Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Un sfert din lungimea unui dreptunghi este cu 18 mai mare decât o treime din lățimea metrul dreptunghiului este 228 , află lungimea și lățimea dreptunghiului.

alpha
Un teren are forma unui pătrat cu latura de
172m. Pentru
5m de gard necesari împrejr cesc 90 de scânduri. Câte scânduri sunt necesare pentru tot terenul?

Un sfert din lungimea unui dreptunghi este cu $18$ mai mare decât o treime din lățimea metrul dreptunghiului este $228$ , află lungimea și lățimea dreptunghiului. $\newline$ $\alpha$ $\newline$ Un teren are forma unui pătrat cu latura de $172 \mathrm{~m}$ . Pentru $5 \mathrm{~m}$ de gard necesari împrejr cesc $90$ de scânduri. Câte scânduri sunt necesare pentru tot terenul?

View step-by-step help

View step-by-step help

Convergent and divergent geometric series

Full solution

Q. Un sfert din lungimea unui dreptunghi este cu

18

mai mare decât o treime din lățimea metrul dreptunghiului este

228

, află lungimea și lățimea dreptunghiului.

\newline

\alpha

\newline

Un teren are forma unui pătrat cu latura de

172 \mathrm{~m}

. Pentru

5 \mathrm{~m}

de gard necesari împrejr cesc

90

de scânduri. Câte scânduri sunt necesare pentru tot terenul?

Identify Relationship: Identify the relationship between the length and width of the rectangle. $\newline$ Let the length be $L$ and the width be $W$ . $\newline$ According to the problem, $\frac{1}{4}$ of the length is $18$ more than $\frac{1}{3}$ of the width: $\newline$ $\frac{1}{4} \times L = \frac{1}{3} \times W + 18$ .
Express L in Terms: Express $L$ in terms of $W$ . $\newline$ Multiply all terms by $12$ to clear the fractions: $\newline$ $3L = 4W + 216$ . $\newline$ Now, solve for $L$ : $\newline$ $L = \frac{4W + 216}{3}$ .
Use Perimeter Formula: Use the perimeter to find a relationship involving $W$ . The perimeter $P$ of a rectangle is given by $P = 2L + 2W$ . Substitute the expression for $L$ into the perimeter formula: $228 = 2((4W + 216) / 3) + 2W$ .
Simplify and Solve for W: Simplify and solve for W. $\newline$ Multiply through by $3$ to clear the denominator: $\newline$ $228 \times 3 = 2(4W + 216) + 6W$ , $\newline$ $684 = 8W + 432 + 6W$ , $\newline$ $684 = 14W + 432$ . $\newline$ Now, solve for W: $\newline$ $14W = 684 - 432$ , $\newline$ $14W = 252$ , $\newline$ $W = \frac{252}{14}$ , $\newline$ $W = 18$ .
Substitute $W$ into $L$ : Substitute $W$ back into the expression for $L$ . $L = \frac{(4 \times 18 + 216)}{3},$ $L = \frac{(72 + 216)}{3},$ $L = \frac{288}{3},$ $L = 96.$

More problems from Convergent and divergent geometric series

Question

Find the sum of the finite arithmetic series.

\sum_{n=1}^{10} (7n+4)

\newline

Posted 2 months ago

Question

Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`

Posted 1 month ago

Question

Type the missing number in this sequence: `2, 4 8`, ______,`32`

Posted 2 months ago

Question

What kind of sequence is this?

2, 10, 50, 250, \ldots

Choices:Choices:

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 2 months ago

Question

What is the missing number in this pattern?

1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_

Posted 1 month ago

Question

Classify the series.

\sum_{n = 0}^{12} (n + 2)^3

\newline

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 1 month ago

Question

Find the first three partial sums of the series.

\newline

1 + 6 + 11 + 16 + 21 + 26 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 1 month ago

Question

Find the third partial sum of the series.

\newline

3 + 9 + 15 + 21 + 27 + 33 + \cdots

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

S_3 =

Posted 1 month ago

Question

Find the first three partial sums of the series.

\newline

1 + 7 + 13 + 19 + 25 + 31 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 2 months ago

Question

Does the infinite geometric series converge or diverge?

\newline

1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots

\newline

\newline

\text{[A]converge}

\newline

\text{[B]diverge}

Posted 1 month ago