Find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places. f(x)=420-5 x; x=25

Find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places. $f(x)=45 ; x=100$

Monochromatic light at 577 nm illuminates a diffraction grating with 325 lines/mm. Determine the highest order that can be observed with this grating at the given wavelength.

Ajinkya Electronic Systems, a company in India that manufactures many different electronic products, has to purchase goods and services from a variety of suppliers (wire, diodes, LED displays, plastic components, etc.). The table below shows several suppliers and the VAT tax rates associated with each. It also shows the purchases (in $1000 units) that Ajinkya made (before tax) from each supplier in the previous accounting period. Assume Ajinkya’s sales to end users were$9.2 million and Ajinkya’s products carry a 15% VAT.

$$\begin{array}{ccc} \text { Supplier } & \text { VAT Rate, } \% & \begin{array}{c} \text { Purchases by } \\ \text { Ajinkya, } \$ 1000 \end{array} \\ \hline \mathrm{A} & 4.0 & 350 \\ \mathrm{B} & 12.5 & 870 \\ \mathrm{C} & 12.5 & 620 \\ \mathrm{D} & 21.3 & 90 \\ \mathrm{E} & 32.6 & 50 \\ \hline \end{array}$$

What was the amount of VAT Ajinkya sent to the Treasury of India?

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. $7(5 t+3)^{-5 / 3}+14(5 t+3)^{-2 / 3}-21(5 t+3)^{1 / 3}$

Work each problem. Let U={1, 2, 3, 4, 5} and A={1, 2, 3}. Find A'.

Calculate the magnitude of the normal force on a 15.0-kg block in the following circumstances: The block is resting on the floor of an elevator that is accelerating upwards at 3.00 $m/s^2$.

North American outlets supply AC electricity with a frequency of f = 60.0 Hz while the European standard is f = 50.0 Hz. What value of capacitance provides a capacitive reactance of $1.00 k \Omega$ in Europe ?

In an effort to reduce pipe breakage, water hammer, and product agitation, a French chemical company plans to install several chemically resistant pulsation dampeners. The cost of the dampeners today is 106,000 Euro, but the chemical company has to wait until a permit is approved for its bidirectional port-to-plant product pipeline. The permit approval process will take at least 2 years because of the time required for preparation of an environmental impact statement. Because of intense foreign competition, the manufacturer plans to increase the price only by the inflation rate of 3% each year. Determine the cost of the dampeners in 2 years in terms of (a) then-current euros, and (b) constant-value euros.

An air-filled parallel-plate capacitor with capacitance $C_0$ stores charge Q on plates separated by distance d. The potential difference across the plates is $\Delta V_{0}$ and the energy stored is $PE_{C,0}.$ If the capacitor is disconnected from its voltage source and the space between the plates is then filled with a dielectric of constant K = 2.00, evaluate the ratios $P E_{\text {C, new }} / P E_{C, 0}$.

A capacitor with plates separated by distance d is charged to a potential difference $\Delta V_{c}$. All wires and batteries are disconnected, then the two plates are pulled apart (with insulated handles) to a new separation of distance 2d. a. Does the capacitor charge Q change as the separation increases? If so, by what factor? If not, why not? b. Does the electric field strength E change as the separation increases? If so, by what factor? If not, why not? c. Do es the potential difference $\Delta V_{\mathrm{C}}$ change as the separation increases? If so, by what factor? If not, why not?

In earlier problem, Rowan noticed that multiplying the x-coordinates by -1 reflects the shape across the y-axis. a. Test this strategy on a triangle formed by the points A (-3, 5), B (1, 2), and C(0, 8). Before you graph, multiply each x-coordinate by -1. What are the new points? b. Graph your original and new triangle on a new set of axes. Did your triangle get reflected across the y-axis?

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. $y=A+B\left(1-e^{-C x}\right)$, for x

Expand each expression. $\log _{7} h^{2} j^{11} k^{-5}$