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xeze [42]
3 years ago
13

There exist infinitely many common fractions $\frac{a}{b}$ , where $a > 0$ and $b > 0$ and for which $\frac{3}{5} < \fr

ac{a}{b} < \frac{2}{3}$ . Of these common fractions, which has the smallest denominator? Express your answer as a common fraction.

Mathematics
1 answer:
vredina [299]3 years ago
3 0

Answer:

3/5 has the smallest denominator

Step-by-step explanation:

Question:

There exist infinitely many common fractions a/b , where a > 0 and b > 0 and for which 3/5 < a/b< 2/3. Of these common fractions, which has the smallest denominator? Express your answer as a common fraction.

Solution

A Common fraction is a rational number written in the form: a/b. Where a and b are both integers.

The denominator and numerator in this case are greater than zero. That is, they are non zeros.

The least common denominator (LCD) of two non- zero denominators is the smallest whole number that is divisible by each of the denominators.

To find the smallest denominator between 3/5 and 2/3, we would convert the fractions to equivalent fractions with a common denominator by finding their LCM (lowest common multiple).

When comparing two fractions with like denominators, the larger fraction is the one with the greater numerator and the smaller fraction is one with the smaller numerator.

In our solution after comparing, the smaller fraction would have the smallest denominator.

Find attached the solution.

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A free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. The goalie is standing on
JulsSmile [24]

How far is the kicker from the right post, to the nearest yard is: 23 yards.

<h3>Distance</h3>

Using sine theorem

Let y represent the numbers of yards

Left triangle=3/sinx=14/sin∝

Right triangle=5/sinx=y/sin(180-∝°)

sin∝°=sin(180-∝°)

Hence,

3/5=14/y

y=5×14/3

y=23 yards

Therefore how far is the kicker from the right post, to the nearest yard is: 23 yards.

Learn more about distance here:brainly.com/question/23848540

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4 0
1 year ago
PLEASE HELP ASAP!!!!!!!!!!!!!!
stiks02 [169]
B I hope it helps ;)
6 0
3 years ago
Ok so I just need to match the letter with the definition but I don’t get it help please!
mr Goodwill [35]

Answer:

m = slope  

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8 0
3 years ago
Find the difference between the actual and estimated value of 55-21​
Airida [17]

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5 0
3 years ago
A sheet of paper 90 cm-by-66 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and f
NNADVOKAT [17]

Answer:

26 - \sqrt{181} cm

Step-by-step explanation:

The volume of the box is:

V = height * length * width

V = x*(66 - 2*x)*(90 - 2*x)

V = (66*x - 2*x^2)*(90 - 2*x)

V = 5940*x - 132*x^2 - 180*x^2 + 4*x^3

V = 4*x^3 - 312*x^2 + 5940*x

where x is the length of the sides of the squares,  in cm.

The mathematical problem is :

Maximize: V = 4*x^3 - 312*x^2 + 5940*x

subject to:

x > 0

2*x < 66 <=> x < 33

In the maximum, the first derivative of V, dV/dx, is equal to zero

dV/dx = 12*x^2 - 624*x + 5940

From quadratic formula

x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}

x = \frac{624 \pm \sqrt{(-624)^2 - 4(12)(5940)}}{2(12)}

x = \frac{624 \pm \sqrt{104256}}{24}

x = \frac{624 \pm \sqrt{2^6*3^2*181}}{24}

x = \frac{624 \pm 8*3*\sqrt{181}}{24}

x_1 = \frac{624 + 24*\sqrt{181}}{24}

x_1 = 26 + \sqrt{181}

x_2 = \frac{624 - 24*\sqrt{181}}{24}

x_2 = 26 - \sqrt{181}

But x_1 > 33, then is not the correct answer.

5 0
2 years ago
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