What is the total kinetic energy of a hoop of radius 1 m and mass 2 kg that rolls at an

While standing on the edge of the grand canyon, you see a rattlesnake and scream. You hear the echo of the scream off canyon flo

bezimeni [28]

Answer:

1904 m

Explanation:

$\pink{\frak{Given}}\begin{cases} \textsf{ You scream after seeing a rattle snake .}\\\textsf{Scream is heard after 11.2 s .} \end{cases}$

Here we need to find out the depth of the canyon . When you will scream after seeing a snake , the sound produced will travel till the end of the canyon and after hitting the end , it will travel back to you .

So if the depth of the canyon is d (say) , then the total distance travelled by the sound wave will be d + d = 2d .

And we know that the speed of the sound is approximately 340m/s in air , so we can use the formula distance = speed * time to calculate the depth of the canyon . So ,

$\sf \longrightarrow Distance = (Speed)(Time) \\$

$\sf \longrightarrow 2d = 340m/s * 11.2 s\\$

$\sf \longrightarrow d = \dfrac{340m/s * 11.2s}{2} \\$

$\sf \longrightarrow \boxed{\bf Depth_{canyon}= 1904m }\\$

6 0

3 years ago

7. These temperatures were recorded in Pasadena for a week in April. 87 85 80 78 83 86 90 Find each of these. (a) Mean (e) Range

slega [8]

Answer:

a) Mean = 84.14

b) Median = 85

c) Mode = no mode (since there is no variable that appears more than once in this dataset)

d) Midrange = 84

e) Range = 12

f) Variance = 14.69

g) Standard deviation = 3.83

Explanation:

The raw data to be processed is

87 85 80 78 83 86 90

a) Mean = (Σx)/N

The mean is the sum of variables divided by the number of variables

x = each variable

N = number of variables = 7

Mean = (87+85+80+78+83+86+90)/7

Mean = 84.14

b) Median is the number in the middle of the dataset when the variables are arranged in ascending or descending order.

Arranging the data in ascending order

78, 80, 83, 85, 86, 87, 90

The number in the middle is the 4th number = 85

Median = 85

c) Mode is the variable that occurs the most in a distribution.

For this question, all of the variables occur only once, with no variable occurring more than once. Hence, there is no mode for this dataset.

d) Midrange is the arithmetic mean of the highest and lowest number in the dataset.

Mathematically,

Midrange = (Highest + Lowest)/2

Midrange = (90 + 78)/2

Midrange = 84

e) Range is the difference the highest and the lowest numbers in a dataset.

Range = 90 - 78 = 12

f) Variance is an average of the squared deviations from the mean.

Mathematically,

Variance = [Σ(x - xbar)²/N]

xbar = mean

Σ(x - xbar)² = (78 - 84.14)² + (80 - 84.14)² + (83 - 84.14)² + (85 - 84.14)² + (86 - 84.14)² + (87 - 84.14)² + (90 - 84.14)² = 102.8572

Variance = (102.8572)/7

Variance = 14.69

g) Standard deviation = √(variance)

Standard deviation = √(14.69)

Standard deviation = 3.83

Hope this Helps!!!

8 0

4 years ago

Read 2 more answers

Define the term mid-ocean ridge in simple, easy-to-understand words. Thanks :)

Likurg_2 [28]

According to wikipedia <em>a mid-ocean ridge is an underwater mountains system formed by tectonic plates.

</em>Happy studying!<em>
</em>

6 0

4 years ago

What would be the average speed of a runner who finished a 400 meter race in 50 seconds?

Rom4ik [11]

Answer:800

Explanation:about

8 0

3 years ago

An engineer has designed the foundation for column system (20 columns) of a 5 story residential building. Preliminary excavation

nevsk [136]

Answer:

Boring depth = 6.76m

Explanation:

Given Data:

No. of columns = 30

No. of storeys = 5

Water level =3.5m below ground level

Axial load = 2500kN

Foundation size = 3mx2m

Depth of footing = 1.5m = Df

Solution:

First we need to calculate estimated net stress on footing

As we know that: q₀ = P/A

By putting values we get

q₀ = 2500/(3*2) = 416.677 kN/m³

Now for the depth of bedrock from the bottom surface of footing,

D₃ = total depth of bedrock - Df = 100 -1.5 = 98.5m

Now for the calculation of D1, here D1 is the distance from bottom surface of footing to depth where change in vertical stress = Δσ¹ = (1/10)q₀ ---------equation (1)

Now, second diagram attached below is drawn according to stress distribution of 2V:1H

Δσ¹ = P/A¹ = (2500)/(3+z)(2+z) ---------equation (2)

From equation 1 and 2 we get

0.1*416.677 = 2500/(3+D1)(2+D1)

D1²+5D1 = 54

D1 = 5.2621 m

Now we will calculate D2 where we have Δσ¹ /σ₀¹ = 0.05

Now,

we will check this ratio for bottom most layer first(i.e. clay layer, ρsat=16.9kN/m³), if it is satisfied then O.K other wise we will continue procedure for top layers.

We have, Δσ¹ = σ₀¹(0.05)

First we need to find vertical stress σ₀¹ at depth z

σ₀¹ = (3.5*17) + 1.5*(ρsat-ρw)sand + (ρsat-ρw)clay*(D2-3.5)

By putting values we get

σ₀¹ = 59.5 + 13.035 _ 7.09D2 - 28.815

Putting it in equation 2 , we get

σ₀¹ = 2500/(3+D2)(2+D2) = 0.05 * (7.09D2 + 47.72)

By simplification, we get

7.09D₂³+83.167D₂²282.147D₂-49714 = 0

D₂ = 15.35 m

So from this calculation it is evident that Δσ¹ /σ₀¹ = 0.05 is at depth of 15.35m which is in clay layer, so no need to check in upper layers.

Now, for the calculation of boring depth depth,

Boring depth = D +Df

1st case = 5.26 + 1.5 = 6.76m

2nd case = 15.35 + 1.5 = 16.85m

13rd case = 98.5 + 1.5 = 100m

Boring depth = 6.76m

3 0

3 years ago