Let ABC be a triangle, and DE parallel to the base BC. Suppose point F is any point on DE. Show that shaded area is less than or equal to one-fourth of the area of the entire triangle. Where α(BDF) + α(CEF) = 1 4α(ABC) if and only if points D and E are the midpoints of AB and AC, respectively.

Q: Draw the solid in the first octant bounded by the following surfaces: Z=1-y; y² = x and x² + y² + z…

A: z=1-y y2=z x2+y2+z2=1

Q: h paper are 100. Find the numb

A:

Q: 49. Sigma notation Evaluate the following expressions. 5 Σ (2p+p²) p=1 g.

A:

Q: Prove: 3(12)^n + 8 is divisible by 11 for all positive integers

A:

Q: Consider the following differential equation to be solved by the method of undetermined…

A:

Q: 2. Show that the nullspace of AT A is also the nullspace of A. TI 2 " T

A:

Q: A population of rabbits on a farm grows by 12% each year. Define a sequence {rn} describing the…

A:

Q: Theorem 4.1. Assume (k, m) = 1. If {a₁,,am) is a complete (resp. reduced) residue sustem modulo 10…

A:

Q: Suppose A is a symmetric matrix (i.e., AT = A) a. Show that the column space of A is perpendicular…

A: Given that A is a symmetric matrix. a. Let the vectors u∈NullA and v∈colA. The vector v can be…

Q: •L₁ f(x) dx (e) 18 Use three rectangles with right endpoints to approximate (a) 6 (b) 12 (c) 16 (d)…

A:

Q: Find the full power Series centered at x=0 and then give the first 5 nonzero terms of the power…

A:

Q: 3. Let A = that A 5 2 PCP 1. 4 Find an invertible matrix P and a matrix C of the form C = such

A: As you have asked more than one question, we shall answer first question only as per answering…

Q: Compute ae in (Z/n)* using only multiplication and division for the following a, e, n: (a) a = 10…

A: For (a), We are given that a=10, e=5, and n=9350647. Here, we will be computing ae! in (ℤ/n)× using…

Q: If a, b and c are three positive real numbers, then find minimum value of a² +1₁ b² +1 + h+c c+a c²…

A:

Q: 4. The series n=0 1-5m² n *** (a) is Absolutely Convergent (b) is Conditionally Convergent, but not…

A: Solution:-

Q: John stands on the roof of a building and throw a ball upwards. The balls height above the ground is…

A:

Q: –42. Midpoint Riemann sums Complete the following steps for the given function, interval, and value…

A:

Q: For each series, determine whether it converges absolutely, converges conditionally, or diverges.…

A: The given problem is to find the given series is convergence or divergence by using series…

Q: A man wants to adopt a puppy from an animal shelter. At the shelter, he finds eight puppies that he…

A:

Q: 3u² Suppose w(x, y) = (x²y+e), where y=vsin(uv) and x=ln √2v value of method. dw dw ди ду when π √2…

A:

Q: Evaluate the series > k=2 (-2)k+1 32k-1

A:

Q: (a) fn is a natural number for all natural numbers (b) fn+6= 4fn+3 + fn (c) f5n is a multiple of 5

A:

Q: Two boats leave a marina at the same time. The first boat travels 6 knots at a bearing of N39°E, and…

A:

Q: 4. Let G be a group and G' be the subgroup generated by the set S = {x¹y¹xy x, y = G}. G' is called…

A: Let G be a group, G' be its commutator and N be a normal subgroup of G such that G/N is abelian.…

Q: (a) (b) m=0 11=0 (-1)" vn+1 (-1)" √√n+1 元+1 n²-3n+1

A:

Q: Describe what the linear transformation determined by the matrix A = [18] does to the square with…

A: As per the question we are given a linear transformation in terms of the transformation matrix A.…

Q: the same nationality are

A:

Q: Approximate the area under the curve graphed below from x = 2 to x = 7 using'a Left Endpoint…

A:

Q: The principal represents an amount of money deposited in a savings account subject to compound…

A:

Q: P (in decimal form) at a depth of x meters is given by P=e *, where k is a constant related to the…

A: P=e-0.0491x where P is the percentage of visible light and x is the depth.

Q: A store purchases baseball hats from two different manufacturers in 3 different colors, summarized…

A:

Q: 2. The initial value problem √4-zy" +=e, y(1) = -1, g(1) = 0 is certain to have a unique solution on…

A: Existence and Uniqueness Theorem Consider the IVP     y''+p(x)y'+q(x)y= r(x) with…

Q: a) 12 in 1. Calculate the volume of each object. b) 13 in 14 in. 5.5 cm 8.7 cm 8.5 cm c) O 20 in. 1…

A:

Q: Problem 3: For each of the two graphs below, determine whether they are planar. Justify your answer:…

A:

Q: The set is given below. 0 = {x E R², || x ||² < 25} Where || x ||² is square of the Euclidian norm…

A:

Q: 5. Evaluate the integral fF.dS where F = (2x,y,z) and S is the boundary of the solid cylinder x² +…

A:

Q: a. R is the relation defined on A as follows: For all x and y in A, x Ry ⇒ x has the same major (or…

A:

Q: et the terms a₁, a2, a3, ..., a, be in G.P. with common rat et S denote the sum of first k terms of…

A:

Q: Given the periodic function: f(x) = x² 0 ≤ x <1 Find the half-range sine expansion of f(x), and…

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

Q: St St X 2 xcosy 3 y dy dx

A:

Q: ∞ (−1)n n ln(n) 6. The series (a) is Absolutely Convergent (b) is Conditionally Convergent, but not…

A: Solution:-

Q: Find vectors x and y with ||x, = 1 and ym 1 such that ||A||₁||Ax|, and A||- ||Aym' where A is the…

A: Given, The matrix  A=4-1-230-3102 We have to find the vectors x and y with xs = 1  and ym = 1 such…

Q: If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

A:

Q: Use the Laplace transform to solve the initial value problem: 3 y" − y − 6y = f(t) = { if 0≤t<2;,…

A:

Q: 6. Find the surface area of the surface defined parametrically as r(u,v) = (v cosu, cosu,sinu), for…

A:

Q: Consider the ordered bases B₁ = {(−1, 1, 0), (0, 1, 1), (1, 0, 0)} of R³ and B₂ = {(1, 2), (1, −1)}…

A: (a) From the given matrix of linear transformation f, we have the following information:      f(-1,…

Q: Find the area of the region bounded by y = eª, y = 12 — eª, and the y-axis.

A:

Q: Suppose ƒ : (a, b) → R is differentiable and that ƒ' : (a,b) → R is bounded. Prove that f: (a, b) →…

A:

Q: Problem 8. Consider the inner product space from Problem 4. Find an orthonormal basis for the…

A:

Q: f(x)=sinh(x)= n 2n+1 (2n+1)! =x+ + f +³ + +. 3! 5! 7!

A: We have to write the series for  f(x)=sinh(x)