5) f(x) = 4 - 2* 10

Q: Prove that for every positive integer n. 1.2+2.3+ .…+n (n+ 1) = n (n+ 1) (n+2)/3.

A: Proof: for n=1 LHS = 1.2 = 2 RHS =1(1+1)(1+2)3=2 LHS =RHS

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Here we have to find the surface area

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A: We will make 2 equations then solve it.

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A: We can solve this as follows:

Q: Find the surface area of the plane ( 15. 5z+20Y3D35) if it is in the first octa

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A: To find the argument of given complex number

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A: We will solve the inequality.

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A: Given, cos(105°) By Half angle identities we know that, cos(x/2)= +or- sqrt[(1+cos x)/2]

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A: I have appended the formula used in the solution part.

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A: topic- probability

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Q: 30 WWLH the equaHIon of the circle Pentered at -a,-8) With rOdius 3.

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Q: Rewrite cos(x) in two different ways to make two unique expressions.

A: To rewrite cosx in two different ways to make two unique expressions.

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Q: (b) Use the Laplace transform method to find the solution of d²y 6+9y= 4e", yo = 2, y1 = 0. dt dy…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Question 8 If E = 2ax + ay - 3az, F = ay - az, and G = 3ax + 5ay + 7az, determine, E - 2F + G. А)…

A: Given that E=2ax+ay-3az,  F= ay-az    and  G=3ax+5ay+7az. We have to determine E-2F+G

Q: Given: (x) = -a + 3s g(=) = 2 – 3 Find: 9(/(3)) O 33 00 O 24 03

A: Solution: f(3) = -(3)2+3(3) f(3) = 0

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Q: a, There are exactly two orthogonal matrices of the form What are they? 3

A: As per the company's guidelines, we are suppose to solve first question for you. Kindly repost the…

Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: A detailed solution is given below.

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