Question 1. Let R be the region below y = 5 x2 and above the x-axis. (a) Find the area of R. (b) Find a positive real number a so that the graph of y = area. ax² + 1 divides the region R into two parts of equal

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Q: Find || projau || if u = (2,4) and a = = (3,-1). NOTE: Enter the exact answer or round the exact…

A: projau=u.aa2a   For two vectors u=u1,u2 and a=a1,a2a.u=a1×u1+a2×u2   For any vector x=x1,x2x=x12+x22…

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Q: real part under the trans formation

A: The given problem is to show that the given transformation z=w3 is harmonic in the w-plane.

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Q: State and informally explain the Fundamental Theorem of Calculus 9.

A: Fundamental Theorem of calculus

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Q: • Show that for any two real numbers x, y, we have xy x² + y² 2

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Q: Determine and y such that 0 [xy 139+223-412,3] = 2x y -5

A: To determine the values of x and y.

Q: -1 0 -6 9- Let D = 4 Find -2D = 2.

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Q: Solve b+b-5--3 4 O a O b b = 26 %3D b = 3 13 b=-1 10

A: 14b+25b-5=-3 to solve the value of b

Q: Example. Compute z/w where z = 2 + 2i and w = 1 – 2i.

A: To compute z/w where z=2+2i and w=1-2i

Q: iSuppose the researcher changes the sample size to 100. How does it affect P-value? (In this case,…

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Q: b3-4bㅎ +4= 0 |

A: The given expression is b13-4b16+4=0.

Q: 5. There exists no integers j, k for which 18j + 6k = 1.

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Q: 5x dy. 10.) Evaluate

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Q: 5) x + 2 :+2 Find de Also, show a check.

A: Topic: integration

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Q: 7. Find a number t such that In(4t +3) = 5 (Give EXACT value)

A: Given that ln(4t+3)=5 we need to find "t"

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Q: Let x be a column of size n and let 2 xTx Mark only correct statements. A = In - x xx¹. a. The…

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Q: At each marked point: draw a short tangent line and estimate the derivatige at that point (write the…

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Q: Find UT Vo 9 3x + 4 2x - 2 U T

A: This question can be solved using the equation(Length of VU)+(Length of UT)=(Length of VT)

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Q: (b) Show that it is real, even though i or 8i is not.

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Q: Consider the set U {a + bx a, b = 2 under the polynomial addition and scalar multiplication. Select…

A: Option: For every u1→, u2→∈U, u1→+ u2→∈U U=a+bx| a,b∈ℤ u1→=a1+xb1  and u2→=a2+xb2  where a1, b1, a2,…

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A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you. If…

Q: Compute u + vand u-4v. u= u+v= - 5 2 V = -3 3 (Simplify your answer.)

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Q: Where did the C come from

A: Here the C stands for “combinations”. In general, if we want to choose r objects from a total of n…