answer:The functions and their derivatives are: 1. {eq}f(u) = tan(u) {/eq} 2. {eq}f'(u) = sec^2(u) {/eq} 3. {eq}g(x) = x^6 {/eq} 4. {eq}g'(x) = 6x^5 {/eq} Now, let's calculate the requested expressions: 1. Composition {eq}f(g(x)) {/eq}: {eq}f(g(x)) = f(x^6) = tan(x^6) {/eq} 2. Derivative of {eq}f(u) {/eq} with respect to {eq}u {/eq}: {eq}f'(u) = sec^2(u) {/eq} 3. Derivative of {eq}g(x) {/eq} with respect to {eq}x {/eq}: {eq}g'(x) = 6x^5 {/eq} 4. Derivative of the composite function {eq}(f circ g)(x) {/eq} with respect to {eq}x {/eq}: {eq}begin{align*} (f circ g)'(x) &= frac{mathrm{d}}{mathrm{d}x}[tan(x^6)] &= sec^2(x^6) cdot frac{mathrm{d}}{mathrm{d}x}(x^6) &= sec^2(x^6) cdot 6x^5 &= boxed{6x^5 sec^2(x^6)} end{align*} {/eq}

answer:56.25

answer:To find the difference x - y, substitute the given values for x and y: x - y = 6isqrt{2} - left(-frac{9 + 13i}{sqrt{2}}right) Now, distribute the negative sign inside the parenthesis: x - y = 6isqrt{2} + frac{9 + 13i}{sqrt{2}} To combine the terms, we need a common denominator, which is sqrt{2}: x - y = frac{6isqrt{2} cdot sqrt{2}}{sqrt{2}} + frac{9 + 13i}{sqrt{2}} Simplify the expression: x - y = frac{12i + 9sqrt{2} + 13i}{sqrt{2}} Combine like terms: x - y = frac{(12i + 13i) + 9sqrt{2}}{sqrt{2}} x - y = frac{25i + 9sqrt{2}}{sqrt{2}} This is the simplified form of x - y. To write it in the form of a complex number, we can separate the real and imaginary parts: x - y = 9sqrt{2} + frac{25i}{sqrt{2}} To rationalize the denominator, multiply both the numerator and the denominator by sqrt{2}: x - y = 9sqrt{2} + frac{25i cdot sqrt{2}}{sqrt{2} cdot sqrt{2}} x - y = 9sqrt{2} + frac{25isqrt{2}}{2} This is the final, simplified form of x - y.

answer:The binomial coefficient binom{n}{k} represents the number of ways to choose k elements from a set of n distinct elements, without regard to the order of selection. In this case, we have n = 11125 and k = 11124. Using the formula for the binomial coefficient, we have: binom{11125}{11124} = frac{11125!}{11124! cdot 1!} Simplifying the expression, we can cancel out the common factor of 11124! in the numerator and denominator: binom{11125}{11124} = frac{11125!}{11124! cdot 1!} = frac{11125 cdot 11124!}{11124! cdot 1!} = 11125 Therefore, the binomial coefficient binom{11125}{11124} is equal to 11125. The answer is 11125