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Dovator [93]
3 years ago
12

In a machine, a large gear completes a revolution every minute while a small gear completes a revolution every 24 seconds. If th

e gears are currently aligned, how much time will pass before they are aligned again?
Mathematics
1 answer:
svlad2 [7]3 years ago
7 0
This question is asking you for the least common multiple of 60 (seconds in 1 minute) and 24 (seconds in 24 seconds).
I think it's 120 (you should check it) and that would be 3 minutes.
You might be interested in
If −5e^x^2 y=x and y(−5)=0, find y′(−5) by implicit differentiation
xenn [34]
Differentiate:
-5×2(xe^x^2)y-5e^x^2dy/dx=1
-5e^x^2(2xy+y´)=1
When x=-5, y=0:
-5e²⁵y´=1, so y´(-5)=-eˉ²⁵/5
6 0
3 years ago
At a point on the ground 46 feet from the foot of a tree, the angle of elevation of the top of the tree is 68 degrees. What is t
Mandarinka [93]

Answer:

114 ft

Step-by-step explanation:

Imagine or construct a right triangle with the 46 ft leg lying on the ground.  This is the "adjacent side" of the triangle; it lies immediately adjacent to the 68 degree angle.  The side opposite this angle is h, the height of the tree.

The tangent function includes angle, opp side and adj side:

tan 68 degrees = opp / adj = h / (46 ft), and so:

(46 ft)*tan (68 degrees) = opp = h

Then the height of the tree is h = (46 ft)(2.47) = 114 ft

6 0
3 years ago
There exist infinitely many common fractions $\frac{a}{b}$ , where $a > 0$ and $b > 0$ and for which $\frac{3}{5} < \fr
vredina [299]

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.

3 0
3 years ago
Solve the equation for all values of x.<br> (8x+9)(49x^2-100)=0
Liono4ka [1.6K]

Answer:

x = \frac{-9}{8} , \frac{-10}{7} , \frac{10}{7}

Step-by-step explanation:

8x+9=0

8x=-9

x = \frac{-9}{8}

or

49x^{2}-100 = 0

(7x)^{2} -10^{2} =0,

(7x+10)(7x-10)=0

7x+10=0, 7x-10=0

7x=-10, 7x=10

x=-\frac{-10}{7}, x = \frac{10}{7}

4 0
2 years ago
Explain two ways to find the LCM​
svp [43]

Answer:

1. List the first several multiples of each number.

Look for multiples common to both lists. ...

Look for the smallest number that is common to both lists.

This number is the LCM.

Find the GCF for the two numbers.

Divide that GCF into the either number; it doesn't matter which one you choose, so choose the one that's easier to divide.

Take that answer and multiply it by the other number.

Step-by-step explanation:

Hope this helps!

4 0
3 years ago
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