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3 years ago

If Usain Bolt can run a marathon (26.2) in 2 hours and 15 minutes, how fast would he run if he ran at the same constant rate?

Mathematics

1 answer:

inn [45]3 years ago

8 0

Answer:

The speed of Usain Bolt is 0.194 miles per minutes to complete the marathon.

Step-by-step explanation:

Given as :

The Distance of marathon = 26.2 unit

The time taken to complete marathon = 2 hours and 15 minutes

= 120 + 15 = 135 minutes

Let The constant speed of Usain Bolt = S unit per minutes

So, Speed = $\frac{Distance }{Time}$

Or, S = $\frac{26.2 }{135}$

∴ S = 0.194 unit per minutes

Hence The speed of Usain Bolt is 0.194 miles per minutes to complete the marathon. Answer

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How many equivalence relations are there on the set 1, 2, 3]?

Alex787 [66]

Answer:

We need to find how many number of equivalence relations are on the set {1,2,3}

A relation is an equivalence relation if it is reflexive, transitive and symmetric.

equivalence relation R on {1,2,3}

1.For reflexive, it must contain (1,1),(2,2),(3,3)

2.For transitive, it must satisfy: if (x,y)∈R then (y,x)∈R

3. For symmetric, it must satisfy: if (x,y)∈R,(y,z)∈R then (x,z)∈R

Since (1,1),(2,2),(3,3) must be there is R, (1,2),(2,1),(2,3),(3,2),(1,3),(3,1). By symmetry,

we just need to count the number of ways in which we can use the pairs (1,2),(2,3),(1,3) to construct equivalence relations.

This is because if (1,2) is in the relation then (2,1) must be there in the relation.

the relation will be an equivalence relation if we use none of these pairs (1,2),(2,3),(1,3) . There is only one such relation: {(1,1),(2,2),(3,3)}

we can have three possible equivalence relations:

{(1,1),(2,2),(3,3),(1,2),(2,1)}

{(1,1),(2,2),(3,3),(1,3),(3,1)}

{(1,1),(2,2),(3,3),(2,3),(3,2)}

6 0

4 years ago

Contest a radio station is giving every third caller a t shirt and every tenth caller a ceramic mug which caller will be the fir

rewona [7]

The 30th caller will receive both.

3 0

4 years ago

Please help due today!

Scrat [10]

Answer:

Polygon, quadrilateral, convex, and equilateral.

Step-by-step explanation:

8 0

4 years ago

Can anyone explain to me how to do this question ? ty !!

julia-pushkina [17]

Step-by-step explanation:

use a little imagination.

the whole thing is a combination of churches and half- circles.

and you know the formula for the area of a circle ?

A = pi×r²

so, the only difficulty is to find the circles and then the radius of each involved circle.

when you look at the picture, the shaded area is almost identical to the lower half of the main circle.

2 bumps "look" over into the other side, but one equally sized bump is removed from this lower half.

so, as a first step we will calculate the area of the lower half of the main circle.

the diameter is 24 m, so the radius is half of that : 12m

the area of the large circle is therefore

pi×12² = 144×pi m²

since we only need the (lower) half, we divide this by 2 :

144×pi / 2 = 72×pi m²

the bumps up and down are actually half-circles too. just of smaller circles.

since AB = BC = CD, we know each of these lines are 1/3 of the main diameter AD.

so, the diameter of the smaller circles is 24/3 = 8 m

and their radius is half of that = 8/2 = 4m

the area of such a small circle is therefore

As = pi×4² = 16×pi m²

and a small half-circle area is then

16×pi / 2 = 8×pi m²

so, for the full shaded area I need to take the large half-circle and add 2 small half-circles, and then subtract 1 small half-circle.

so, in total I only need to add 1 small half-circle.

Ashaded = 72×pi + 8×pi = 80×pi m²

5 0

3 years ago

What is the solution to log (9x)-log2^3= 3?

olga_2 [115]

For this case we have that by definition of properties logarithm is met:

$log_ {b} (x) -log_ {b} (y) = log_ {b} (\frac {x} {y})$

So, rewriting the expression we have:

$log (\frac {9x} {2 ^ 3}) = 3\\log (\frac {9x} {8}) = 3$

By definition of logarithm we have to:

$log_ {b} (x) = y$ is equivalent to $b ^ y = x$

So:

$10 ^ 3 = \frac {9x} {8}\\9x = 8 * 10 ^ 3\\9x = 8 * 1000\\9x = 8000\\x = \frac {8000} {9}$

ANswer:

$x = \frac {8000} {9}$

3 0

3 years ago

Read 2 more answers