Need help on both these questions please thank you

Mathematics

1 answer:

Elena L [17]3 years ago

8 0

Remember that the volume of a cone is $1/3 \pi r^2h$
Thus;

1. 2^2 = 4
4pi(7) = 28pi
28/3 = $9 \frac{1}{3}$
ANS = $9 \frac{1}{3} \pi$ or ~29.32

2. d = 18, r = 9
9 ^ 2 = 81
81pi (18) = 1458pi
1458 / 3 = 486
ANS = $486 \pi$ or ~1526.81

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Explain why x and 4x - 10 are factors of the expression x(4x - 10)3 rather than terms of the expression. What are the terms of t

andriy [413]

Solution :- Let p(x) be the polynomial such that

$p(x) = x(4x-10)^3\\\text{and let f(x) be another polynomial such that }\\f(x)=4x-10\\\text{To find , Put } f(x)=0\\\Rightarrow4x-10=0\\\Rightarrow4x=10\\\Rightarrow x=5/2\\\text{Now substituting value of x in p(x),we get}\\p(x)=\frac{5}{2} .(4(5/2)-10)^3\\\Rightarrow\frac{5}{2}.(10-10)^3=0\\\text{Similarly let g(x)=x ,we get x=0 by putting g(x)=0}\\\text{now f(x)=0 for x=0}\\\text{So by Factor theorem f(x) and g(x) are the factors of polynomial p(x)}\\$

$\text{Now} p(x) = x(4x-10)^3\\=64x^4-480x^3+1200x^2-1000x\\\text{so the terms of terms of } p(x) \text{are} 64x^4,-480x^3,1200x^2,-1000x\\\text{here, by using Factor theorem x is a factor of all the terms but 4x-10 is not. }$