Let 01(x) = * 0(t) dt, for x > 1, where 0 is Chebyshev's function. Let A1(n) = log n if n is prime, and A₁(n) = 0 otherwise. Prove that 01(x) = (x − n) A1(n), n
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- The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.Suppose that Find f¹(3). ƒ¹ (3) = f(x) = 4e-4² ln(x).Suppose that |?′(30)|=1.8|f′(30)|=1.8 and ?(30)=52f(30)=52. Fill in the blanks (including units where needed) and select the appropriate terms to complete the following statement about the temperature of the coffee in this case. At minutes(30) after the coffee was put on the counter, its(temp) is(52degC) and will (decrease) by(unknown) about in the next 60 seconds. (rest of answers correct).
- Please explain how to slove the questiona. Given f(x) = x² − 3 and g(x) = √x + 3. Find (f o g) (x) and write the · domain of (fog) (x) in interval form. b. Solve: log5x +log(x-1)=2 c. Solve: 25x-1 = 1254x d. Solve the inequality -4x(2 − x)²(x + 5) < 0Consider the function f(x)=x2+6(5x−10)(x+4)f(x)=x2+6(5x-10)(x+4). For each prompt below, if no solution exists - enter "DNE". If there is more than one solution, enter your answer as a comma-separated list (like "1, 3"). You may find it helpful to rewrite the numerator or denominator in a different form to help you complete some of the parts. Determine the vertical intercept of ff. f(0)=f(0)= Determine the zeros (or "roots") of ff. x=x= Determine the vertical asymptote(s) of ff. x=x= Determine the horizontal asymptote of ff. y=y=
- If the half life of a radioactive substance is 14 days and there are 6.6 grams present initially, when will there be 1 gram remaining? [?] days Use the function f(t) = Pert and round your answer to the nearest day. yright © 2003-2023 International Academy of Science. All Rights Reserved. Accessibility: investigate Q Search 5 J O & EX3 I' RTYU DELL 7 8 F9 F10 Enter A FocThe population (in millions) of a country as a function of time t (years) is P(t) = 30 · 20.1t . Show that the population doubles every 10 years. Show more generally that for any positive constants a and k, the function g(t) = a2kt doubles after 1/k years.If a function h satisfies h(-x) = h(x) for every number x in its domain, then h is called an even function. If h satisfies h(-x) = -h(x) for every number x in its domain, then h is called an odd function. Suppose that sh(x) dx = Answer the following: −1 and ſ³ h(x)dx = 2 -3 A. Suppose that h is an even function. Evaluate ſ³, h(x)dx. B. Suppose that h is an odd function. Evaluate ſ³, h(x)dx. C. Evaluate (2h(x) + 1)dx. D. Evaluate fh(x + 1)dx.
