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Ymorist [56]
3 years ago
5

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 =<em>14x+10</em>

<em>Area         =</em>  =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

                                        =<em>14x+10</em>

<em>Hope you got it</em>

<em>If you have any problem just ask me</em>

bekas [8.4K]3 years ago
4 0

<em>Answer:</em>

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  <span> 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.</span>
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.

_____

<em>Additional comment</em>

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
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