Without graphing, identify these key features: vertex, axis of symmetry, direction of opening, number of x-intercepts, compression/expansion f(x)=2(x-3)² +5

Q: f(x)=x^3+6x^2+3x+18 by factoring (use grouping) and using Cardano's formula.

A: f(x) = x3 + 6x2 + 3x + 18 f(x) = (x + 6)x2 + 3(x + 6) f(x) = (x + 6)(x2 + 3) The roots of f(x) = 0…

Q: 3 a)Find the area of the parallelogram with vertices: P(0,0,0), Q(4,-3,-1), R(4,-2,-2), S(8,-5,-3).…

A:

Q: Find y' if sec xy + tan y = 4x. O 4 sec ay tan ay+sec² y 4 a secay tan ay+sec² y 4-sec ay tan ay sec…

A: To find the derivative of given function

Q: Q1: The Trapezoidal rule for f f(x) dx = 5 and Midpoint rule f f(x) dx = 4 .What value does Simpsons…

A: Solve

Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

A: Topic = Vector

Q: 12. Let s(t) = -5² +40t+ 1 describe a toy rocket's motion as it is launched vertically into the air.…

A: We shall use the fact that the rocket reaches its maximum height when its velocity is 0

Q: If it takes someone t minutes to drive, run, or walk a mile, then their average speed s(t), in miles…

A: We will put the value of t to find s(t)

Q: Q8. change from x = -1 to x = 5 (14) (5-را-) Given the graph of the function f below, determine the…

A: Question-     Given the graph of the function f below, determine the average rate of change from x=…

Q: Find the area of the region bounded by the lines y = x² and y = 2-x². (No tolerance. The final…

A: Given and  Graph

Q: Where does the line with parametric equations −1+3t y = 2 - 2t 2 = 3+ t intersect the plane 3x + y -…

A: Given parametric equation of line x = -1 + 3t y = 2 - 2t z = 3 + t Given plane 3x + y - 4z = -4

Q: 10. Determine f" if f(x) = √√√x³ +2.

A: Given : f(x)=x3+2To Find :f''

Q: Question 2 Solve the following simultaneous equations xy = 256, 3log (v) = 1

A: Explanation of the answer is as follows

Q: If f(x) f'(x) = f'(4) = = 3x + 5 52+6 " find:

A:

Q: Consider the points A(-4,2,0), B(7, 3, -2) and C(-2, -3, 1). 1. Find a vector of length √6 in the…

A: Solution is given below:

Q: Regarding e as a function of a, b, and 0, determine the differential de and use the result to…

A:

Q: a) α (²)+(!)-(3) Suppose the above equation is expressed as Ax = b with x = matrix form as (Ab)= = α…

A:

Q: · -21, x ≥ 0 r+? r 1.Given the integral: f(x) = {¹x Slx Evaluate: ₂f(x) dx

A: We have to solve the given integral

Q: 11. Solve the following Bernoulli equation with initial condition: - y = e²xy³ with y(0) = 1.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: If f(x): f'(x) = f'(5) = = √x-7 √x+7 " find: 0.0

A:

Q: Find the area of the region bounded by the graphs of the given equations. y = 7x², y = 7√x

A: The region is bounded by the graphs y=7x2 and y=7x. We have to find the area of the bounded region.

Q: ere are two possible values for cos. Find both. is known that tanis negative, then only one of the…

A: we will  find the required.

Q: 1. The amount of pollution in a certain a certain lake is P(t)= (tª + 3)³, where t is measured in…

A:

Q: you

A: Topic:- function

Q: On which intervals is the graph of f(x)=2x4-12x² concave up? None of the choices. (1,+∞) only (-∞,…

A:

Q: MIN Find the value of tan(0) given the right triangle. 2 13 2 O V 13 3 2|3 e 6/13 18

A:

Q: Solve the differential equation given below. 77-2 141H

A: The given differential equation is: dydx=7y-24x-1

Q: 07 * a Which is the derivative of f(5x)? (a) 5 f'(x) (b) 5 f'(5x) (c) f'(5x)

A:

Q: 5. To find the -intercepts, set x equal to 0.

A: Intercepts are those points where the graph of a function intersect the axis

Q: Can we apply L'Hôpital's Rule for: lim O a. Yes O b. TBH, I don't know. O c. No O d. Maybe. x -?…

A: let  I=limx→0(x4e4x)we know  e0=1

Q: What type of quadratic surface with equation x2 + 6y² – 4z² = 2. a. hyperbolic paraboloid b.…

A:

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval Enter…

A: Use the definite integration to find the area under the given function with x-axis.

Q: To raise funds, the student council sells yogurt fruit smoothies every day during lunch. They sell…

A:

Q: 3 Foo = Find the Show 3x-1 X-1 Interse function F"(x) of Fcx) the domain and range of the inverse…

A:

Q: 1. The section of a certain solid contains a semicircle, a rectangle, and a triangle, as shown. The…

A:

Q: Find the particular solution of the differential equation y′–xey=2ey, given the initial condition,…

A: We can solve the given differential equation by using the variable separable method.

Q: . A steel ball, initially at 100°C is dropped in a water bath at 25°C. After 5 seconds, the…

A:

Q: 3. 4 Determine the volume of the solid obtained by rotating the region bounded by y = √x, y = 3 and…

A: As per Bartleby guidelines we only give first question answers. Please repost for other parts.

Q: Find y' if sin¹(xy) O1+sin ry√1-x²y² 1-r²y² O O x+(sin y)√1-x²y² sin y √1-x²y² 0700 None of these =…

A:

Q: 口 4. Find the vertex of the given function: y=x² + 3x-4 O (-1.5, 6.25) O (-1.5, -6.25) O (1.5,…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: A closed rectangular box with a volume of 2058ft³ is made from two kinds of materials. The top and…

A:

Q: 7. Determine the y-intercept of the exponential function j(x) = a(b)*, if a > 0, b>0. A. 0 B. 1 C. a…

A: To determine the y‐intercept of the following exponential function. jx=abx, if a>0, b>0

Q: whats the distance of JK, where J(4,3) and K(2,-3)?

A: Concept Let two points  P( x1 , y1 ) & Q( x2 , y2 ) Then PQ = ( x2 - x1 )2 + ( y2 - y1 )2

Q: Let R be the region bounded by the graphs of f(x) = x2, g(x) = 4, and the vertical line x = 1.…

A:

Q: Consider the curve given by x² – 6y² – 5 – 4xy . x+2y dy dx 2(3y-x) Show that

A: Given : x2-y2=5-4xy   To Show : dydx=x+2y2(3y-x)

Q: Step 1 To find the x-intercept, set y = 0 in the equation 3x - y - 9 = 0, and then solve for x. 3x -…

A:

Q: Consider the vector function r(t) = (t, t¹, t8) Compute r' (t) = ( T(1) = ( r"(t) = ( r(t) xr' (t) =…

A:

Q: 2. A thermometer reading 70°F is placed in an oven preheated to a constant temperature. Through a…

A:

Q: Let ā= (2, 5, 7) and 6 = (1, 3, 4). (a - b) × (a + b) = X (3,16,33) X

A:

Q: Let u = (-2, 7, 2) and 7 = (2, 7, 5). Compute the following: ü x v = vxu= úxu = 10(u x v) üx (107) =…

A: Given,            The two vectors are u→=<-2,-7,2> and v→=<2,7,5>.

Q: Consider the augmented matrices below. For each matrix, state whether it is in row echelon form, or…

A: A matrix is in reduced row echelon form, also known as row canonical form if it meets the…