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aivan3 [116]
3 years ago
8

A cube with 40-cm-long sides is sitting on the bottom of an aquarium in which the water is one meter deep. (Round your answers t

o the nearest whole number. Use 9.8 m/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.)
Mathematics
1 answer:
Molodets [167]3 years ago
3 0

Answer:

940.8 N

1254.4 N

Step-by-step explanation:

I would think the questions would be to calculate the forces at the top of the cube and at the sides. Thus:

On the top:

F = pressure * area

P = density * gravity * height

the height would be:

1m - 0.4m = 0.6m

replacing:

P = 1000 * 9.8 * 0.6 = 5880

A = (0.4) ^ 2 = 0.16

F = 5880 * 0.16

F = 940.8 N

On the sides:

dF = d * g * h * dA

dA = 0.4 * dh replacing

dF = 1000 * 9.8 * h * 0.4 * dh

dF = 3920 * h * dh

We integrate both sides and we have:

F = 3920 * (h ^ 2/2), h = 0.6 up to h = 1

F = (3920/2) * (1 ^ 2 - 0.6 ^ 2)

F = 1254.4 N

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Fynjy0 [20]

The estimated number of ramps that can be cut from the board in discuss is; 6 ramps which is a reasonable assumption provided that each ramp is about 2 feet long.

b). The number of ramps that can be cut from the 12 1/2 feet long board is 6 and hence, the length of wood left is; 1/2.

<h3>What is the number of ramps that can be cut from the 12 1/2 feet long board?</h3>

It follows from the task content that skateboard ramps are made from a 12 1/2 feet long ramp.

Consequently, on the assumption that the quantity by measure of length of the board required to make one skateboard ramp is 2 feet, it follows that the estimated number of ramps that can be made from the board is; 12/2 = 6 skateboard ramps.

Ultimately, the amount of wood which is left over upon making the ramps is; 12 1/2 - 12 = 1/2.

Read more on division;

brainly.com/question/917110

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4 0
1 year ago
At a given moment, a plane passes directly above a radar station at an altitude of 6 km6 km and the plane's speed is 800 km/h.80
Valentin [98]

Answer: see explanation

Step-by-step explanation:

so you have a plane at constant altitudeof 6km (6000m) flying at 800 km/h (222.222 m/s) (see the image)

the plane is moving with constant speed therefore x(t) = 222.222*t => no forces are interacting horizontally with the plane therefore acceleration is 0, then v is constant and x(t) is a linear function which coefficient is v.

now we have a triangle with an angle theta, one side is x(t), and the other is 6000m. we can get theta by tan(theta) = 6000/(222.222*t). 24 minutes are 1440 seconds so if we replace such value, we get the theta angle by  solving for theta => theta = arctan(6000/(222.222*1440)) = 0.019 radians or 1.074 degrees. Now if you want to know the exchange rate of theta we have to differentiate the expression with respect to t:

\frac{d}{dt} \theta = \frac{d}{dt}(arctan(\frac{6000}{222.222*t} )) = \frac{1}{1+\frac{6000}{222.222*t} } * -\frac{27}{t^2}  = -\frac{27}{t^2+729.001}

then replace t with 1440 and you will get that theta is changing by -0.000013 (1.3E-5) radians or -7.458E-4 degrees every second which has a lot of sense since the plane is getting out of your line of sight due to the earth's curvature

5 0
3 years ago
A linear equation is any equation with a constant rate of change (slope)?
denis-greek [22]

Answer:

I believe that is correct. But there are other ways to define a linear equations along with this one :)

6 0
3 years ago
In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if i
Ray Of Light [21]

Answer:

Infinite sequence with terms t_{n+1}=t_n\cdot ab or t_{n+1}=2a\cdot (ab)^n=2a^{n+1}b^n.

t_7=2a^7b^6.

Step-by-step explanation:

Consider the pattern

2a,\ 2a^2b,\ 2a^3b^2,\ 2a^4b^3,\ ...

First term of this pattern is

t_1=2a,

second -

t_2=t_1\cdot ab,

third -

t_3=t_2\cdot ab,

fourth -

t_4=t_3\cdot ab,

fifth -

t_5=t_4\cdot ab=2a^4b^3\cdot ab=2a^5b^4,

sixth -

t_6=t_5\cdot ab=2a^5b^4\cdot ab=2a^6b^5,

seventh -

t_7=t_6\cdot ab=2a^6b^5\cdot ab=2a^7b^6.

This equence is infinite and each next term is obtained from the previous multiplying by ab.

7 0
3 years ago
3x - 7 - 2x + 5 = 6​
IceJOKER [234]
First combine like terms
3x - 7 - 2x + 5 = 6
x - 2 = 6
Get x by itself by adding 2 on both sides
x - 2 = 6
x = 8
Your answer is x = 8
7 0
3 years ago
Read 2 more answers
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