Sarah can bicycle a loop around the north part of lake washington in 2 hours and 30 minutes. if she could increase her average speed by 1 km/hr, it would reduce her time around the loop by 7 minutes. how many kilometers long is the loop?

The length of the loop is approximately 49.58 km.

Step-by-step explanation:

Given:

Time required to ride bicycle in loop = 2 hours and 30 mins

Now we know that;

60 mins = 1 hour

30 mins =0.5 hour

so 2 hour and 30 mins =

∴ Time required to ride bicycle in loop = 2.5 hrs

Let the speed at which she is riding the bicycle be 's'.

and let Total distance of the loop be 'd'

Now we know that;

Distance is given by speed multiplied by time.

framing in equation form we get;

Now Given:

If she increase the speed by 1 km/hr, it would reduce her time around the loop by 7 minutes.

Hence we can say;

Speed =

Also time will be reduce to 7 mins.

7 mins  =0.12 hrs

Now time = 2.5-0.12 =2.38

Again Distance is given by speed multiplied by time.

framing in equation form we get;

Now distance is same for both so we will calculate the speed by equating the equations.

Now Speed = 19.83 km/hr

Length of the loop (d) =

Hence the length of the loop is approximately 49.58 km.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is