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2 years ago

4x - 3y = 12 4x - 5y = -4 Solve using Elimination

Mathematics

2 answers:

mr_godi [17]2 years ago

8 0

Answer:

${ \rm{4x - 3y = 12 - - - \{eqn(a) \}}} \\ { \rm{4x - 5y = - 4 - - - \{eqn(b) \}}}$

• subtract eqn(b) from eqn(a);

${ \underline{ \rm{ - \binom{4x - 3y = 12}{4x - 5y = - 4} }}} \\ { \rm{0x + 2y = 16}} \\ \\ { \rm{2y = 16}} \\ \\ { \boxed{ \tt{ \: \: y = 8 \: \: }}} \\$

• find x :

${ \rm{4x - 3y = 12}} \\ { \rm{4x - 3(8) = 12}} \\ { \rm{4x = 36}} \\ \\ { \boxed{ \tt{ \: \: x = 9 \: \: }}}$

olga_2 [115]2 years ago

3 0

I think the answers is

Y=8
X=9

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eimsori [14]

Answer:

$64

Step-by-step explanation:

Since there were 4 of them and the coupons were $10 off, they saved a total of $40

To find how much they would have spent without the coupons, add 40 to 216:

216 + 40

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To find the normal cost of one ticket, divide this by 4:

256/4

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So, the price of one concert ticket without the coupon is $64

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3 years ago

A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

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