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MrRa [10]
3 years ago
7

Subtract 3a^2+5ab−4b^2 from 8a^2−6ab+4b^2

Mathematics
1 answer:
liberstina [14]3 years ago
3 0

Answer:

\large\boxed{(8a^2-6ab+4b^2)-(3a^2+5ab-4b^2)=5a^2-11ab+8b^2}

Step-by-step explanation:

(8a^2-6ab+4b^2)-(3a^2+5ab-4b^2)\\\\=8a^2-6ab+4b^2-3a^2-5ab-(-4b^2)\\\\=8a^2-6ab+4b^2-3a^2-5ab+4b^2\qquad\text{combine like terms}\\\\=(8a^2-3a^2)+(-6ab-5ab)+(4b^2+4b^2)\\\\=5a^2-11ab+8b^2

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Compute the line integral with respect to arc length of the function f(x, y, z) = xy2 along the parametrized curve that is the l
SIZIF [17.4K]

Answer:

\displaystyle\frac{15\sqrt{3}}{4}-90\sqrt{146}

Step-by-step explanation:

The line integral with respect to arc length of the function f(x, y, z) = xy2 along the parametrized curve that is the line segment from (1, 1, 1) to (2, 2, 2) followed by the line segment from (2, 2, 2) to (−9, 6, 5) equals the sum of the line integral of f along each path separately.

Let  

C_1,C_2  

be the two paths.

Recall that if we parametrize a path C as (r_1(t),r_2(t),r_3(t)) with the parameter t varying on some interval [a,b], then the line integral with respect to arc length of a function f is

\displaystyle\int_{C}f(x,y,z)ds=\displaystyle\int_{a}^{b}f(r_1,r_2,r_3)\sqrt{(r'_1)^2+(r'_2)^2+(r'_3)^2}dt

Given any two points P, Q we can parametrize the line segment from P to Q as

r(t) = tQ + (1-t)P with 0≤ t≤ 1

The parametrization of the line segment from (1,1,1) to (2,2,2) is

r(t) = t(2,2,2) + (1-t)(1,1,1) = (1+t, 1+t, 1+t)

r'(t) = (1,1,1)

and  

\displaystyle\int_{C_1}f(x,y,z)ds=\displaystyle\int_{0}^{1}f(1+t,1+t,1+t)\sqrt{3}dt=\\\\=\sqrt{3}\displaystyle\int_{0}^{1}(1+t)(1+t)^2dt=\sqrt{3}\displaystyle\int_{0}^{1}(1+t)^3dt=\displaystyle\frac{15\sqrt{3}}{4}

The parametrization of the line segment from (2,2,2) to  

(-9,6,5) is

r(t) = t(-9,6,5) + (1-t)(2,2,2) = (2-11t, 2+4t, 2+3t)  

r'(t) = (-11,4,3)

and  

\displaystyle\int_{C_2}f(x,y,z)ds=\displaystyle\int_{0}^{1}f(2-11t,2+4t,2+3t)\sqrt{146}dt=\\\\=\sqrt{146}\displaystyle\int_{0}^{1}(2-11t)(2+4t)^2dt=-90\sqrt{146}

Hence

\displaystyle\int_{C}f(x,y,z)ds=\displaystyle\int_{C_1}f(x,y,z)ds+\displaystyle\int_{C_2}f(x,y,z)ds=\\\\=\boxed{\displaystyle\frac{15\sqrt{3}}{4}-90\sqrt{146}}

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Answer:

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Ok. 50 soda bottles are made in 2 minutes. We need to know how many could be made in 1. Dividing 2 by 2 gives us one minute. So if we divide 50 by 2, keeping the ratio the same, gives us 25. Thus, 25 bottles can be made in 1 minute. Hope that helps!!!
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<h3>What is a percentage?</h3>

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = \frac{a}{b} \times 100\%

In this problem, we suppose that 520 out of 1000 respondents believe in global warming, hence a = 520, b = 1000, and the percentage is of:

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More can be learned about the percentage concept at brainly.com/question/10491646

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