Ayman Sherif

Numerade Educator
Graduate Assistant

Biography

Involved in the field of civil engineering of structural analysis, concrete design and projects' management. Having more than 8 years experience in both the Academic and professional life.

Education

Ayman has not yet added their education credentials.

Educator Statistics

Numerade tutor for 6 years
89 Students Helped

Topics Covered

Mastering Integrals: Tips and Tricks for Calculus Success
Unlocking the Power of Functions: Boost Your Programming Skills
Mastering Partial Derivatives: Essential Techniques and Tips
Exploring Probability Topics: From Basics to Advanced Strategies

Ayman's Textbook Answer Videos

09:50
Calculus Early Transcendentals

(a) Let $A_{n}$ be the area of a polygon with n equal sides inscribed in a circle with radius $r .$ By dividing the polygon into n congruent triangles with central angle $2 \pi / n,$ show that
$$\mathrm{A}_{\mathrm{n}}=\frac{1}{2} \mathrm{nr}^{2} \sin \left(\frac{2 \pi}{\mathrm{n}}\right)$$
(b) Show that lim $_{\mathrm{n} \rightarrow \infty} \mathrm{A}_{\mathrm{n}}=\pi \mathrm{r}^{2} .[$ Hint: Use Equation 3.3 $.2 .]$

Chapter 5: Integrals
Section 1: Areas and Distances
Ayman Sherif
07:09
Calculus for AP

Find the extreme values of $f(x, y)=x^{2}+2 y^{2}$ subject to the constraint $g(x, y)=4 x-6 y=25 .$
\begin{equation}\begin{array}{l}{\text { (a) Show that the Lagrange equations yield } 2 x=4 \lambda, 4 y=-6 \lambda} \\ {\text { (b) Show that if } x=0 \text { or } y=0 \text { , then the Lagrange equations give }} \\ {x=y=0 . \text { simce }(0,0) \text { does not satisfy the constraint, you may }} \\ {\text { assume that } x \text { and } y \text { are nonzero. }} \\ {\text { (c) Use the Lagrange equations to show that } y=-\frac{3}{4} x}\\{\text { (d) Substitute in the constraint equation to show that there is a unique }} \\ {\text { critical point } P .} \\ {\text { (e) Does } P \text { correspond to a minimum or maximum value of } f ? \text { Referto }} \\ {\text { Figure } 11 \text { to justify your answer. Hint: Do the values of } f(x, y) \text { increase }} \\ {\text { or decrease as }(x, y) \text { moves away from } P \text { along the line } g(x, y)=0 ?}\end{array}\end{equation}

Chapter 12: DIFFERENTIATION IN SEVERAL VARIABLES
Section 8: Lagrange Multipliers: Optimizing with a Constraint
Ayman Sherif
07:10
Calculus for AP

In Exercises $4-13,$ find the minimum and maximum values of the function subject to the given constraint.
$$f(x, y, z)=x y+3 x z+2 y z, \quad 5 x+9 y+z=10$$

Chapter 12: DIFFERENTIATION IN SEVERAL VARIABLES
Section 8: Lagrange Multipliers: Optimizing with a Constraint
Ayman Sherif
12:41
Calculus for AP

The surface area of a right-circular cone of radius $r$ and height $h$ is $S=\pi r \sqrt{r^{2}+h^{2}}$ , and its volume is $V=\frac{1}{3} \pi r^{2} h_{\text { . }}$
\begin{equation}\begin{array}{l}{\text { (a) Determine the ratio } h / r \text { for the cone with given surface area } S \text { and }} \\ {\text { maximum volume } V .} \\ {\text { (b) What is the ratio } h / r \text { for a cone with given volume } V \text { and mimimum }} \\ {\text { surface area } S ?} \\ {\text { (c) Does a cone with given volume } V \text { and maximum surface area exist? }}\end{array}\end{equation}

Chapter 12: DIFFERENTIATION IN SEVERAL VARIABLES
Section 8: Lagrange Multipliers: Optimizing with a Constraint
Ayman Sherif
04:50
Applied Statistics and Probability for Engineers

A biotechnology manufacturing firm can produce diagnostic test kits at a cost of $\$ 20 .$ Each kit for which there is a demand in the week of production can be sold for $\$ 100$. However, the half-life of components in the kit requires the kit to be scrapped if it is not sold in the week of production. The cost of scrapping the kit is $\$ 5 .$ The weekly demand is summarized as follows: How many kits should be produced each week to maximize the firm's mean earnings?

Chapter 2: Probability
Section 8: Random Variables
Ayman Sherif
01:58
Applied Statistics and Probability for Engineers

Assume the following characteristics of the inspection process in Exercise $2-207$. If an operator checks a bolt, the probability that an incorrectly torqued bolt is identified is $0.95 .$ If a checked bolt is correctly torqued, the operator's conclusion is always correct. What is the probability that at least one bolt in the sample of four is identified as being incorrectly torqued?

Chapter 2: Probability
Section 8: Random Variables
Ayman Sherif
1 2

Ayman's Quick Ask Videos

01:44
Calculus 1 / AB

Distance Traveled by a Projectile An object is shot straight upward from sea level with an initial velocity of 400 ft/sec.
(a) Assuming gravity is the only force acting on the object, give an upper estimate for its velocity after 5 sec have elapsed. Use $g=32 \mathrm{ft} / \mathrm{sec}^{2}$ for the gravitational constant.
(b) Find a lower estimate for the height attained after 5 sec.

Ayman Sherif
02:55
Algebra

The four cases in which we can solve a triangle are ASA SSA SAS SSS
$$\begin{array}{l}{\text { (a) In which of these cases can we use the Law of Sines to }} \\ {\text { solve the triangle? }} \\ {\text { (b) Which of the cases listed can lead to more than one solu- }} \\ {\text { tion (the ambiguous case)? }}\end{array}$$

Ayman Sherif
02:23
Calculus 1 / AB

Moment of inertia of wire hoop A circular wire hoop of constant density $\delta$ lies along the circle $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$ in the $x y$ -plane.Find the hoop's moment of inertia about the $z$ -axis.

Ayman Sherif
02:27
Calculus 2 / BC

A crane with a counterweight is shown in the figure. Find the horizontal distance between points $A$ and $B$ to the nearest foot.

Ayman Sherif
01:33
Calculus 1 / AB

Sketch the graph of the amount of a particular brand of coffee sold by a store as a function of the price of the coffee.

Ayman Sherif
01:45
Calculus 3

Describe and sketch a solid with the following properties. When illuminated by rays parallel to the z-axis, its shadow is a circular disk. If the rays are parallel to the y-axis, its shadow is a square. If the rays are parallel to the x-axis, its shadow is an isosceles triangle.

Ayman Sherif
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