The straight line y=x +B is tangent to the graph of f(x) = 2^{x at the point where x = A. Find A and B. %3D

Q: Estimate the slope of the tangent line to f(x) = tax(x) at the point x = 9π/4

A:

Q: The radius of a right circular cylinder is increasing at a rate of 4 inches per minute, and the…

A:

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: One side of the right triangle is measured as 9.5 inches and opposite angle is equal to 26.75° with…

Q: A right triangle has legs of 30 inches and 40 inches whose sides are changing. The short leg is…

A:

Q: Sarah is asked to find the maximum value of a function. Not having a complete understanding of the…

A: If we want to find the maximum or minimum values of a function then follows the steps mentioned…

Q: The rate of change of atmospheric temperature with respect to altitude is equal to the slope of the…

A: The rate of change of atmospheric temperature with respect to altitude is equal to the slope of the…

Q: What is the rate of change of the area?

A:

Q: A right triangle has legs of 6 inches and 8 inches whose sides are changing. The short leg is…

A: Given, A right triangle has legs of 6 inches and 8 inches whose sides are changing. The short leg is…

Q: The height of a right circular cone is increasing at 3 mm/s and its radius is decreasing at 2 mm/s.…

A:

Q: The top of an elastic rope (whose length can change) is fixed on the wall at the height of 3 meters…

A: Suppose the bottom end of the rope is x m away from the wall while it's length is l m after t…

Q: Estimate the instantaneous rate of change of y(x) = 2x² + 2 at the point: In other words, choose…

A: To estimate the instantaneous rate of change of yx=2x2+2 at the point: x=-2.

Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given,dAdt=-4 cm2/minA=100cm2Let,x=side of the equilateral triangle find dxdt when dAdtis decreased…

Q: Find the equation of tangent line at the specified point  x power 2 by 3 - y power 2 by 3 - y =1…

A: Given curve is x23-y23-y=1. To find the equation of tangent line at the point 1,-1. Solution:…

Q: The Gateway Arch in Saint Louis is modeled by the curve: y = 210 − 20 cosh ( x/30) . At what height…

A: yx = Height of the Gateway archyx = 210 - 20coshx30         Blue curve---------------------formulae…

Q: A right triangle has legs of 3 inches and 4 inches whose sides are changing. The short leg is…

A: dhdt=7 in/sec , dbdt = -10 in/sec

Q: At a certain instant the radius of a right circular cylinder is 6 inches and is increasing at the…

A: At a certain instant the radius of a right circular cylinder is 6 inches and is increasing at the…

Q: An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

A: We will estimate the volume of cylindrical metal as following. Inside radius = 2 cm Inside height =…

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – the…

A:

Q: Explain why the slope of the tangent line can be interpreted as aninstantaneous rate of change

A: The average rate of change of a function fx over the interval x, x+h is the slope of the secant line…

Q: A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The length…

A: Given:A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The…

Q: Average velocity is equal to the slope of a secant line through two points on a graph. Which graph?

A: Average velocity formula is:

Q: The slope of a tangent line at a given point on a curve tells the rate of change for the function at…

A: Let the given curve be f(x) -  Then f'(x) will be the slope of a tangent line at a given…

Q: A rectangle has a length of 11 inches and a width of 5 inches whose sides are changing. The length…

A: In the given rectangle  Width b = 5 inches Length l = 11 inches Length increasing rate dl/dt = 9…

Q: When a circular plate of metal is heated in a oven, its radius increases at a rate of 0.05 cm/min.…

A: drdt=0.05cm/minradius, r=52cmArea=πr2Derivative formuladdxxn=n xn-1

Q: A point is moving along the graph of x3y2 = 200. When the point is at (2, 5), its x-coordinate is…

A: Given that a point is moving along the graph x3y2=200 and it's x-coordinate is changing at the rate…

Q: a hemischperical dome has a diameter of 50 m. use differentials to estimate the amount of paint…

A: the problem concerns an application of differentials

Q: Explain the relationships among the slope of a tangent line, theinstantaneous rate of change, and…

A: The slope of a tangent line of f on x is,msec=f(x)-f(a)x-a

Q: Find how fast the area of a triangle increases as the length of the base of the triangle increases…

A: (a) We need to find dAdb where A is the area of the triangle and b is the base of the triangle.

Q: A right triangle has legs of 24 inches and 32 inches whose sides are changing. The short leg is…

A: Given, Measure of two legs of a right triangle: 24 inches, 32 inches. Let x be the short leg and y…

Q: A bacteria culture is known to grow at a rate proportional to the amount present. If the population…

A: This is a problem of the application of differential equations.

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: A right triangle has legs of 18 inches and 24 inches. The short leg is decreasing by 3 in/sec. The…

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: to find:- dH/dt.

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – 3x and…

A:

Q: A rectangle has a length of 11 inches and a width of 10 inches whose sides are changing. The length…

A:

Q: The radius of a circle is increasing at a constant rate of 0.2 meter per second. What is the rate of…

A: Given Where r is radius. and

Q: A rectangle has a length of 12 inches and a width of 6 inches whose sides are changing. The length…

A: The length of a rectangle is l=12 inThe width of a rectangle is w=6 inTo find the rate at width the…

Q: A rectangle has a length of 9 inches and a width of 10 inches whose sides are changing. The length…

A: Length of the rectangle, l =9 inches Width of the rectangle, w = 10 inches The length is increasing…

Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

Q: What is the relationship between the secant line, slope of the tangent line, derivative of a…

A: Solved below

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A:

Q: A rectangle has a length of 7 inches and a width of 8 inches whose sides are changing. The length is…

A:

Q: The radius of a right circular cone is increasing at a rate of 3 inches per second and its height is…

A:

Q: Find the first derivative by increment method. Show your complete solution. V12x – 3 Irolim Exam…

A:

Q: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

A: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

Q: A right triangle has legs of 21 inches and 28 inches whose sides are changing. The short leg is…

A: Length of the legs are 21 inches and 28 inches and the short leg is increasing by 10 in/sec and the…

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg…

Q: 2 2. f(x) = 5-x², (3,-4)

A:

Q: The radius of a right circular cylinder is increasing at the rate of 3 inches per ninute and the…

A: Given:The rate of change in radius =3 in/mThe rate of change in height =4 in/mThe radius =9 The…

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 33 inches and 44 inches . The short leg is decreasing by 4…

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: