Which is the best estimated√43 to the nearest tenth

What was the average speed in km/h of a boat that moves 15.0 km across a lake in 45 min

Slav-nsk [51]

Answer:

20 km/h

Step-by-step explanation:

7 0

4 years ago

A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we sa

sashaice [31]

The question is incomplete so, here is the complete question.

A tank in form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. When friction and contraction of water at the hole are ignored, the height h of water in the tank is described by

$\frac{dh}{dt} = - \frac{A_{h} }{A_{w} } \sqrt{2gh}$ , where $A_{h}$ and $A_{w}$ are cross-sectional areas of the hole and the water, respectively. (a) Solve for h(t) if the initial height of the water is H. By hand, sketch the graph of h(t) and give its interval I of definition in terms of the symbols Aw, Ah and H. Use g = 32ft/s². (b) Suppose the tank is 12 feet high and has radius 4 feet and the circular hole har radius 1/2 inch. If the tank is initially full, how long will it take to empty?

Answer: a) h(t) = $(\sqrt{H} - 4 \frac{A_{h} }{A_{w} }t )^{2}$ , with interval 0≤t≤ $\frac{A_{w}\sqrt{H} }{4A_{h} }$

b) It takes 133 minutes.

Step-by-step explanation: a) The height per time is expressed as

$\frac{dh}{dt} = - \frac{A_{h} }{A_{w} } \sqrt{2gh}$

Using g=32ft/s²: $\sqrt{2gh}$ = $\sqrt{2.32.h}$ $= 8\sqrt{h}$

$\frac{dh}{dt} = - \frac{A_{h} }{A_{w} } \sqrt{2gh}$

$\frac{dh}{\sqrt{h} }$ = - 8. $\frac{A_{h} }{A_{w} }$ dt

$\int\limits^a_b {\frac{dh}{\sqrt{h} } } = - \int\limits^a_b {8.\frac{A_{h} }{A_{w} } } \, dt$

Calculating the indefinite integrals:

2 $\sqrt{h}$ = - 8 $\frac{A_{h} }{A_{w} }$ .t + c

According to the question, when t=0 h₀ for water is H. so

2 $\sqrt{H}$ = - 8 $\frac{A_{h} }{A_{w} }$ .0 + c

c = 2 $\sqrt{H}$

2 $\sqrt{h}$ = - 8 $\frac{A_{h} }{A_{w} }$ .t + 2 $\sqrt{H}$

Dividing each term by 2, then, the equation h(t) is

h(t) = ( $\sqrt{H} -$ $4\frac{A_{h} }{A_{w} } .t$ )²

Now, to find the interval, when the tank is empty, there is not water height so:

0 = ( $\sqrt{H} -$ $4\frac{A_{h} }{A_{w} } .t$ )²

0 = ( $\sqrt{H} -$ $4\frac{A_{h} }{A_{w} } .t$ )

4t $\frac{A_{h} }{A_{w} }$ = $\sqrt{H}$

t = $\frac{A_{w} \sqrt{H} }{4.A_{h} }$

Thus, the interval will be : 0 ≤ t ≤ $\frac{A_{w}\sqrt{H} }{4A_{h} }$

b) $r_{w}$ = 4 ft $h_{w}$ = 12 ft and $r_{h}$ = 1/2 in

Area of the water:

$A_{w} = \pi r^{2}$

$A_{w} = \pi .4^{2}$

$A_{w}$ = 16πft²

Area of the hole:

1 in = $\frac{1}{12}$ ft

so, $r_{h}$ = $\frac{1}{2}.\frac{1}{12}$ = $\frac{1}{24}$

$A_{h} = \pi .r^{2}$

$A_{h} = \pi .\frac{1}{24} ^{2}$

$A_{h}$ = $\frac{\pi }{576}$ ft²

As H=10 and having t = $\frac{A_{w} \sqrt{H} }{4.A_{h} }$ :

t = $\frac{16.\pi .\sqrt{12} }{4.\frac{\pi }{576} }$

t = 4.576. $\sqrt{12}$

t = 7981.3 seconds

t = $\frac{7981.3}{60}$ = 133 minutes

It takes 133 minutes to empty.

8 0

3 years ago

Simplity 2(- 4)+7(x + 2).

Evgesh-ka [11]

Answer:

Step-by-step explanation:

To find your answer you first have to multiply the numbers that aren’t in parentheses and you multiply 2 and 7 and you get 14 then you don’t have to worry about the x because it is a variable so now add -4 +2. but first we have to turn negative into positive so you add -4 + 8

7 0

3 years ago

Factor the polynominal 5x^2y + 6x^2y^3 - 3x^3y^2

Mariana [72]

Answer: x^(2)y(5+6y^(2)-3xy)

Step-by-step explanation: Factor x^(2)y out of 5x^(2)y + 6x^(2)y^(3)- 3 x^(3)y^(2)

brainliest or a thank you please! :) <33

6 0

3 years ago

Kiana wants to cover a triangular area of her background with red, concrete patio stones. Each stone costs $0.42 and covers 29.2

Alex73 [517]

1. The problem says that the stone covers 29.26 square inches. So, the first thing you must do, is to convert 29.26 square inches (in²) to square feet (ft²):

1 in²=0.00694 ft², then:

29.26x0.00694= 0.20 ft²

2. The triangular area has the following surface:

A=bxh/2
A=(6 ft)(8 ft)/2
A=24.0 ft²

3. <span> Finally, the number of stones (N) that cover the triangular area is:
</span>
N= 24.0 ft²/0.20 ft²
N=120 stones

Answer: <span>Kiana should buy 120 stones to cover the triangular area in her backyard.</span>

8 0

4 years ago