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question:Multiply and expand the polynomials p(x) = -11 x^2-6 x+1 and q(x) = 7 x^2-6 x-3.
answer:To multiply and expand the polynomials, we can use the FOIL method (First, Outer, Inner, Last). First, we multiply the first terms of each polynomial: (-11 x^2) cdot (7 x^2) = -77 x^4 Next, we multiply the outer terms of each polynomial: (-11 x^2) cdot (-6 x) = 66 x^3 Then, we multiply the inner terms of each polynomial: (-6 x) cdot (7 x^2) = -42 x^3 Finally, we multiply the last terms of each polynomial: (1) cdot (-3) = -3 Now, we add up the like terms: -77 x^4 + (66 x^3 - 42 x^3) + 76 x^2 + 12 x - 3 Simplifying, we get: -77 x^4 + 24 x^3 + 76 x^2 + 12 x - 3 Therefore, the product of p(x) and q(x) is -77 x^4+24 x^3+76 x^2+12 x-3. The answer is -77 x^4+24 x^3+76 x^2+12 x-3
question:Multiply and expand the following polynomials: p(x) = -frac{8x^2}{pi} - frac{13x}{pi} - frac{46}{pi} and q(x) = -frac{31x^2}{pi} - frac{31x}{pi} - frac{11}{pi}.
answer:To multiply the two polynomials, we'll use the distributive property twice: p(x)q(x) = left(-frac{8x^2}{pi} - frac{13x}{pi} - frac{46}{pi}right)left(-frac{31x^2}{pi} - frac{31x}{pi} - frac{11}{pi}right) Now, distribute each term of the first polynomial with each term of the second polynomial: =left(-frac{8x^2}{pi}right)left(-frac{31x^2}{pi}right) + left(-frac{8x^2}{pi}right)left(-frac{31x}{pi}right) + left(-frac{8x^2}{pi}right)left(-frac{11}{pi}right) + left(-frac{13x}{pi}right)left(-frac{31x^2}{pi}right) + left(-frac{13x}{pi}right)left(-frac{31x}{pi}right) + left(-frac{13x}{pi}right)left(-frac{11}{pi}right) + left(-frac{46}{pi}right)left(-frac{31x^2}{pi}right) + left(-frac{46}{pi}right)left(-frac{31x}{pi}right) + left(-frac{46}{pi}right)left(-frac{11}{pi}right) After simplifying each product, we get: =frac{248x^4}{pi^2} + frac{248x^3}{pi^2} + frac{408x^3}{pi^2} + frac{403x^2}{pi^2} + frac{403x^2}{pi^2} + frac{143x^2}{pi^2} + frac{1506x}{pi^2} + frac{1506x}{pi^2} + frac{506}{pi^2} Combining like terms, we obtain the final expanded form: =frac{248x^4}{pi^2} + left(frac{248}{pi^2} + frac{408}{pi^2}right)x^3 + left(frac{403}{pi^2} + frac{403}{pi^2} + frac{143}{pi^2}right)x^2 + left(frac{1506}{pi^2} + frac{1506}{pi^2}right)x + frac{506}{pi^2} Simplifying further: =frac{248x^4}{pi^2} + frac{651x^3}{pi^2} + frac{1917x^2}{pi^2} + frac{3012x}{pi^2} + frac{506}{pi^2} The coefficient of x is incorrect in the provided answer. The correct coefficient should be frac{3012}{pi^2}, not frac{1569}{pi^2}.
question:How do you convert 201 grams to milligrams?
answer:To convert grams to milligrams, we need to multiply the given value in grams by 1000, since there are 1000 milligrams in 1 gram. Therefore, to convert 201 grams to milligrams, we can use the following formula: 201 grams * 1000 milligrams/gram = 201000 milligrams So, 201 grams is equal to 201000 milligrams.
question:Identify the part of the neuron responsible for transmitting signals to other cells and describe its function.
answer:The axon is responsible for transmitting signals to other cells. It is a long process that carries electrical impulses away from the cell body, releasing neurotransmitters at its terminals to communicate with other neurons or target organs.