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3 years ago

Can someone please help me with this? Preferably ASAP

Mathematics

1 answer:

adoni [48]3 years ago

8 0

So x is one number and x + 1 is another

1. x + x + 1 = 57;
2. 2x + 1 = 57;
-1 -1
4. 2x = 56
5. x = 56/2
6. x = 28

So, x + 1 = 28 + 1 = 29
So 28 and 29 are the 2 consecutive integers of 57

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the angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 31 degrees. if the vertical distance

Eduardwww [97]

Answer:

The ride lasts 10 minutes.

Step-by-step explanation:

The triangle that is formed is attached.

In order to find out how long the ride lasts, we need to figure out the horizontal distance $d.$

From trigonometry we have:

$tan(31^o)=\frac{902}{d}.$

Therefore

$d=\frac{902\:feet}{tan(31^o)}=1501\:feet.$

Now the amount of time $t$ the gondola ride lasts is equal to the distance $d$ divided by the speed of the gondola:

$t=\frac{1501ft}{155ft/sec} =\boxed{9.69\:minutes.}$

To the nearest minute this is 10 minutes.

7 0

4 years ago

Consider a set of one-dimensional points: 6, 12, 18, 24, 30, 42, 48.

Vinvika [58]

Answer:

1) With initial centroids 10-40, final clusters are

first cluster (6,12,18,24,30)

second cluster (42,48)

And the Sum of Squared Errors (SSE) for the clustering result is 378

2) With initial centroids 10-20, final clusters are

first cluster (6,12,18,24)

second cluster (30,42,48)

And the Sum of Squared Errors (SSE) for the clustering result is 348

Step-by-step explanation:

K-means works as follows

the points will be clustered according to their distance to the centroids.
Then centroids are updated as the cluster means.
This process continues until clusters doesn't change anymore

1) initial centroids 10-40

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

new centroids 15-40

first cluster (6,12,18,24,30) mean:18

second cluster (42,48) mean:45

final centroids 18-45

first cluster (6,12,18,24,30) mean:18

second cluster (42,48) mean:45

Sum of Squared errors = $(18-6)^{2}$ + $(18-12)^{2}$ + $(18-18)^{2}$ + $(18-24)^{2}$ + $(18-30)^{2}$ + $(45-42)^{2}$ + $(45-48)^{2}$ =378

2)initial centroids 10-20

first cluster (6,12) mean:9

second cluster (18,24,30,42,48) mean:32.4

new centroids 9-32.4

first cluster (6,12,18) mean:12

second cluster (24,30,42,48) mean:36

new centroids 12-36

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

final centroids 15-40

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

Sum of Squared errors = $(15-6)^{2}$ + $(15-12)^{2}$ + $(15-18)^{2}$ + $(15-24)^{2}$ + $(40-30)^{2}$ + $(40-42)^{2}$ + $(40-48)^{2}$ =348

6 0

4 years ago

a cylindrical tank with radius 7 m is being filled with water at a rate of 4 m3/min. how fast is the height of the water increas

Rzqust [24]

Answer:

0.026 m / min.

Step-by-step explanation:

Volume V = π7^2h

V = 49πh

dV/dh = 49π

Rate that the volume is increasing is 4 m3/min.

So dV/dt = 4

dV/dt = dh/dt * dV/dh

4 = dh/dt * 49π

dh/dt = 4/49π

= 0.026 m / min.

8 0

3 years ago

Simplify. (f3 – 5f + 25) – (4f2 – 12f + 9)

Neko [114]

Answer:

2f + 16

Step-by-step explanation:

6 0

3 years ago

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Apply the distributuve property to factor out the greatest commmon facto 32+ 44

VARVARA [1.3K]

4 is the greatest common factor of 32 and 44

3 0

3 years ago

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