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3 years ago

Solve the following system of equations using the substitution method 5x+3y=1 X+2y=3

Mathematics

2 answers:

DedPeter [7]3 years ago

4 0

Answer:

(x, y) = (-1, 2)

Step-by-step explanation:

Substitution is easier if you already have an expression for the variable you want to make a substitution for. Here, we don't have that, but we have an equation with x having a coefficient of 1. We can use that to write an expression for x:

x = 3 -2y . . . . . subtract 2y from both sides of the second equation

5(3 -2y) +3y = 1 . . . . substitute for x in the first equation

15 -10y +3y = 1 . . . . . eliminate parentheses

-7y = -14 . . . . . . . . . . subtract 15, collect terms

y = 2 . . . . . . . . . . . . . divide by -7

Use this value in the equation for x:

x = 3 -2(2) = -1

The solution is (x, y) = (-1, 2).

max2010maxim [7]3 years ago

3 0

Answer:

x= -1

y= 2

Step-by-step explanation:

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We have that the equation of the volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

We have that the radius of a sphere is half the diameter of it:

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r = 6cm/2 = 3cm

<h2>Finding the volume of a sphere</h2>

We replace r by 3 in the equation:

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot3^3 \end{gathered}$

Since 3³ = 3 · 3 · 3 = 27

$\begin{gathered} V=\frac{4}{3}\pi3^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot27 \end{gathered}$

If we use π = 3.14:

$\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=\frac{4}{3}\cdot3.14\cdot27 \\ \downarrow \\ V=4.18\bar{6}\cdot27 \end{gathered}$

Rounding the first factor to the nearest hundredth (two digits after the decimal), we have:

4.18666... ≅ 4.19

Then, we have that:

$\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=4.19\cdot27 \\ =113.13 \end{gathered}$

Then, we have that:

<h2>Finding the volume of a cone</h2>

We have that the volume of a cone is given by:

$V=\frac{1}{3}\pi r^2h$

where r is the radius of its base and h is the height:

Then, in this case

r = 3

h = 6

and

π = 3.14

Replacing in the equation for the volume:

$\begin{gathered} V=\frac{1}{3}\pi r^2h \\ \downarrow \\ V=\frac{1}{3}\cdot3.14\cdot3^2\cdot6 \end{gathered}$

Then, we have:

3² = 9

$\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot3^2\cdot6 \\ \downarrow \\ V=\frac{1}{3}\cdot3.14\cdot9\cdot6 \\ V=\frac{1}{3}\cdot3.14\cdot54 \\ V=56.52 \\ \end{gathered}$

Answer: the volume of the cone that has the same circular base and height is 56.52 cm³

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1 year ago