01/30/24

Evaluate the integral

∫(from 0 to √(3)/4) dx/(1+16x2)

01/30/24

Use the form of the definition of the integral given in this theorem to evaluate the integral. 0 to 1 of (x^3 − 4x^2) dx

Use the form of the definition of the integral given in this theorem to evaluate the integral. 0 to 1 of (x^3 − 4x^2) dx

01/30/24

Describe the given translation as it relates to the graph of the parent function. y=(x−5)2 Translation of the graph of y=x2 1 of 1. Select Choice 5 units.

Describe the given translation as it relates to the graph of the parent function.y=(x−5)^2 Translation of the graph of y=x2 Select Choice 5 units.choices: right left up down 

01/30/24

Differentiate the logarithmic function

y=log2(xlog5x)For this one, should I try to change the base to lnx? Or should I just proceed and differentiate the function + chain rule everything? So like, 1/[(xlog5x)ln2]*d/dx[xlog5x]?

01/30/24

The region bounded by the given curve is rotated about the specified axis. Find the volume V of the resulting solid by any method. x^2 + (y − 4)^2 = 16; about the y-axis

The region bounded by the given curve is rotated about the specified axis. Find the volume V of the resulting solid by any method.x2 + (y − 4)2 = 16;    about the y-axisV=?

Consider the differential equation

d2x/dt2 - dx/dt - x = cos(t)This equation could describe a forced damped oscillator, as we will see in Chapter 9. We are told that the differential equation has a solution of the form x(t) =... more

01/30/24

Precalculus 12 grade

Convert 257.285 degrees to degrees, minutes, seconds

01/28/24

Evaluate the integral 4secxtanx from -pi/3 to pi/3

Definite Integrals and Fundamental Theorem of Calculus

Help with Exact Equation Problem

I need help solving this exact equation problem:x(xy+1)y' + y(xy+1) = 0I solved the problem up to the function with respect to y and got this:fy(x,y) = x^2/2 + x + h'(y)I am not sure how to go from... more

01/26/24

Trigonometric Functions of Angles

Simplify tan(t)sec(t)

01/26/24

precalculus questions

having a hard time getting a few questions answered and understanding how to get the correct answers.first problem:Expand the logarithm as much as possible. Rewrite the expression as a sum,... more

01/26/24

Evaluate the following integrals

∫3x/(1+x4)dxI separated the two equations into 3x(1/(1+x^4) and tried u substitution but neither 3x nor 1+x^4 really worked so I wasn't sure how to do this equation. ∫1/(√3-2x-x2)dx [Hint:... more

01/26/24

Evaluate the definite integral from 1 to -3 of (-x/2+1) dx

Definite Integrals׬ ቀെ ௫ ଶ ൅1ቁ ିଷ ଵ 푑푥

01/26/24

Use the fact that limx→0 sin(x)/x = 1 to compute the following limits.

(A.) lim x→0 sin(5x)/2x =(b.) lim t→0 sin2(3t)/t =(c) lim θ→0 sin(3θ)/tan(θ) =

writing equations

The price of gas at a local gas station is currently $3.50 per gallon. You have a $50 budget for gas this week. How many gallons of gas can you buy with your budget?

01/25/24

Periodic Functions

Outside temperature over a day can be modelled using a sine or cosine function. Suppose you know the high temperature for the day is 96 degrees and the low temperature of 74 degrees occurs at 2 AM.... more

01/24/24

Volumes of cylinders and composite objects

a. This cake is made of three cakes, each 15 cm high, and with diameters 20 cm, 30 cm and 40 cm. Calculate the total volume of the cake.b. How many litres of liquid concrete were used to make this... more

01/23/24

Find a unit vector that has the same direction as the given vector.

−5i + 9j

01/23/24

Solve for r when given A = 2πr^2+2πr

This is identical to solving for x in the standard form of a quadratic equation ax2+bx+c=0 only that in this case, a=2π, b=2π and c=A, and x=r. Consider substituting in these values and then... more

01/23/24

Differentiate the natural logarithmic function

y=esin2x+sin(e2x)

01/23/24

Evaluate the limit of the natural logarithm:

the limit as x approaches infinity, e-2xcosx

01/23/24

Help with mixture problem

A candy distributor needs to mix a 10% fat-content chocolate with a 60% fat-content chocolate to create 150 kilograms of a 46.7% fat-content chocolate. How many kilograms of each kind of chocolate... more

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