What are two contributions to math that Leonardo Fibonacci made

1 answer:

7 0

Fibonacci is famous for his contributions to number theory.

In his book, Liber abaci he introduce the Hindu-Arabic place-valued decimal systems and the use of Arabic Numerals into Europe.He introduced the bar we use in fractions, previous to this, the numerator has quotations around it. The square root notation is also is Fibonacci method.

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In the figure above, PQRS is a circle. If PQT and SRT<br>are straight lines, find the value of x.

Elena L [17]

Given:

PQRS is a circle, PQT and SRT are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

$m\angle SPQ+m\angle QRS=180^\circ$

$81^\circ+m\angle QRS=180^\circ$

$m\angle QRS=180^\circ-81^\circ$

$m\angle QRS=99^\circ$

Now, SRT is a straight line.

$m\angle QRT+m\angle QRS=180^\circ$ (Linear pair)

$m\angle QRT+99^\circ=180^\circ$

$m\angle QRT=180^\circ-99^\circ$

$m\angle QRT=81^\circ$ ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

$m\angle PQR=m\angle QRT+m\angle QTR$

$x=81^\circ+22^\circ$

$x=103^\circ$

Therefore, the value of x is 103 degrees.

4 0

3 years ago

A cup of raw Arborio rice weighs 7 ounces. One cup will serve 1 people. Arborio rice is purchased in 2-pound boxes for $1.99. Ho

kow [346]

The rice will cost $17.6 for serving 40 people

<h3><u>Solution:</u></h3>

We need to determine the cost of serving 40 people with rice

Arborio rice is purchased in 2-pound boxes for $1.99

The price of 1 pound box will be $\frac{\$ 1.99}{2}=\$ 0.995$

1 Pound (lb) is equal to 16 ounces (oz)

Therefore, the price of 16 ounces is $0.995

A cup of raw Arborio rice weighs 7 ounces and it serve 1 people

$\begin{array}{l}{\text { The cost per person is } \frac{\$ 0.995}{16} \times 7=\$ 0.44} \\\\ {\text { The cost for serving } 40 \text { people }=\$ 0.44 \times 40=\$ 17.6}\end{array}$