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Concept explainers
SALES TAX In a certain state, the sales tax
a. Express
b. Find
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Chapter 1 Solutions
EBK FINITE MATHEMATICS FOR THE MANAGERI
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- 4. Prove: If x {0, 1} then x² - -x=0. 5. 6. Prove by contrapositive: Suppose x is a real number. If x>0 then x + 16 0. Prove by contradiction: Suppose n is an integer. Then n² - n+10. Hint: You might try organizing the proof by cases on whether n is even or odd. Is n² - n+1 even or odd?arrow_forwardLet f(x)=7x²-2x and g(x) = 5x+3. Find f[g(k)].arrow_forwardUse the method of reduction of order to find a second solution to ty"-(4t+4)+(4t+8)y = 0, t> 0 Given y₁(t) = e²t Y2(t) = Give your answer in simplest form (ie no coefficients)arrow_forward
- 1. Suppose the domain of discourse is kinds of minerals. Let A be kinds of minerals that dissolve in acid, let S be minerals that can be scratched by an iron nail, and let C be minerals that are clear. Write expressions using set operations that represent the following sets of minerals: (a) Minerals that dissolve in acid and can be scratched by an iron nail. (b) Minerals that dissolve in acid and are not clear. (c) Minerals that are either clear or both dissolve in acid but cannot be scratched by an iron nail. (d) Minerals that are neither dissolvable in acid nor scratable by an iron nail. (e) Minerals that are either both dissolvable in acid and scratchable by an iron nail or both dissolvable in acid and not clear.arrow_forwardExpress the integrand as a sum of partial fractions and evaluate the integral. 2 32s+ 32 (s²+1) (s-1)3 ds Express the integrand as a sum of partial fractions. (Simplify your answer.)arrow_forwardSolve the problemarrow_forward
- Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. 30x³-60x²+8 dx 2 x-2x After performing the long division, write the resulting proper fraction as a sum of partial fractions. Evaluate the integral. 30x³-60x²+8 2 x² -2x dx=arrow_forwardEvaluate the following integral. x/6 S tan 2x dx x/12arrow_forwardEvaluate the integral by using a substitution prior to integration by parts. 7) sin (In (6x)) dxarrow_forward
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