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3 years ago

10

Is (2, 10) a solution to the inequality y>4×+1?

1 answer:

OLEGan [10]3 years ago

5 0

Answer:

yes

Step-by-step explanation:

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The diagram below shows 5 identical bowls stacked one inside the other. The height of 1 bowl is 2 inches. The height of 5 bowls

padilas [110]

(Bowls, Height) (1, 2) (5,5)

Slope is (5-2)/(5-1) = 3/4 inch
y = (3/4)x + b
(2) = (3/4)(1) + b
(2)-(3/4) = b

B=1.25. Y= 0.75*x + 1.25.

Part B
X is the number of bowls in the stack and Y is the corresponding height of the stack.

7 0

3 years ago

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

3 years ago

Which is the best estimate?

kotegsom [21]

7.5 bbbbbbbbbbbbbbbbbb

6 0

2 years ago

Read 2 more answers

Plz help ill give u brainlist

Travka [436]

The surface area of the box will be 112 in²

Explanation

According to the given diagram, the shape of the box is Right Rectangular prism.

The formula for the surface area is :

$A= 2(w*l+h*l+h*w)$ , where $l=$ length, $w=$ width and $h=$ height of the rectangular prism

Given in the diagram that, $l= 8, w=4 , h=2$

So, plugging the values into the formula...

$A= 2(4*8+2*8+2*4)\\ \\ A= 2(32+16+8)\\ \\ A=2(56)\\ \\ A=112$

So, the surface area of the box is 112 in²

3 0

3 years ago

How do you solve 4x-7x=13

Rufina [12.5K]

13=-3x

3x=-13

x=-13/3=-4 1/3

3 0

3 years ago

Read 2 more answers