A triangle has vertices (0, 0, 0), (1, 1, 1), and (0, −8, 9). Find its area.

Q: For a particular function h, we know h 0 (2) = 6 and h(2) = −3. Write an equation for the line…

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Q: Solve by the method of your choice:Using 15 flavors of ice cream, how many cones with three…

A: Given: n = 15 r = 3 Formula Used: Prn = n!(n-r)!

Q: Use the formula for nCr to evaluate the expression 10C6.

A: The expression is given by, C610 n=10r=6

Q: (7) sin √x dx. (First substitution, then by parts)

A: The solution for the given integral is as follow.

Q: Determine whether or not the following equation is exact: 3 dy xy + (²x² + 2y² − 20) = 0, y(0)=1. dx…

A: See this solution in below

Q: (e) Write out the first five terms of the sequence, determine whether the sequence converges, and if…

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Q: The equation y = 1x - c2 2 defines a family of parabolas,one parabola for each value of c. On one…

A: Given, y=x-c2                     ... 1

Q: 4. Consider Line L with defining equation 2 y - ²x + 1/ . = 6 A. Find two ordered pairs (x₁, y₁) and…

A: see below the answer and calculation

Q: Geometry A wire of length x is bent into the shape of asquare.(a) Express the perimeter p of the…

A: Given: A wire of length x is bent into the shape of a square. (a) To express the perimeter p of the…

Q: A baseball diamond is in the shape of a square with 50 ft sides. How far is it from home plate to…

A: A baseball diamond is in the shape of as quare with 50 ft sides. To determine how far is it from…

Q: Find the slope of the tangent line to the curve f(x) = x³ - 4x at the point where x = 0. A) 0 B) - 4…

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Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1

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Q: Consider the function f(x)=eXx. Select all that apply. Select 3 correct answer(s) f(0) is positive.…

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Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Given: To find: limx→2- fx , limx→2+ fx, limx→2 fx

Q: Evaluate (2x + 4)(3x + 2) d dx A) 6 C) 12x + 16 B) 6x² + 16x + 8 D) 30x² + 43x + 8

A: Given query is to find the Indicated derivative.

Q: Devise an exponential decay function that fits the given data, then answer the accompanying…

A: Here, the equation used is: P=P0ekt...(1) where P is the pressure of the atmosphere at t=0 and k is…

Q: y=5(x^(2)+3)^(5)+9(x^(2)-1)^(2x) then (dy)/(dx)

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Q: Find the exact length of the curve. X = t 2 + t y = In (2 + t), 0≤t≤1

A: Given: x=t2+t, y=ln(2+t) We know that exact length of the curve is given by  s=∫t1t2dxdt2+dydt2dt

Q: Use the formula for nCr to solve:An election ballot asks voters to select three city commissioners…

A: Given: n = 6 r = 3 Formula Used: Crn = n!r!(n-r)!

Q: Find the area of the shaded region. r² = sin(20) 4

A: See this solution in below.

Q: Integrate the following. 6° 0 8x 12e dx =

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Q: In this problem you will calculate the area between f(x) = x² and the x-axis over the interval [3,…

A: a) ∆x=b-an

Q: Let f(x) be the function 9 x² − 3 x + 4. Then the quotient a = Number and b = Number f(4+h)-f(4) h…

A:

Q: (a) Find the distance from P1 = 1 - 2, - 32 to P2 = 13, - 52.(b) What is the midpoint of the line…

A: Given, P1=-2, -3 and P2=3, -5

Q: Find the slope and equation of the tangent line to the graph off at the given point 17.) f(x) = ln…

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Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D.4 O E. None of the Choices alt + dx…

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Q: Describe what nPr represents.

A: what nPr represents:- The permutation is a specific orderly arrangement of the components.

Q: 15. Evaluate each expression using the given table of values: -2 -1 1 f(x) 1 0 -2 1 2 g(x) -1 b.…

A: To use the table of values for finding the values of given function.

Q: Evaluate lim 1 1 x 2 X-2 X-2 direct substitution. 1 1 X 2 O lim X-2 X-2 1 1 X 2 O lim X-2 X-2 O lim…

A: The objective of the question is evaluate the limit and choose the correct option.

Q: A solid lies between planes perpendicular to the y-axis at y = 0 and y = 1. The cross-sections…

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Q: If you are dealt one card from a standard 52-card deck, find the probability of being dealt a king.

A: Given data, No. of cards drawn 1. n(A)=4 n(S)=52

Q: Find the average rate of change of f1x2 = 3x2 - 2, from 2to 4.

A: Given, fx=3x2-2,    2, 4

Q: Find the average rate of change of f1x2 = 8x2 - x:(a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 4

A: Given: Given expression: f(x) = 8x2-x Formula Used: The Average rate of change ARC = f(b)-f(a)b-a

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A:

Q: Use the Fundamental Counting Principle to solve:Five singers are to perform at a night club. One of…

A: Given data:- There are five singers, one singer is want to show open and another singer wants to…

Q: 1. Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

A: We need to find partial derivative. NOTE - As per Bartleby guidelines we can solve one question.…

Q: For the graph of the linear function f1x2 = mx + b, m isthe and b is the .

A: Given, fx=mx+b

Q: State in interval notation where the graph is differentiable. A) (-∞, -1) U (-1,3) U (3,00) B)(− ∞,…

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Q: In Exercises 1–6, find the domain and range of each function.1. ƒ(x) = 1 + x2     2. ƒ(x) = 1 - 2x3.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Evaluate the following integrals: 8 3 S(4 + 3√x) (2x + √x ³) "dx

A: SOLUTION-

Q: campus of 5000 students, one student returns from vacation with a contagious and long-lasting flu…

A: Here we have The total number of students infected after t days. y=5000  (1 + 4999e-0.8t)…

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A: Solution

Q: -6 (-3,1) -5 86°F Sunny I 1 -4/ -3 -2 1 / -1 4 3 2 - 0 -1 -2 -3 -4 -5 -6 2 W Use the graph to…

A: Given query is to find the slope of the tangent line.

Q: Evaluate the following limits. If needed, enter oo for ∞ and -oo for - 00. 32x 3 - 6x (a) lim 16 (b)…

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Q: Supply and Demand Suppose that the quantity supplied Sand the quantity demanded D of hot dogs at a…

A: Supply and demand is the relationship between the quantity of a commodity that producers wish to…

Q: Find the equation of the tangent line to the graph of f(x) = √x + 100 at the point (0, 10).

A: Given query is to find the equation of the tangent.

Q: If f (x) = x2 - 2x, find f (a + 1) and f (a + 2).

A: Given fucnction, fx=x2-2x

Q: Give the implicit solution of y'=y=xy²e Oe-2x = y²(x²+c) O e ²x = y²-c O e²x = x²(y²-c) е…

A: We will find the required  solution of given differential equation.

Q: You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and…

A: Given data:- The given angle is, θ=80° The given diameter is, d=12 in So, the radius is, r=6 in.

Q: According to one model that takes into account air resistance, the acceleration a(t) in m/s" of a…

A: Here is the solution: