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3 years ago

FIRST CORRECT ANSWER WILL GET BRAINLIEST!!! PLS helppp prove that 5^7+5^6 is divisible by 6

Mathematics

1 answer:

seraphim [82]3 years ago

4 0

First, I solve the equation: 5^7+5^6...

I got 93750

The divisibility rules of 6 are:

It must be divisible by 2

It must be divisible by 3

So, let's check if 93750 is divisible by 2 first.

It's in even number which automatically means that it is divisible by 2.

No odd numbers are divisible by 2

Now let's check if it is divisible by 3 second.

The divisibility rules of 3 are:

The digits added must be divisible by 3

So, 9 + 3 + 7 + 5 + 0 = 17

17 is NOT divisible by 3.

Therefore, your equation is not divisible by 6!

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3 years ago

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A projectile is fired with muzzle speed 250 m/s and an angle of elevation 45° from a position 30 m above ground level. Where doe

qaws [65]

The projectile's horizontal and vertical positions at time $t$ are given by

$x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ\,t$

$y=30\,\mathrm m+\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ\,t-\dfrac g2t^2$

where $g=9.8\dfrac{\rm m}{\mathrm s^2}$ . Solve $y=0$ for the time $t$ it takes for the projectile to reach the ground:

$30+\dfrac{250}{\sqrt2}t-4.9t^2=0\implies t\approx36.2458\,\mathrm s$

In this time, the projectile will have traveled horizontally a distance of

$x=\dfrac{250\frac{\rm m}{\rm s}}{\sqrt2}(36.2458\,\mathrm s)\approx6400\,\mathrm m$

The projectile's horizontal and vertical velocities are given by

$v_x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ$

$v_y=\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ-gt$

At the time the projectile hits the ground, its velocity vector has horizontal component approx. 176.77 m/s and vertical component approx. -178.43 m/s, which corresponds to a speed of about $\sqrt{176.77^2+(-178.43)^2}\dfrac{\rm m}{\rm s}\approx250\dfrac{\rm m}{\rm s}$ .

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3 years ago

Solve the system of equations by substitution. 2x + y = 3z x + y = 6z What is the value for y from the first equation, that coul

Archy [21]

Answer:

y = 3z - 2x

Step-by-step explanation:

Systems of equations can be solved by a number of know techniques, such as substitution, elimination or graphical approach.

We are required to solve the system of equations given via substitution;

2x + y = 3z

x + y = 6z

The question requires us to determine the value for y from the first equation, that could be substituted into the second equation.

We simply need to make y the subject of the formula from the first equation;

2x + y = 3z

To do this we subtract 2x on both sides of the equation;

2x + y -2x = 3z - 2x

y = 3z - 2x

This is the value of y from the first equation, that can be substituted into the second equation.

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4 years ago