A cyclist traveled kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel kilometers, the
1 answer:
The speed of skaters was 10 km per hr.
<h3>How to solve? </h3>
Mathematically, the speed of an object is directly proportional to the distance traveled and inversely proportional to the time taken. In simple words, the more the speed, the distance traveled is more in a short period and vice-versa.
Let the speed of the skater be x
We know, speed =
According to the question:
Cross multiplying both sides,
20(x+10) = 40x
20x + 200 = 40x
20x = 200
x = 10
Thus, the speed of skaters was 10 km per hr.
To know more about Speed-distance questions visit:
#SPJ4
You might be interested in
Answer:
Option 4 -
Step-by-step explanation:
To find : Which set of rational numbers is arranged from least to greatest?
Solution :
The set of rational numbers are
Writing all number in one form,
Now, -1.4<-0.5<0.2<3
From least to greatest the set of natural numbers are
So,
Therefore, option 4 is correct.
Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :
√(<em>x</em> ² - 4) = 1
<em>x</em> ² - 4 = 1
<em>x</em> ² = 5
<em>x</em> = ±√5
We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.
This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.
Now apply the inverse function theorem:
If <em>f(a)</em> = <em>b</em>, then (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.
We have
<em>f(x)</em> = √(<em>x</em> ² - 4) → <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)
So if <em>a</em> = -√5 and <em>b</em> = 1, we get
(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)
(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5
The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.
