Use cross products to find the area of the triangle in the xy-plane defined by (1,2), (3,4), and (–10, 10).

Q: Use the compound interest formula to find the account balance A, where P is principal, r is interest…

A: Principal =$140000 Rate=4.5% Compounded =annually  Time=20.

Q: Convert the Cartesian equation x 2 + y 2 - 6x = 0 to a polar equation.  r² = 6cosθ r = 6sinθ r =…

A: The given Cartesian equation x 2 + y 2 - 6x = 0 ................................... (1)

Q: Find two unit vectors orthogonal to a = (-2, 1,2) and b = (-2, 0, 1) %3D Enter your answer so that…

A:

Q: Suppose that f and h are integrable and that: frx) = -1 , , f(x) dx = 5 , ,h (x) dx = 4 ,Find: a. -2…

A: We have to find the given integrals.

Q: Determine if the following series is convergent or divergent: 3n 7n – 2 - n=1 O Convergent O…

A:

Q: If  ?⃗×?⃗ = ⟨−3,5,−4⟩ and ?⃗⋅?⃗ = 4, find tan(?), where ? is the angle between ?⃗ and ?⃗.

A:

Q: Find the sum of the following infinite series. If it is divergent, type "Diverges" or "D". 1 Σ 8. n…

A:

Q: 0.5 x° tan- (x2) dx –1

A:

Q: Describe the transformation of g (x) = 2f (2x +1)-1. O a) A vertical stretch by a factor of 2, a…

A: The transformation of function f(x): f (x) + b shifts the function b units upward. f (x) − b shifts…

Q: Q2. Let a card be selected at random from an ordinary deck of 52 cards. Let A = [ the card is a…

A:

Q: 6 3 х+7

A:

Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

A:

Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A: We have to find the antiderivative of the given function.

Q: 30+y 25+ 20 6, 18) 15+ 10 Find the area of the shaded region enclosed by f(x) = x3 + x2 - 6x and…

A: Explanation of the answer is as follows

Q: Assume the annual rate of change in the national debt of a country (in billions of dollars per year)…

A:

Q: 8 Convert the polar equation r 2 = -2 sin 2θ to a Cartesian equation. x2 + y2 = 2 xy ( x2 + y2) 2…

A:

Q: The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the…

A:

Q: Solve 8 sin (6x) = 3 for the two smallest positive solutions A and B , with A

A:

Q: 1 6. cos-xdx cos* xdx xprt.

A: We need to solve the integral.

Q: ( 3x2-3x-3, if x<3 f(x)=. | 2x² +5x+1, if x 23 Find the value of f(2)+f(3). O a. 32 O b. None О с.…

A: option (e) is correct see below the answer and calculation

Q: Select the answer option that corresponds with polar coordinates (2, ). 90° 2 135° 45 150° 30 15° 12…

A: We can find the answer as below by naming the coordinate.

Q: Find the limit of the 4n +2 sequence lim Show your work. n- co V2 n+ 4 ; Determine whether the…

A:

Q: Activity 1.1 Evaluate the required function values and the indicated limits using the given graph of…

A: Here we have to find the values by observing the graph.

Q: 3. Evaluate the following integrals: cos e OP (1+ sin 6) Vsin e G = H = sin (-9x) dr I +1 dr 1² In…

A: We have to find the integrals.

Q: the function f(x) = x2 − x2- 6x a. Determine the average rate of change in f(x) on each of the…

A:

Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

A:

Q: 2. Let A = (1,0, 2) and B = (6, –2, 3). Solve for projĄB.

A:

Q: Q3 A symmetrical parabolic segment y = 4x(2 -x) rotates around the x-axis as shown in the figure.…

A:

Q: Choose the point which shows the correct location for the polar coordinate (2, 57). 90 WIN 135 45 1…

A: We will use the concepts of Cartesian coordinates.

Q: Direction: Find the derivative of each of the following functions. Write your solutions on a…

A: We have to find the derivative

Q: Suppose that $83,000 is invested at 3-% interest, compounded quarterly. a) Find the function for the…

A: $83,000 is invested at 312% interest, compounded quartely

Q: y = (1+) - (1+)*

A: We have to find dy/dx for the given function.

Q: o begin evaluating | sin“x cos x dx , express A sin*x to (sin?x)* and use the identity sin?x = 1-c…

A: Given query is to find the identity used to integrate.

Q: Write the integral that can be used to find the region bounded by x = -3y² + 4 and x = y³.

A: We have to construct  the integral to find the region bounded by given curves.

Q: y = (x-p)(x-r) and p+r=6. Find the x coordinate of the vertex of the parabola. O a. None O b. 6 O c.…

A:

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A:

Q: 4. Calculate the area of the bounded region x= y+3 y=3 x= 1 1112 A. 52/3 (. 32/3 B. 8/3 D. 15/3

A:

Q: Find T(t) and N(t) at the given point. r(t) = 2 cos(t)i + 2 sin(t)j + tk; t = 2 T -25 i + 15 k NE) =…

A:

Q: Use the graphing utility to plot the graph of y = tan on the interval [1, 50]. y = 2-8 y 2:45 2-1…

A: Let's find.

Q: 2. Set up the integral to calculate the area between the curves | (f(x)-g(x)) dx f(x) = x²+2x+1 А.…

A:

Q: Select the answer option that corresponds with polar coordinates (-1,-210\degree). 90° WIN 150° 4…

A: The given polar coordinates is (-1, -210°)

Q: sẽ the point which shows the correct location for the polar coordinate (-2, 180°). 90° 2 4/2 135° 7…

A: point (-2,180) here -2 show radius of circle  180 is angle with x axis here one circle is 1 unit…

Q: 3. Compute ahi-fin Lireh-fi for the following functions: and lim h40 a. f (x) = sin x

A:

Q: 5 if x 1 5 4 5 -5 -4 -3 -2 -1 -1 3 4 -2 -3 -4 -5- 2.

A:

Q: On Melissa's 6th birthday, she gets a $4000 CD that earns 3% interest, compounded semiannually. If…

A:

Q: The New River Gorge Bridge is 880 feet above the water below. A bottle rocket is launched upward off…

A: To find out the velocity and acceleration.

Q: amplitude: period: phase shift: 6.

A: Follow the procedure given below.

Q: Direction: Evaluate f'(2) for the given functions. Show your solutions on a separate sheet of paper.…

A:

Q: Find the slope of the line 3x-4y-10=0 О а. 4/3 O b. 3/4 О с. 3 O d. 4

A: Solve the following

Q: x²+6x , |2x-4 , x<a Find all values of a such that the function, g(x)= is continuous xz a…

A: g(x) is continuous everywhere if it is continuous at x=a as…