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2 years ago

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Mathematics

1 answer:

Readme [11.4K]2 years ago

4 0

Answer:

a. 36

b. 4

c. -11

d. 2

e. -20

Step-by-step explanation:

20 + 16 = 36

20 + (-16)

20 - 16 = 4

5 + (-16)

5 - 16 = -11

-9 + 11

11 - 9 = 2

-9 + (-11)

-9 - 11 = -20

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x^2+2x+7=21 the approximate value of the greatest solutoon to the equation, rounded to the nearest hundreth

daser333 [38]

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Answer:

x ≈ 2.87

Step-by-step explanation:

We can subtract 6 to put the equation into a form easily solved.

x^2 +2x +1 = 15

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x +1 = √15 . . . . . for the greatest solution, we only need the positive root

x = √15 -1 ≈ 2.87

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2 years ago

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Step-by-step explanation:

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3 years ago

Water is leaking out of an inverted conical tank at a rate of 6800 cubic centimeters per min at the same time that water is bein

ivanzaharov [21]

Answer:

1508527.582 cm³/min

Step-by-step explanation:

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 6800 cm³/min,

dV/dt = k - 6800

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 12 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

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3 years ago

Which ratio is greater than 11/16?<br> a. 22:32<br> b. 3:8<br> c. 1:2<br> d. 3:4

Allushta [10]

Answer:

3/4

Step-by-step explanation:

Due it having a ratio of .75 instead of the .6875 of the other answers.

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3 years ago

Consider the function. What is the y-intercept of f–1(x)? –16 –12

Mekhanik [1.2K]

<h2>Explanation:</h2><h2></h2>

Hello! Remember you have to write clear questions in order to get good and exact answers. Here, I'll assume the function as:

$f(x)=x^2+2x-16$

The y-intercept of a function is the point at which the graph of the function touches the y-axis. This occurs when we set $x=0$ . In other words, we define the y-intercept (let's call it $b$ as:

$b=f(0)$

Setting $x=0$ in our function we have:

$b=f(0)=(0)^2+2(0)-16 \\ \\ \boxed{b=f(0)=-16}$

So <em>in this context the y-intercept is -16</em>

7 0

2 years ago