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diamong [38]
3 years ago
10

The library in Ben's town is 3 blocks east and 7 blocks north of his house. He finds a short cut by walking diagonally from his

house to the library. How much shorter is the shortcut than walking the blocks?
Mathematics
2 answers:
Mariana [72]3 years ago
6 0

Answer:

Step-by-step explanation:

A right angle triangle is formed.

The diagonal or shortcut that he found represents the hypotenuse of each right angle triangle. The number of blocks he used to walk due due east and north represents the adjacent and opposite sides of the right angle triangle. To determine the number of blocks he would have to walk when he takes the shortcut,d, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore

d² = 7² + 3²

d² = 49 + 9 = 58

d = √58

d = 7.6 blocks

The normal distance is

3 + 7 = 10 blocks

The number of blocks by which the shortcut is shorter than walking the blocks is

10 - 7.6 = 2.4

Step2247 [10]3 years ago
3 0

Answer:

The answer to your question is 2.4 units shorter.

Step-by-step explanation:

Data

3 blocks east and 7 blocks north.

Process

1.- Calculate the distance walking the blocks

     distance = 3 + 7

     distance = 10

2.- Calculate when walking diagonally using the pythagorean theorem

     distance² =  3² + 7²

     distance² = 9 + 49

     distance² = 58

     distance = 7.62

3.- Calculate the difference of distances

     Δd = 10 - 7.62

     Δd = 2.38 units

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Juan scored a total of 168 points in basketball this season. He scored 147 of those points in the regular season, and the rest w
Natalka [10]

Answer:

The answer to your question is 12.5 %

Step-by-step explanation:

Data

Total points = 168

Points scored in the regular season = 147

Percent of points scored in the playoff game = ?

Process

1.- Calculate the points scored in the playoff game

  Points in playoff game = 168 - 147

                                          = 21

2.- Calculate the percent of points scored in the playoff game using proportions

                      168 points -------------------- 100%

                        21 points --------------------- x

                        x = (21 x 100) / 168

                        x = 2100 / 168

                        x = 12.5 %

8 0
3 years ago
Read 2 more answers
A man hits a baseball when it is 4 ft above the ground with an initial velocity of 120 ft/sec. The ball leaves the bat at a 30 d
Sauron [17]
<span>et us assume that the origin is the floor right below the 30 ft. fence

To work this one out, we'll start with acceleration and integrate our way up to position.

At the time that the player hits the ball, the only force in action is gravity where: a = g (vector)
ax = 0
ay = -g (let's assume that g = 32.8 ft/s^2. If you use a different value for gravity, change the numbers.

To get the velocity of the ball, we integrate the acceleration
vx = v0x = v0cos30 = 103.92
vy = -gt + v0y = -32.8t + v0sin40 = -32.8t + 60

To get the positioning, we integrate the speed.
x = v0cos30t + x0 = 103.92t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + 60t + 4

If the ball clears the fence, it means x = 0, y > 30

x = 0 -> 103.92 t - 350 = 0 -> t = 3.36 seconds

for t = 3.36s,
y = -16.4(3.36)^2 + 60*(3.36) + 4
= 20.45 ft

which is less than 30ft, so it means that the ball will NOT clear the fence.


Just for fun, let's check what the speed should have been :)

x = v0cos30t + x0 = v0cos30t - 350
y = 1/2*(-32.8)t² + v0sin30t + y0 = -16.4t² + v0sin30t + 4

x = 0 -> v0t = 350/cos30
y = 30 ->
-16.4t^2 + v0t(sin30) + 4 = 30
-16.4t^2 + 350sin30/cos30 = 26
t^2 = (26 - 350tan30)/-16.4
t = 3.2s

v0t = 350/cos30 -> v0 = 350/tcos30 = 123.34 ft/s

So he needed to hit the ball at at least 123.34 ft/s to clear the fence.

You're welcome, Thanks please :)
</span>
6 0
3 years ago
The coordinates of point P are (−3, 4). What are the coordinates of the point that is a reflection of point P over the y-axis? (
ahrayia [7]
The answer would be ( 3 , 4 )
7 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20-%20%20%5Cfrac%7B7%7D%7B216%7D%20%7D%20%5Ctimes%20%20%5Csqrt%7B42%7D%20%20" id
Natalija [7]

Answer:

IM GOING TO THIS but what do I gotta do evaluate? simplify?

6 0
4 years ago
What is thirty times twenty
wariber [46]

Answer:

600

Step-by-step explanation:

How to do it in your head (secret):

3*2 = 6

add 2 zeros after the 6 since there are 2 zeros in total in this equation 2<u><em>0 </em></u>and 3<u><em>0</em></u> so:

30*20 = 600

:D

6 0
3 years ago
Read 2 more answers
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