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xenn [34]
3 years ago
13

One number is twice another. The sum of their reciprocals is 3/2 . Find the numbers.

Mathematics
1 answer:
MissTica3 years ago
7 0

Answer:

The two numbers are 1 and 2.

Step-by-step explanation:

Let the two numbers be <em>a </em>and <em>b</em>.

One number is twice another, so let's let <em>b=2a</em>.

Their reciprocals are 3/2. Thus:

\frac{1}{a}+\frac{1}{b} =\frac{3}{2}

Substitute and solve for <em>a: </em>

<em />\frac{1}{a}+\frac{1}{2a} =\frac{3}{2}\\<em />

Combine the fractions by forming a common denominator by multiplying the left term by 2:

\frac{2}{2a} +\frac{1}{2a}=\frac{3}{2}

Combine and cross-multiply:

3/2a=3/2\\6a=6\\a=1\\b=2(1)=2

Thus, the two numbers are 1 and 2.

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Answer:

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Step-by-step explanation:

So to solve this we use a system of equations. Let's use "j" to represent Jack, "t" to represent Tyler, and "d" to represent the dad. Set the system up and it will look something like this:

j = t - 13 (Jack is 13 years younger than Tyler)

d = 2t (Dad is twice Tyler's age)

d + j + t = 91 (The sum of the ages is 91)

And then solve, I solved by isolating the "j" variable on the last equation, giving us j = 91 - t - d, then plugged that into the first equation, giving us 91 - t - d = t - 13, and got d = 104 - 2t. Then I plug that into d = 2t, giving us 104 - 2t = 2t, and solve for t. T is 26, meaning Tyler is 26 years old, and then I just subtract 13 from that, giving us 13 years old.

And finally, I obviously checked my answer, because now we know dad is 52, and I got 91.

5 0
3 years ago
URGENT...Please help me with this question!!!!!!
Hunter-Best [27]

Answer:

option 2

Step-by-step explanation:

The problem can be solved using Pythagoras' identity for a right triangle.

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Note that since cos90° = 0 the equation reduces to

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