Which expressions are equal to 6^3•2^6/ 2^3

Mathematics

1 answer:

True [87]3 years ago

3 0

Answer:

2^6 x 3^3 and 12^3

Step-by-step explanation:

First, solve

6^3 x 2^6/2^3

216 x 64/8

13824/8 = 1728

lets solve for the answers

6^3 = 216

Therefore, 6^3 is not an answer

2^6 x 3^3= 64 x 27 = 1728

because both expressions are equal to 1728, this is an answer. this answer can also eliminate 2^3 x 3^3 because it has a lower exponent than the answer that is equal to 1728. therefore, the value of it must be smaller than 1728

12^3 = 1728

This answer is correct, because both values are equal to each other, meaning that 12^6 is larger than 1728

Therefore, your answers will be 2^6 x 3^3 and 12^3

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Doug hits a baseball straight towards a 15 ft high fence that is 400 ft from home plate. The ball is hit 2.5ft above the ground

Scorpion4ik [409]

Answer:

$125.4\ \text{m/s}$

Step-by-step explanation:

u = Initial velocity of baseball

$\theta$ = Angle of hit = $30^{\circ}$

x = Displacement in x direction = 400 ft

y = Displacement in y direction = 15 ft

$y_0$ = Height of hit = 2.5 ft

$a_y$ = g = Acceleration due to gravity = $32.2\ \text{ft/s}^2$

t = Time taken

Displacement in x direction

$x=u_xt\\\Rightarrow x=u\cos\theta t\\\Rightarrow t=\dfrac{x}{u\cos\theta}\\\Rightarrow t=\dfrac{400}{u\cos30^{\circ}}\\\Rightarrow t=\dfrac{400}{u\dfrac{\sqrt{3}}{2}}\\\Rightarrow t=\dfrac{800}{u\sqrt{3}}$

Displacement in y direction

$y=y_0+u_yt+\dfrac{1}{2}a_yt^2\\\Rightarrow y=y_0+u\sin\theta t+\dfrac{1}{2}a_yt^2\\\Rightarrow 15=2.5+u\sin30^{\circ}(\dfrac{800}{u\sqrt{3}})+\dfrac{1}{2}\times -32.2\times (\dfrac{800}{u\sqrt{3}})^2\\\Rightarrow \dfrac{400}{\sqrt{3}}-\dfrac{10304000}{3u^2}-12.5=0\\\Rightarrow 218.44=\dfrac{10304000}{3u^2}\\\Rightarrow u=\sqrt{\dfrac{10304000}{3\times218.44}}\\\Rightarrow u=125.4\ \text{m/s}$