Find the intersections between the two given functions algebraically. {Y = -x^2-10x Y = x^2+5

Q: Differentiate the function. f(x)  = x5 + 5x

A: Given function:

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A: Object is attached with a string and it's oscillating. It's height is represented by an equation…

Q: The sum of two numbers is 66. Express the product of the numbers, P, as a function of one of the…

A: It is given that the sum of two numbers is 66. Let one of the two numbers is x Then the other number…

Q: Differentiate the function. (2x- 1)

A: Given:y=12x-15

Q: Find the domain for the function. X-3 V3x-2 a) (-0, 00) b) (- ∞, 3) U (3, 0)

A:

Q: 1) Write the function h(x)=1/(x-2)^2 as a composition of two functions 2)Write the function h(x)=…

A:

Q: у 3 хе 2x xe %3D

A: Given function: y=xe2x

Q: A 1 lb sponge initially contains 5 lb of water. As it is lifted up from the ground, the sponge loses…

A: Answer is option d here decrement in water is linearly (as constant rate)

Q: Differentiate the function. 1 g(x) = - (2x3 + 3x + 5)3/4 g'(x) =

A:

Q: Determine the (exact) equation of the function that has zeros at 3/2, 3(order2), and 5(order 3) and…

A: Solution:- We have to find the exact equation of the function that has zeros at 3/2, 3(order2), and…

Q: Find two numbers whose sum is 78 and whose product is as large as possible. [Hint: Let x and 78-x be…

A:

Q: Differentiate the function. 2 15 F(x) = 5 F'(x) =

A:

Q: Explain Functions of More Than Two Variables?

A: A real valued function of n variables is a function that takes as input n real numbers, commonly…

Q: f(x)=-2(x-1)^3(x+2)^2

A: on solving this we get

Q: Determine the net change between the given values of the variable. f(x)= 6x-4 x=2, x=3

A: f(x)= 6x-4;  x=2, x=3 f(2) = 6*2-4 = 8 f(3) = 6*3-4 = 14

Q: The sum of two positive numbers is 210, then the function that models the product of the numbers is…

A: Let x be a positive number Given that: Sum of two positive numbers = 210

Q: Find the points of intersection of the graphs of the functions y = x2 + 1 and y = 4x

A: Given functions:                     y = x2+1   ... (1)                     y = 4x      ... (2)

Q: Find the slope of the graph of the function at the given point.                       f(x) = √(1 −…

A:

Q: differentiate the function f(x) = x^2(2x+3)^5

A: The given function is f(x) = x^2(2x+3)^5

Q: Differentiate the function. y= (7x -x+4) (-x³ +5) - x + 4) ( – xº +5) y' = %3D

A:

Q: Differentiate the function. 5 6 G(x) = x° + 6x G'(x) =O

A: We have to differentiate the given function: Gx=x6+6x5 Rewriting the given function,…

Q: The sum of two positive numbers is 60. Find a function that models their product P in terms of x,…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: -4 -6 -2 4 -6

A: To find the interval where the function is positive first we  choose  some points in the given…

Q: Differentiate the function.  y= x 5/3 - x 2/3

A: We have to differentiate the function: y=x53-x23 We know the formula of differentiation: dxndx=nxn-1…

Q: Graph the step function. 0 < x < 1 1 < x < 2 1, 3, if 2 < x < 3 if 3 < x < 4 if if 7. f(x) = 4, 6,

A: Please refer the attached image for complete solution.

Q: Differentiate the function ƒ(x)=(1+2·x)^5

A: ƒ(x)=(1+2·x)^5

Q: Differentiate the function. y = 2(5 - x)3(6x - 1)

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Differentiate the function. 2 3 4 f(x) = 12(3x +2)° (4x- 3) f'(x) =|

A:

Q: Find the difference of the two functions A(x)=1x-6 and B(x)=x+8x-2 at 6

A:

Q: Differentiate the function. h(x) = (x – 4)(2x + 3) h'(x) =

A:

Q: Differentiate the function. h(x) = (x - 2)(5x + 3) h'(x)

A: Solution: The objective is to find the derivative of the given function

Q: Is the table below linear or exponential and why? Please write a function of this table. x y 0 -16…

A: Consider the given table. Since, every next value is equal of y to the multiple of 12 and first…

Q: Find all points of intersection between the graphs of the functions. 5 =x+y 7 =x +y

A:

Q: the sum of two numbers is 40. express their products as a function of one of the numbers.

A: Let's express product of two numbers as a function of one number.

Q: Find the point on the graph of the function that is closest to the given point. (х) 3 (x - 1)2, (-5,…

A:

Q: Find the domain of the function : √(x+2)

A: Given function is fx=x+2

Q: Differentiate the function. f(x) = (5x2 – 7x)eX f'(x) =

A: →Product Rule of differentiation:                 duvdx = udvdx + vdudx→dexdx =ex→dxndx = n xn-1

Q: Differentiate the function y = -5e".

A: Given that, the function is y=-5e0. In order to find the derivative of y=-5e0, simplify the function…

Q: how can you figure out the end behavior of the function 1/2(x-1)(x+1)^3(x-2)^2

A: Given:The function is

Q: Differentiate the function. h(x) =  3 4(x5 − 4x3 + 7)8 h'(x) =

A: We have to find the derivative of the given function

Q: Differentiate f(x) 2- 9x +5 f'(x) =

A:

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x2 - 8, (0,…

A:

Q: I. Differentiate the given functions: 1. y = 5x-2 – 2x +3 2. y =+ 3. y = (x – 2)(3x³ + 5)

A: Given : 1. y = 5x-2 - 2x + 3 2. y = 2x-3 + 32x23 3. y = (x - 2)(3x3 + 5)    To differentiate the…

Q: The sum of two positive numbers is 95. Find a function that models their product P in terms of x,…

A: Let two positive number x, y then  x+y=95 Thus y=95-x Therefore the first number is x and the second…

Q: Differentiate f ( x ) = 2e* – 8*

A:

Q: Differentiate the function ƒ(x)=(4x+3/5x−2​)^3.

A: fivenf(x)=(4x+35x-2)3 diffrentiate by division rulef'(x)=3(4x+35x-2)3-1((5x-2)4-(4x+3)5(5x-2)2)

Q: Differentiate the function. f(x) = (2x - 2)24 f'(x) =

A:

Q: You have 800 feet of fencing to enclose a rectangular field. However, one side of the field lies…

A: Rectangular field: You have 800 feet of fencing to enclose a rectangular field. One side of the…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.