All categories

3 years ago

If it takes sound 1 aecond to travel 1.5km how many km will it travel in 3.7 seconds

Mathematics

1 answer:

kiruha [24]3 years ago

7 0

Lets set up an equation to easier understand this.

1/1.5 = 3.7/x (x represents the unknown km)

We know that whatever you do to the top you do to the bottom.

And we can see that 1 x 1.5 = 1.5

So we can multiply the same thing by 3.7

1.5 x 3.7 = 5.55

So in this case you would travel 5.55 km in 3.7 seconds.

GOOD LUCK :)

You might be interested in

What is the value of the 3 in 46.132 is blank times the value of the 3 in 8.553

nika2105 [10]

Answer:

Step-by-step explanation:

0.03 in 46.132

0.003 in 8.553

0.03 = 0.003 × 10

0.03 is 10 times 0.003

3 0

3 years ago

If 15 percent of the sixth graders have blonde hair, and there are 120 sixth graders, how many of them have blonde hair?

Vlada [557]

15/100 = 0.15 x 120 = 18

8 0

3 years ago

Urgent, It is a Calculus question and I’ll appreciate your help. Thanks

BaLLatris [955]

Answer:

4733

Step-by-step explanation:

Please refer to the attached diagram.

Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.

Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.

We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...

(12p)(12r) = -1

r = -1/(144p)

The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:

slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified

The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...

tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))

Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...

slope AB = ((slope AC) +2)/(1 -(slope AC)(2))

$6(p+r)=\dfrac{12p+2}{1-(12p)(2)}\\\\3(p+r)(1-24p)=6p+1\qquad\text{multiply by $1-24p$}\\\\3\left(p-\dfrac{1}{144p}\right)(1-24p)=6p+1\qquad\text{use the value for r}\\\\3(144p^2-1)(1-24p)=144p(6p+1)\qquad\text{multiply by 144p}\\\\ 3456 p^3+ 144 p^2+ 24 p+1 =0\qquad\text{put in standard form}\\\\144p^2(24p+1)+(24p+1)=0\qquad\text{factor by pairs}\\\\(144p^2+1)(24p+1)=0\qquad\text{finish factoring}\\\\p=-\dfrac{1}{24}\qquad\text{only real solution}\\\\r=\dfrac{-1}{144p}=\dfrac{1}{6}$

So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...

d^2 = (6r^2 -6p^2)^2 +(r -p)^2

d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216

Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...

Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b

Then a+b = 125 +4608 = 4733.

_____

Comment on the solution

The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.