Step 1

It represents line equation in XY- plane whose equation if given by \(x=y\) where x and y are not negative

It represents line equation in XY- plane whose equation if given by \(x=y\) where x and y are not negative

Question

asked 2021-06-07

Describe in words the surface whose equation is given. \(\phi = \frac{\pi}{4}\) (select the correct answer)

1)the top half of the right circular cone with vertex at the origin and axis the positive z-axis

2)the plane perpendicular to the xz-plane passing through z = x, where \(x \geq 0\)

3)the plane perpendicular to the xy-plane passing through y = x, where \(x \geq 0\)

4)the base of the right circular cone with vertex at the origin and axis the positive z-axis

5)the plane perpendicular to the yz-plane passing through z = y, where \(y \geq 0\)

1)the top half of the right circular cone with vertex at the origin and axis the positive z-axis

2)the plane perpendicular to the xz-plane passing through z = x, where \(x \geq 0\)

3)the plane perpendicular to the xy-plane passing through y = x, where \(x \geq 0\)

4)the base of the right circular cone with vertex at the origin and axis the positive z-axis

5)the plane perpendicular to the yz-plane passing through z = y, where \(y \geq 0\)

asked 2021-06-09

Change from rectangular to cylindrical coordinates. (Let \(r\geq0\) and \(0\leq\theta\leq2\pi\).)

a) \((-2, 2, 2)\)

b) \((-9,9\sqrt{3,6})\)

c) Use cylindrical coordinates.

Evaluate

\(\int\int\int_{E}xdV\)

where E is enclosed by the planes \(z=0\) and

\(z=x+y+10\)

and by the cylinders

\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)

d) Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

\(z=\sqrt{x^{2}+y^{2}}\)

and the sphere

\(x^{2}+y^{2}+z^{2}=8\).

a) \((-2, 2, 2)\)

b) \((-9,9\sqrt{3,6})\)

c) Use cylindrical coordinates.

Evaluate

\(\int\int\int_{E}xdV\)

where E is enclosed by the planes \(z=0\) and

\(z=x+y+10\)

and by the cylinders

\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)

d) Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

\(z=\sqrt{x^{2}+y^{2}}\)

and the sphere

\(x^{2}+y^{2}+z^{2}=8\).

asked 2021-06-05

Use the following Normal Distribution table to calculate the area under the Normal Curve (Shaded area in the Figure) when \(Z=1.3\) and \(H=0.05\);

Assume that you do not have vales of the area beyond \(z=1.2\) in the table; i.e. you may need to use the extrapolation.

Check your calculated value and compare with the values in the table \([for\ z=1.3\ and\ H=0.05]\).

Calculate your percentage of error in the estimation.

How do I solve this problem using extrapolation?

\(\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}\)

Assume that you do not have vales of the area beyond \(z=1.2\) in the table; i.e. you may need to use the extrapolation.

Check your calculated value and compare with the values in the table \([for\ z=1.3\ and\ H=0.05]\).

Calculate your percentage of error in the estimation.

How do I solve this problem using extrapolation?

\(\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}\)

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.