answer:Yes, triglycerides are a type of fat. They are compounds formed by glycerol combined with three fatty acid molecules. In the context of nutrition, fats often encompass both triglycerides and other lipid forms like mono- and diglycerides. While the term "fat" is commonly used in everyday language, in a scientific context, fats are a part of the broader lipid category, which also includes sterols, waxes, lipid-soluble vitamins, and steroid hormones. In cooking, fats can be solid (like butter) or liquid (like oil), and both typically consist of triglycerides. When discussing health, we may refer to dietary fats and blood lipids, which include triglycerides as a significant component.

answer:Given: int dfrac{1}{sqrt{4x^2 - 16x + 16}} dx Solution: Let us first simplify the given internal by converting the expressions into whole square form. begin{align} int dfrac{1}{sqrt{4x^2 - 16x + 16}} dx &= int dfrac{1}{sqrt{4(x^2 - 4x + 4)}} dx [0.3cm] &= int dfrac{1}{sqrt{4(x-2)^2}} dx [0.3cm] &= int dfrac{1}{2(x-2)} dx [0.3cm] end{align} Now, we can use the substitution method: begin{align} u &= x-2 [0.3cm] du &= dx end{align} Applying these substitutions, we get: begin{align} int dfrac{1}{2(x-2)} dx &= int dfrac{1}{2u} du [0.3cm] &= dfrac{1}{2} ln |u| + C [0.3cm] &= dfrac{1}{2} ln |x-2| + C end{align} Therefore, boldsymbol{int dfrac{1}{sqrt{4x^2 - 16x + 16}} dx = dfrac{1}{2} ln |x-2| + C}

answer:Journal entries based on the bank reconciliation are crucial for adjusting the company's records to align with the bank statement. These entries are needed for: a. Additions to the cash balance as per the company's records: This includes unrecorded deposits, interest earned, or any understatements of the cash balance due to errors in the company's books. Journal entries are made to credit cash and debit the respective revenue or other appropriate accounts. b. Deductions from the cash balance as per the company's records: This involves unrecorded checks, bank fees, service charges, or any overstatements of the cash balance in the company's records. In such cases, journal entries are prepared to debit cash and credit the corresponding expense or other relevant accounts. The bank reconciliation process ensures the accuracy and completeness of the company's financial statements by identifying and reconciling discrepancies between the company's records and the bank's records. Thus, both types of journal entries (a and b) are essential.

answer:To differentiate the given function, we will apply the following differentiation rules: 1. Sum rule: {eq}displaystyle frac{d}{dx}(u pm v) = frac{du}{dx} pm frac{dv}{dx} {/eq} 2. Derivative of a constant multiplier: {eq}displaystyle frac{d}{dx}(c cdot f(x)) = c cdot frac{df}{dx} {/eq} 3. Product rule: {eq}displaystyle frac{d}{dx}(u v) = u frac{dv}{dx} + v frac{du}{dx} {/eq} 4. Power rule: {eq}displaystyle frac{d}{dx}(a t^n) = a n t^{n-1} {/eq} Let's differentiate: {eq}begin{align*} frac{dy}{dt} &= frac{d}{dt}(ccos t + t^2sin t) &= c cdot frac{d}{dt}(cos t) + (t^2) cdot frac{d}{dt}(sin t) + (sin t) cdot frac{d}{dt}(t^2) &= c cdot (-sin t) + t^2 cdot cos t + 2t cdot sin t &= mathbf{-csin t + t^2cos t + 2tsin t} end{align*} {/eq} The derivative of the function {eq}y = ccos t + t^2sin t {/eq} with respect to {eq}t {/eq} is {eq}-csin t + t^2cos t + 2tsin t {/eq}.