In a triangle ABC, points E and F are on the sides AC and BC respectively, such that AE is 1/3 of AC and BF is 1/3 of BC. Find relationships between EF and BC using vectors

Q: 13. A certain type of glass is such that a slab 1" thick absorbs one-quarter of the light which…

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Q: Determine whether the series +∞o 1 Σκος (7) - co ¹ ( ² ) - COS ¹ (2 + ₁)] \n n=1 converges or…

A: We have to find whether the series converges or diverges.

Q: Convert the degree measure to radian measure as a multiple of π and as a decimal rounded to three…

A: To convert each degree angle into radians.

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 2580 yd of fencing to enclose a…

A: The owner of the Rancho Los Feliz has 2580 yd. of fencing to enclose a rectangular piece of grazing…

Q: Evaluate the sine, cosine, and tangent of each angle. Do not use a calculator. (If an answer is…

A: To find the given sine, cosine and tangent values.

Q: For the differential equation y(n) + p₁(t)y(n-¹)+...+Pn(t)y = 0 with solutions y₁, ·, yn Abel's…

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Q: Divide. If the divisor contains 2 or more terms, use long division. 21x²-37x+12 7x-3 Divide. 5 9 4x…

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Q: II. L' Hôpital's Rule. Evaluate the following limits using L' Hôpital's Rule. 3-x 1. lim 1-3 2-8

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

Q: Given the same three points P (1, 4, 6), Q (-2, 5, -1) and R (1, -1, 1). Find the perpendicular…

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Q: A periodic function f(x) is defined as 3, f(x) = {x, f(x+2) -1≤x<0, 0≤x<1. Based on the above…

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Q: The interest rate for a savings fund was 3.80% compounded semi-annualy for the first 4 years and…

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Q: Find the interest rate needed for an investment of $9,000 to triple in 7 years if interest is…

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Q: Find the equation of the tangent line to the graph of the function f(2)=sin(7√) at the point (²,0).…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  so we can take

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: y² = 8x,x=2, AOR = Y AXIS

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Q: Integral Calculus (

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Q: Wallis Formula Evaluate the following integrals. sin (3x) cos5 (3x) dx 1. 2. 16 4 [*³* sin³(2x) dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1. Condense 3 log, x + -log(x-1) - 4 log(x + 2) into one logarithmic expression. 2. Solve 7³t = 100.…

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Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) 4 (a) lim f(x)= x-c+…

A: A function is continuous at x = c iff limx→c+f(x)=limx→c-f(x)=f(c)

Q: 16. Use properties of logarithms to expand log (²₁¹). t14

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Q: (5). a. The length of one side of a square tile is 1½ feet. Determine the area of the tile in square…

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Q: (a) Find the domain of the following function, giving you answer in interval notation. f(x) = ln(x²…

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Q: (1) Use the definition to prove that if x₂ → 2 then (2x, +1)/x → 5/2.

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Q: Evaluate the function at the given values of the independent variable. Simplify the results. f(x) =…

A: The given function, fx=6x-1

Q: The equation implicitly defines z as a function of t. Find dz dt +² 22 - sin (5 z) = -8

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Q: Question 1 [ Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) = xy…

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Q: The graph of f is given. Find the following or write d.n.e. if it doesn't exist. If a limit is…

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Q: -1 O -5 -10 -4 2, IP 2 IP 3 4 10 5 X X -1 y 10 -1⁰ IP 2 3 4 X -5 -4 -3 IP -2 -1

A: Topic:- application of derivatives

Q: 8 26 Type your answer without fractional or negative exponents. Use sqrt(x) for √√T. Find the…

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Q: work. a) ( i) Find the exact length of the curve 1 <2

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Q: Find the partial derivatives: af (x, y, z)/dx, f(x, y, z)/dy, df(x, y, z)/dz for the following three…

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Q: Consider y=(3x^(2) +4)^(-5x)  Please find dy/dx and evaluate y'(0)

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Q: Let r(t) = 21²i+tj+t²k. (a) Find the unit tangent vector T(t) and T(3). (b) Find the principal unit…

A: As per our guidelines we are supposed to answer only first 3 sub-parts. kindly repost others.…

Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

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Q: Evaluate the integral, which has irreducible quadratic factors. (Use C for the constant of…

A: We will find the integral.

Q: Q4 (a) Calculate the surface integral: [] (² + (y² + 2yz) dS where o is the first octant of the…

A: To evaluate the surface integral Given plane 2x+y+2z=6

Q: III. Improper Integrals. Determine if the following integral is convergent or divergent. If it is…

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Q: 0 T 2 T 2 f² sin(x - y) dxdy is eg elect one: True False

A: Topic:- application of integration  Yes given statement is true .

Q: Let v = (2, -1, 5) and u = (5, -7,3). Find 37 - 5u

A: We have to find 3v - 5u

Q: Calculate the following line integrals in a counterclockwise direction around the triangular path as…

A: Let's solve given double integration.

Q: 5. lim 248 100 5+2³+ [In(In r)] 7² +6²+ [In(In x)]200

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Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface x² – 2y² − 3 ² = −4…

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Q: -1.0 -0.5 π/2 2 r = 1 + cos 0 0.5 1.0 1.5 2/0

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Q: Use the geometric series formula x5 1 + x = ∞ n=0 1 1 - Y = ∞ Σy" to express the function as a…

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Q: Evaluate the function at the given value of the independent variable. Simplify the results. f(x) =…

A: Evaluate the function at the given function of the independent variable.

Q: A loan of $38,800 at 4.39% compounded semi-annually is to be repaid with payments at the end of…

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Q: (a) cos(8): = √2 2

A: answer is in next step. please give a like .

Q: Find the length of the dashed zig-zag path in the following figure. 34 0.75- 0.5+ 0.25+ 00.25 0.5…

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Q: A company's revenue from selling x units of an item is given as R = 1000x - x² dollars. If sales are…

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Q: Find the point on the parabola y=22 that is the closest to the point (8,11/2) on the Cartesian…

A: Since multiple subparts are asked, I am answering first 3 subparts