answer:The square root of 45, √45, is closest to the integer 7. Here's a step-by-step explanation: Since √36 = 6 and √49 = 7, it's clear that √36 < √45 < √49. Therefore, the integer 6 is less than √45, and √45 is less than the integer 7. This indicates that √45 is closest to the integer 7.

answer:To evaluate the integral {eq}int{dfrac{dx}{sqrt{x^{2} + 16}}} {/eq}, we use trigonometric substitution. Let {eq}x = 4tan u {/eq}, which implies {eq}dx = 4sec^2 u,du {/eq}. This gives us: {eq}int{dfrac{4sec^2 u,du}{sqrt{16tan^2 u + 16}}} {/eq} Since {eq}tan^2 u + 1 = sec^2 u {/eq}, the integral simplifies to: {eq}int{dfrac{4sec^2 u,du}{sqrt{16sec^2 u}}} {/eq} Dividing by the square root of 16, we get: {eq}int{dfrac{4sec^2 u,du}{4sec u}} = int{sec u,du} {/eq} The integral of {eq}sec u {/eq} is {eq}ln |sec u + tan u| + C {/eq}. So, {eq}int{sec u,du} = ln |sec u + tan u| {/eq} Substituting back {eq}tan u = frac{x}{4} {/eq}, we find: {eq}sec^2 u = 1 + tan^2 u = 1 + frac{x^2}{16} {/eq} Hence, the integral becomes: {eq}ln left| frac{sqrt{16 + x^2}}{4} + frac{x}{4} right| + C {/eq} Therefore, the solution to the integral is: {eq}int{dfrac{dx}{sqrt{x^{2} + 16}}} = ln left| frac{sqrt{16 + x^2}}{4} + frac{x}{4} right| + C {/eq}

answer:The plasma membrane, often referred to as the fluid-mosaic model, exhibits its fluidity due to the presence of cholesterol, which prevents the fatty acid chains from solidifying. The "mosaic" aspect of the model is a result of the varied and mobile proteins that are integrated into the lipid bilayer, giving the membrane a diverse and dynamic structure. The smallest components of the cytoskeleton are the microfilaments. These are composed of actin and play essential roles in maintaining cell shape, facilitating cell movement, and enabling intracellular transport.

answer:Oversampling an input signal with an ADC that has a bandwidth beyond the Nyquist rate can provide several advantages. 1. Increased Resolution: By sampling at a higher rate, the quantization noise is spread out, effectively increasing the resolution of the digitized signal. This can lead to a more accurate representation of the signal's details. 2. Improved Timing Precision: For pulsed signals, oversampling can enhance the precision in measuring timing parameters, such as rise/fall times and the intervals between pulses. The increased sampling rate allows for a finer granularity in time measurements, which can be crucial for applications requiring precise temporal information. 3. Digital Filtering Flexibility: Oversampled data enables more flexibility in digital filtering, as you can apply various techniques to remove unwanted frequencies and enhance the desired components of the signal without introducing significant distortion. In summary, using an ADC with a bandwidth in excess of the filter bandwidth for a pulsed input signal can lead to higher resolution, improved timing precision, and more flexibility in digital signal processing.