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3 years ago

Find the area and perimeter of a rectangle with a length of 3x + 2 and a width of 4x + 3.

Mathematics

2 answers:

vovikov84 [41]3 years ago

7 0

Answer:

Perimeter =14x+10

Area = = $12x^{2}$ +17x+6

Step-by-step explanation:

Area of a rectangle=Length *width

=(3x+2)(4x+3)

=3x(4x+3)+2(4x+3)

= $12x^{2}$ +9x+8x+6

= $12x^{2}$ +17x+6

Then find x using quadratic equation and substitute the values

Perimeter of a rectangle =2(length +width)

=2(3x+2+4x+3)

=6x+4+8x+6

=14x+10

Hope you got it

If you have any problem just ask me

bekas [8.4K]3 years ago

4 0

Answer:

170ft^2

The area is 170ft^2.

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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.

6 0

3 years ago

The function f(x)=125(0.9)x models the population of a species of fly in millions after x years.

SSSSS [86.1K]

A word to the wise: It's f(x)=125(0.9)^x, where ^ represents exponentiation.

In this case the ave. value over the interval [11, 15] is

125(0.9)^15 - 125(0.9)^11
------------------------------------- = (125/4) [ 0.9^15 - 0.9^11)
15 - 11 = (31.25) [ 0.2059 - 0.3138 ] = a negative result
= (31.25)(-0.1079) = -3.372 (av. r. of c.
over the interval [11,15] )

Do the same thing for the time interval [1,5]. Then compare the two rates of change.

6 0

3 years ago

Read 2 more answers

Please help me find BD

Tanzania [10]

9514 1404 393

Answer:

14 units

Step-by-step explanation:

The angle bisector divides the sides proportionally, so you have ...

(x+4)/8 = (2x+1)/12

3(x +4) = 2(2x +1) . . . . . . multiply by 24

3x +12 = 4x +2 . . . . . . . . eliminate parentheses

10 = x . . . . . . . . . . . subtract (3x+2)

Then BD = x+4 = 10 +4.

The length of BD is 14 units.

_____

Additional comment

The "triangle" cannot exist, as the side lengths are shown as 8, 12, and 35. The long side is too long. Nice math; bad geometry.

8 0

3 years ago

If a 36-foot tree casts a 28-foot shadow at the same time near by building casts a 70-foot shadow, how tall is the building?

Arada [10]

Actual length / shadow ratio is equal
Let the height of the building be x, then
36/28 = x/70
x = (36 x 70)/28 = 2,520/28 = 90.

Therefore, the height of the building is 90 feet.

7 0

3 years ago

Read 2 more answers

Is 2/5 equal to 0.4 please help me

igor_vitrenko [27]

1/5 is 2% or 0.2, therefor 2/5 is 4% or 0.4

8 0

3 years ago