Numerade

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Let $\vec{F} = 3y\vec{i} + 4x\vec{j}$, $\phi = 2x^3 + 3xy$, and $h = y - 3x^2$. (a) Find each of the following: $\vec{F} - \nabla\phi = \boxed{}$ $\nabla h = \boxed{}$ How are $\vec{F} - \nabla\phi$ and $\nabla h$ related? $\vec{F} - \nabla\phi = \boxed{}$ $\nabla h$ (Note that this shows that $\vec{F} - \nabla\phi$ is parallel to $\nabla h$.) (b) Use $\phi$ and the Fundamental Theorem of Calculus for Line Integrals to evaluate $\int_C \vec{F} \cdot d\vec{r}$, where $C$ is the oriented path on a contour of $h$ from $P(0, 4)$ to $Q(6, 112)$. $\int_C \vec{F} \cdot d\vec{r} = \boxed{}$

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4. (3 points) Find the determinant of the matrix $A = \begin{pmatrix} 1 & 0 & 1 & 0 \\ 0 & 3 & 1 & 4 \\ 1 & 1 & 4 & 0 \\ -1 & -1 & 2 & 3 \end{pmatrix}$

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What does "coccus" mean in regards to bacteria shape? Spherical in shape Rod-shaped Spiral in shape

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Why is the dna synthesis of the lagging strand considered discontinuous

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Chapter 05 Homework 14. Application: Demand elasticity and agriculture The following graph illustrates the market for walnuts. It plots the monthly supply of walnuts and the monthly demand for walnuts. Suppose new gathering technology is invented, allowing growers to produce more crops using the same amount of resources. Show the effect this shock has on the market for walnuts by shifting the demand curve, supply curve, or both. Note: Select and drag one or both of the curves to the desired position. Curves will snap into position, so if you try to move a curve and it snaps back to its original position, just drag it a little farther.

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A charge of $Q_1 = 3 \times 10^{-4}$ C at M(1, 2, 3) and a charge of $Q_2 = -10^{-4}$ C at N(2, 0, 5) in a vacuum.\ Using Coulomb's law find the force exerted on $Q_2$ by $Q_1$

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A five-year project has an initial fixed asset investment of $290,000, an initial NWC investment of $25,000, and an annual OCF of -$35,000. The fixed asset is fully depreciated over the life of the project and has no salvage value. If the required return is 11 percent, what is this project's equivalent annual cost, or EAC? Initial fixed asset investment $ 290,000 Initial NWC investment $ 25,000 Annual OCF $ (35,000) Required return 11% "Depreciation staight-line over life 5 Complete the following analysis. Do not hard code values in your calculations. You must use the built-in Excel functions to answer this question. Cash flows Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 NPV EAC

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A particle describes an ellipse under a force $\frac{\mu}{r^2}$ and has a velocity V at a distance R from the centre of force. Show that the time period is $\frac{2\pi}{\sqrt{\mu}} \left[ \frac{2}{R} - \frac{V^2}{\mu} \right]^{-3/2}$.

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A given thick spherical shell has a volume charge distribution of $\rho = A/r$. An additional point charge Q is placed at the center ($r=0$). The value of A is selected so that the electric field inside the thick shell is constant (does not depend on r). What is the electric field inside the shell (in units of N/C)? Use: a = 5.9 m b = 16 m Q = 0.8 \times 10^{-9} C

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Problem 3.31: Find a counter-model showing that the following is not valid. [âˆƒx P(x) âˆ§ âˆ€x Q(x)] â†’ âˆ€x [P(x) âˆ§ Q(x)] (Just define your counter-model. You do not need to verify that it is correct.)

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