts, set x equal to 0.

A: Intercepts are those points where the graph of a function intersect the axis

Q: Question 3 Evaluate lim,-1+ f(x) if f(x) = = x +4 -x+1 x -1

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Q: factor each number correctly 62 30

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Q: Factor the following expression completely: 6X2 + X – 12

A: We will find the required.

Q: Question 2 Solve the following simultaneous equations xy = 256, 3log (v) = 1

A: Explanation of the answer is as follows

Q: If f(t) = = (t² + 2t + 5) (7t² + 2), find ƒ’(t). Find f'(5).

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Q: Given the right triangle shown below with one non-right angle of 59 degrees and hypotenuse of length…

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Q: The position function of a particle is given by r(t) = (2+², −2t, t² + 3t). At what time is the…

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Q: A boutique sells blouses and purses. The blouses cost $27 each and the purses cost $44 each. On a…

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Q: Calculate the integral, assuming that (Give your answer as a whole or exact number.) 5 S³ f(x) dx =…

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Q: Consider the curve defined by the equation y — sin y = x − 1 for 0 ≤ y ≤ 2π Find d²y/dx² in terms of…

A: Solution: To find the second derivative of y with respect to x, we need to first find an expression…

Q: Let f(x) = x³ 3x². - Find the absolute maximum value of f(x) on the interval [1,4].

A: Let's find absolute maximum value of given function.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Use the Gauss-Jordan method to solve each system of equations. 2x - 3y = 2 4x - 6y = 1

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Q: Find sin 2x, cos 2x, and tan 2x if tanx = - N/W 3 2 and x terminates in quadrant IV.

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Q: Question 2 Solve the following simultaneous equations xy = 256, 3log, (v) = 1 (4 marks)

A: Using logarithmic property Logxy=z then apply exponant both side we get y=xz

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

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Q: 13. Explain why f(x) = X - does not have an extreme value on the interval [0, 5]. x-1

A: We have to prove function f(x) does not have extreme value on the interval [0, 5]

Q: 7. G(x) is decreasing over (-∞, 4) and (9, ∞) and increasing over (4, 9).

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Q: Find the area of the region bounded by the graphs of the given equations. y = 2x²y = 2√x Answer

A: Topic - Area between curves We are given curves y=2x2y=2x

Q: Evaluate the given integral by changing to polar coordinates. (a) ff xy dA, Where D is the disk with…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (x, y): (?, ?) y = √√√25x² x

A: we can use the formula for centroid x¯ = ∫xdA∫dA     &      y¯ = ∫ydA∫dA

Q: Find the an equation of the plane passing through points (−5,3,8), (10,9,8), and (-6,-3,8)

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Q: . The symmetric equation of the line that passes through the points (3,0, 11) and (2,6,7

A: We have to find the symmetric equation of the line that passes through the points (3, 0, 11) and (2,…

Q: 4. An athletic -equipment supplier experiences weekly cost of C(x) = x³ +40x + 700 in producing x…

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Q: What is S² S 2 9. b. C. k|x EN d. = www 2 sin 0 1 r cos² 0 drd0?

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Q: To raise funds, the student council sells yogurt fruit smoothies every day during lunch. They sell…

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Q: A rancher has 1500 feet of fence and would like to enclose a rectangular area that borders a river…

A: Given total length of the fencing = 1500 ft

Q: 2. The limit of the sequence {cos cos an n+1 is

A: The given sequence is: an=cos(πn)n+1

Q: SOLVE USING BERNOULLI EQUATION y y' + √√y=0 x

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Q: 1. The position function of an object moving horizontally along a straight line as a function of…

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Q: Find the value of a when 7 log3 (1) x = without using a calculator. Select all that apply 1. x = -61…

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Q: h(t) = t 5t 24

A: h(t) = t2 + 5t + 24 The above equation represents the height at any time t. The rate of…

Q: 2. Determine the area bounded by the parabola y² - 8x + 6y + 17 = 0 and the line 2x - y - 13 = 0. A.…

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Q: 4. Let ₁ and ₂ be two nonvertical lines with slopes of m₁ and m₂ (respectively), and assume that mi…

A: Note: Since, the student has mentioned to solve question Part no. (D), so we are solving according…

Q: A painting is purchased as an investment for $175. If its value increases continuously so that it…

A: A painting is purchased as an investment for $175.If its value increases continuously so that it…

Q: Determine whether the line and plane intersect; if so, find the coordinates of the intersection. (a)…

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Q: If f(x)=3x, g(x)=x+4 , and h(x)=x^(2)-1 , find f[g(7)] .

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