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murzikaleks [220]
3 years ago
8

Mr. Rr the Rreliable Rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting

from the moment he is turned on. (For example, he does his first jumping jack $42$ seconds after he is turned on.)
How many times during the first $15$ minutes after activation will Mr. Rr whistle and do a jumping jack at the same instant?
Mathematics
1 answer:
sveta [45]3 years ago
7 0

Answer:

7 times during the first 15 minutes

Step-by-step explanation:

Remember that

1\ min=60\ sec

so

15\ min=15(60)=900\ sec

Decompose the numbers 18 and 42 in prime factors

we know that

18=(2)(3^2)

42=(2)(3)(7)

Find the least common multiple (LCM)

The LCM is

(2)(3^2)(7)=126\ sec

we need to find all multiples of 126 that are less than or equal 900.

126*1=126\ sec\\126*2=252\ sec\\126*3=378\ sec\\126*4=504\ sec\\126*5=630\ sec\\126*6=756\ sec\\126*7=882\ sec

therefore

7 times during the first 15 minutes

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kumpel [21]

Answer:

y'   = (2x + y cosxy)/(2y + x cosxy)

Step-by-step explanation:

Using implicit differentiation:

y^2 = x^2 + sin xy

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2y y' = 2x + xy' cos xy + y cos xy

2y y' - xy' cosxy = 2x + ycos xy

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4 0
3 years ago
Answer this true or false question please:4x-1&lt;2x+7 when x =0​
Ksenya-84 [330]
True!
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3 years ago
X^{2} - 8x + 7 = 0<br> Solve by completing the square. Also can you include steps?
iren [92.7K]

Answer:

{1, 7}

Step-by-step explanation:

Start with x^2 - 8x + 7 = 0.

We want to modify the first two terms to resemble x^2 - ax + b - b, where a is the coefficient (here -8) of the x term and b is the square of half of a.

Here, a = -8.  Half of that is -4.  The square of -4 is 16, and this is the value of b.

Write out x^2 - 8x     as    x^2 - 8x + 16 - 16.  This is the perfect square of -4, added to x^2 - 8x and then subtracted from the result

Then the original equation, x^2 - 8x + 7 = 0, can be rewritten as:

x^2 - 8x + 16 - 16 + 7 = 0, and then as (x - 4)^2 - 9, or (x - 4)^2 = 9.

We want to solve this result for x.  To do this, take the square root of both sides:

x - 4 = ±√9, or x - 4 = ±3.

Adding 4 to both sides, we get:

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6 0
3 years ago
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Answer:

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Group like terms

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Step-by-step explanation:

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3 years ago
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5 0
3 years ago
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