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3 years ago

What is the least common denominator of the four fractions listed below 20 7/10, 20 3/4, 18 9/10, 20 18/25

1 answer:

7 0

So what you do is see all the denomenators and factor them (denomenaotrs are the bottom numbres)

10,4,10,25
10=2 times 5
4=2 times 2
10=2 times 5
25=5 times 5
we need to include all of them so we need at leas two 2's, and two 5's
2 times 2 times 5 times 5=100
leact common denomator is 100

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I ALREADY ASKED THIS QUESTION BUT SINCE NO ONE ACTUALLY HELPED ME IM ASKING AGAIN BC I REALLY NEEDA TURN IT IN SO PLEASEEE HELP!

stich3 [128]

Answer:

A. 19.3ft B. 5.2ft

Step-by-step explanation:

So the ladder leaning against the wall forms a triangle. The hypotenuse of

triangle is the ladder (20) and the angle given between ladder an ground is 75 degrees. Use trig to find the height of the wall which is the leg of the triangle.

Sine of Angle is opposite side/hypotenuse

Cosine of Angle is adjacent side/hypotenuse

so Sine of 75 degrees = Wall height/20

Wall height = 20 times Sine of 75 degrees

Sine of 75 degrees = .9659

20 times (.9659) = 19.3ft

So now use Cosine to find the other leg of the triangle (the distance between the bottom of ladder to the wall)

Cosine of 75 degrees = Distance wall to base of ladder / 20

Cosine of 75 degrees = .2588

20 times (.2588) = 5.2ft

7 0

3 years ago

Please help to answer with working.

dusya [7]

Answer:

When r=0.2, m=0.016g

When m=0.25, r=0.5cm

When r=0.7, m=0.686g

When m=11.664, r=1.8cm

Step-by-step explanation:

General outline of steps for proportionality problems:

Identify the type or proportionality.
Find the proportionality constant using a known input/output pair.
Use the proportionality equation to find other unknowns.

<h3><u>Background on proportionality relationships</u></h3>

There are two main types of proportionality, "direct" and "inverse", and then there are modifications that can be made to them. Several examples are listed below:

<u>Direct proportionality examples</u>

y is directly proportional to x: $y=kx$
y is directly proportional to the square of x: $y=kx^2$
y is directly proportional to the cube of x: $y=kx^3$

<u>Inverse proportionality examples</u>

y is inversely proportional to x: $y=\dfrac{k}{x}$
y is inversely proportional to the square of x: $y=\dfrac{k}{x^2}$

In each case, irregardless of which type, the two quantities are related with some extra letter "k", called the proportionality constant. Either way, the proportionality constant "k" is always in the numerator, and the quantity is either multiplied to or divided from the proportionality constant "k".

Notice that for direct proportionality, in each case, the equation always ends up as "k times" the quantity.

On the other hand, notice that for inverse proportionality, in each case, the equation always ends up as "k divided by" the quantity.

<h3><u>Step 1. Identify the type or proportionality </u><u>(Setting up our proportionality equation)</u></h3>

The problem says "... the mass, <em>m</em> g, of a sphere is directly proportional to the cube of its radius, <em>r</em> cm...", so our equation will look like $m=kr^3$ .

<h3><u>Step 2. Finding the proportionality constant</u></h3>

To find the proportionality constant for our situation, one must know a full input/output pair. Notice that in the 4th column, $r=1.5$ and $m=6.75$ .

Substituting these values into our equation, we can find "k".

$(6.75)=k(1.5)^3$

$6.75=k*3.375$

$\dfrac{6.75}{3.375}= \dfrac{k*3.375}{3.375}$

$2=k$

So, the proportionality constant for this situation is 2, and our equation for this situation becomes: $m=2r^3$

<h3><u>Step 3. Finding the other inputs/outputs</u></h3>

Now that we know the proportionality constant for this situation, if we have either the input OR the output, we can solve for the other unknown.

$m=2r^3$

$m=2(0.2)^3$

$m=2(0.008)$

$m=0.016$

Recall the the question said that the mass, m, was measured in grams, and the radius, r, was measured in centimeters. So, if the radius is 0.2cm, then the mass of the sphere would be 0.016g.

$m=2r^3$

$(0.25)=2r^3$