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2 years ago

Answer this equation -3(5g+1)+8g=

Mathematics

2 answers:

maksim [4K]2 years ago

6 0

Answer:

-7g - 3

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Combining like terms

Step-by-step explanation:

Step 1: Define expression

-3(5g + 1) + 8g

Step 2: Simplify

Distribute -3: -15g - 3 + 8g
Combine like terms: -7g - 3

Sauron [17]2 years ago

5 0

Answer:

-7g - 3

Step-by-step explanation:

First, do distributive property. -3(5g+1)+8g= -15g-3+8g

Now combine like terms. (-15g + 8g) -3 =

-7g - 3 This is the answer since you can't combine a coefficient with a number without a variable.

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Step-by-step explanation:

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Suppose that \nabla f(x,y,z) = 2xyze^{x^2}\mathbf{i} + ze^{x^2}\mathbf{j} + ye^{x^2}\mathbf{k}. if f(0,0,0) = 2, find f(1,1,1).

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The simplest path from (0, 0, 0) to (1, 1, 1) is a straight line, denoted $C$ , which we can parameterize by the vector-valued function,

$\mathbf r(t)=(1-t)(\mathbf i+\mathbf j+\mathbf k)$

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Then with $x(t)=y(t)=z(t)=1-t$ , we have

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Complete the square in the quadratic term of the integrand: $t^2-2t+2=(t-1)^2+1=(1-t)^2+1$ , then in the integral we substitute $u=1-t$ :

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Make another substitution of $v=u^2$ :

$\displaystyle=-\int_{v=0}^{v=1}e^v(v+1)\,\mathrm dv$

Integrate by parts, taking

$r=v+1\implies\mathrm dr=\mathrm dv$

$\mathrm ds=e^v\,\mathrm dv\implies s=e^v$

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So, we have by the fundamental theorem of calculus that

$\displaystyle\int_C\nabla f(x,y,z)\cdot\mathrm d\mathbf r=f(1,1,1)-f(0,0,0)$

$\implies-e=f(1,1,1)-2$

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