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2 years ago

13

Which formula is best used to prove that a figure has congruent sides?

1 answer:

inysia [295]2 years ago

5 0

Answer:

a) Distance formula

Step-by-step explanation:

Generally, if you want to show lengths are the same, it is useful to use a formula for length: the distance formula.

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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 $\sqrt{176.77^2+(-178.43)^2}\dfrac{\rm m}{\rm s}\approx250\dfrac{\rm m}{\rm s}$ .

7 0

3 years ago

Sofia made a scale drawing of a house. The scale she used was 1 millimeter : 6 meters. If the actual length of the garage is 12

romanna [79]

Answer:

2 millimeters.

Step-by-step explanation:

1 millimeter : 6 meters

x millimeters : 12 meters

x = (12÷6) × 1

x = 2×1

x = 2 millimeters

6 0

2 years ago

What is the value of |−32|?<br><br> Numerical answer expected

Sever21 [200]

32

The absolute value takes the distance from zero, it doesn’t matter weather it is positive or negatively

4 0

2 years ago

Read 2 more answers

The average number of traffic tickets issued in a city on any given day

Anton [14]

Answer:

The most tickets were written on Saturday .On Saturday 325 tickets were issued

Step-by-step explanation:

The average number of traffic tickets issued in a city on any given day Sunday-Saturday can be approximated by

$T(x) = -6x^2 + 84x + 37$

Where x represents the number of days after Sunday

T(x) represents the number of traffic tickets issued.

Sunday = x=0

Monday = x=1

Tuesday = x=2

Wednesday = x=3

Thursday = x =4

Friday = x=5

Saturday = x=6

Substitute x= 0

$T(x) = -6x^2 + 84x + 37\\T(x) = -6(0)^2 + 84(0) + 37\\T(x)=37$

On Sunday 37 tickets were issued

Substitute x= 1

$T(x) = -6x^2 + 84x + 37\\T(x) = -6(1)^2 + 84(1) + 37\\T(x)=115$

On Monday 115 tickets were issued

Substitute x= 2

$T(x) = -6x^2 + 84x + 37\\T(x) = -6(2)^2 + 84(2) + 37\\T(x)=181$

On Tuesday 181 tickets were issued

Substitute x= 3

$T(x) = -6x^2 + 84x + 37\\T(x) = -6(3)^2 + 84(3) + 37\\T(x)=235$

On Wednesday 235 tickets were issued

Substitute x= 4

$T(x) = -6x^2 + 84x + 37\\T(x) = -6(4)^2 + 84(4) + 37\\T(x)=277$

On Thursday 277 tickets were issued

Substitute x= 5

$T(x) = -6x^2 + 84x + 37\\T(x) = -6(5)^2 + 84(5) + 37\\T(x)=307$

On Friday 307 tickets were issued

Substitute x= 6

$T(x) = -6x^2 + 84x + 37\\T(x) = -6(6)^2 + 84(6) + 37\\T(x)=325$

On Saturday 325 tickets were issued

Hence the most tickets were written on Saturday .On Saturday 325 tickets were issued

6 0

2 years ago

I NEED HELP PLEASE HELP ME OUT ILL GIVE YOU EXTRA POINTS

kati45 [8]

Answer: dont know just search it up

4 0

1 year ago