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3 years ago

Solve the system. 4x+y=2 x-y=3

Mathematics

2 answers:

Anettt [7]3 years ago

6 0

Answer:

Step-by-step explanation:

$\underline{+\left\{\begin{array}{ccc}4x+y=2\\x-y=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad5x=5\qquad\text{divide both sides by 5}\\.\qquad\boxed{x=1}\\\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\4(1)+y=2\\4+y=2\qquad\text{subtract 4 from both sides}\\4-4+y=2-4\\\boxed{y=-2}$

torisob [31]3 years ago

3 0

Answer:

do i solve by substitution or addition/elimination? my answer will be in the comments after you've replied

Step-by-step explanation:

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3 years ago

The function f(x) varies inversely with x and f(x) =6 when x =4 what time s f(x) when x = 8

denpristay [2]

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$\bf \textit{we also know that } \begin{cases} \stackrel{f(x)}{y}=6\\ ~~ x=4 \end{cases}\implies 6=\cfrac{k}{4}\implies 24=k~\hfill \boxed{y=\cfrac{24}{x}} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad \qquad y=\cfrac{24}{8}\implies y=3$

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3 years ago

Integration of (3X(X^2+3)^4) dx<br><img src="https://tex.z-dn.net/?f=%20" id="TexFormula1" title=" " alt=" " align="absmiddle" c

dimaraw [331]

Answer:

Step-by-step explanation:

$\int 3x(x^2+3)^4 \ dx$ .

It is apparently obvious we could expand the bracket and integrate term-by-term. This method would work but is very time consuming (and you could easily make a mistake) so we use a different method: integration by substitution.

Integration by substitution involves swapping the variable $x$ for another variable which depends on x: $u(x)$ . (We are going to choose $u$ for this question).

The very first step is to choose a suitable substitution. That is, an equation $u=f(x)$ which is going to make the integration easier. There is a trick for spotting this however: if an integral contains both a term and it's derivative then use the substitution $u=\text{The Term}$ .

Your integral contains the term $x^2 + 3$ . The derivative is $2x$ and (ignoring the constants) we see $x$ is also in the integral and so the substitution $u=x^2+3$ will unravel this integral!

Step 2: We must now swap the variable of integration from x to u. That means interchanging all the x's in the integrand (the term being integrated) for u's and also swapping (dx" to "du").

$u=x^2+3 \Rightarrow \frac{du}{dx}=2x \Rightarrow dx = \frac{1}{2x} du$

Then,

$\int 3x(x^2+3)^4 \ dx = \int 3x \cdot u^4 \cdot \frac{1}{2x} du = \int \frac{3}{2}u^4\ du$ .

The substitution has made this integral is easy to solve!

$\int \frac{3}{2}u^4\ du= \frac{3}{10}u^5 + C$

Finally we can substitute back to get the answer in terms of x:

$\int 3x(x^2+3)^4 \ dx = \frac{3}{10}(x^2+3)^5+C$

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3 years ago

A 38-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third

KengaRu [80]

Let the length of the first piece be x inches. Then:-

x + 2x + 4x + 3 = 38

7x = 38 - 3

x = 35/7 = 5 inches

Answer: the 3 pieces have lengths 5, 10 and 23 inches.

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4 years ago