Question

asked 2021-05-03

Describe in words the surface whose equation is given. (assume that r is not negative.) \(\theta=\frac{\pi}{4}\)

a) The plane \(y = −z\) where y is not negative

b) The plane \(y = z\) where y and z are not negative

c) The plane \(y = x\) where x and y are not negative

d) The plane \(y = −x\) where y is not negative

e) The plane \(x = z\) where x and y are not negative

a) The plane \(y = −z\) where y is not negative

b) The plane \(y = z\) where y and z are not negative

c) The plane \(y = x\) where x and y are not negative

d) The plane \(y = −x\) where y is not negative

e) The plane \(x = z\) where x and y are not negative

asked 2021-05-17

The integral represents the volume of a solid. Describe the solid.

\(\pi\int_{0}^{1}(y^{4}-y^{8})dy\)

a) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{2}\}\) of the xy-plane about the x-axis.

b) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{2}\leq x\leq y^{4}\}\) of the xy-plane about the x-axis.

c) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{2}\}\) of the xy-plane about the y-axis.

d) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{2}\leq x\leq y^{4}\}\) of the xy-plane about the y-axis.

e) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{8}\}\) of the xy-plane about the y-axis.

\(\pi\int_{0}^{1}(y^{4}-y^{8})dy\)

a) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{2}\}\) of the xy-plane about the x-axis.

b) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{2}\leq x\leq y^{4}\}\) of the xy-plane about the x-axis.

c) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{2}\}\) of the xy-plane about the y-axis.

d) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{2}\leq x\leq y^{4}\}\) of the xy-plane about the y-axis.

e) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{8}\}\) of the xy-plane about the y-axis.

asked 2021-06-02

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.

Passing through (3,-1) and perpendicular to the line whose equation is x-9y-5=0

Write an equation for the line in point-slope form and slope-intercept form.

Passing through (3,-1) and perpendicular to the line whose equation is x-9y-5=0

Write an equation for the line in point-slope form and slope-intercept form.

asked 2021-05-16

Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.

A. Let y=f(x) be the equation of C. Find f(x).

B. Find the slope at P of the tangent to C.

C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?

D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.

E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.

Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.

A. Let y=f(x) be the equation of C. Find f(x).

B. Find the slope at P of the tangent to C.

C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?

D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.

E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.

Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.