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2 years ago

A sum of money amounts to Rs 1380 in3 years and to Rs 1500 in 5 years.Find the rate of interest.

Mathematics

1 answer:

Stella [2.4K]2 years ago

6 0

Answer:98

Step-by-step explanation:

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Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3

nlexa [21]

Answer:

$(x,y) = (5,-6)$

Step-by-step explanation:

$\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\$

$~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)$

$\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\$

$\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5$

$y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6$

$\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)$

7 0

1 year ago

What term describes a polygon that has no "dents" in it?

svetoff [14.1K]

A convex polygon
Hope this helps :)

3 0

3 years ago

Lucy and Donavan measured the length of the school garden. Lucy's measurement is 11.3 meters and Donavan's measurement is 113 ce

Zolol [24]

Yes because of u convert 113 centimeters into inches you still get 11.3 but the garden could be a square I think this is right I don't know for sure

8 0

3 years ago

A television with a price of $300 is to be purchased with an initial payment of $60 and weekly

Sav [38]

Answer:

Equation which can be used to find the number of weekly payments w

is 300 = 60 + 3 w.

Step-by-step explanation:

Here, the selling price of the TV =$300

The initial TV payment = $60

Per week payment of TV = $30

The number of weeks, the payment is made = w

So, the amount paid for TV in w weeks = w x ( Payment in 1 week)

= w x ( $30) = 30 w

So, The total SP of TV = Initial Payment + Payment made in w weeks

⇒ 300 = 60 + 3w

Hence, equation which can be used to find the number of weekly

payments w is 300 = 60 + 3 w.

3 0

2 years ago

Peter filled 5 cups each with 1one-half pounds of candy. How much candy did the 5 cups contain altogether?

Natasha_Volkova [10]

Answer:

5 cups contain <u>7one-half pounds</u> of candy.

Step-by-step explanation:

Given:

Peter filled 5 cups each with 1one-half pounds of candy.

Now, to find the total candy 5 cups contain altogether.

1 cup of candy contain = $1\frac{1}{2} \ pounds$

So, to get candy 5 cup contain we multiply 5 by $1\frac{1}{2} \ pounds$ .

$5\times 1\frac{1}{2} \\=5\times \frac{3}{2} \\=\frac{15}{2} \\=7\frac{1}{2}$

Therefore, 5 cups contain 7one-half pounds of candy.

4 0

2 years ago