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hram777 [196]
3 years ago
7

The equation y = 13x represents the rate, in gallons per minute, that Tank A at an aquarium fills with water. The table represen

ts the rate that Tank B fills with water. Determine which tank fills faster.

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
6 0

Answer:

Tank A fills up faster.

Step-by-step explanation:

Tank A is y = 13x

Tank B is y = 11x

Plz mark as Brainliest!

You might be interested in
13. Find the vertex of f(x)=x2 -6x +8 .
Mekhanik [1.2K]

9514 1404 393

Answer:

  a  (3,-1)

Step-by-step explanation:

The number that "completes the square" is the square of half the x-coefficient, (-6/2)^2 = 9. Rearranging the given function to include the square trinomial, we have ...

  f(x) = x^2 -6x +9 -1 . . . . . . . here, we have 8 = 9 - 1

  f(x) = (x -3)^2 -1 . . . . . . . . . . vertex form

Comparing this to the generic vertex form ...

  f(x) = (x -h)^2 +k . . . . . . . vertex at (h, k)

we see that h=3 and k=-1.

The vertex is (h, k) = (3, -1).

6 0
3 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is incre
Ainat [17]

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = \frac{d}{dx}[x^{4}ln(x)]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = 4x^{3}ln(x) + x_{4}.\frac{1}{x}

f'(x) = 4x^{3}ln(x) + x^{3}

f'(x) = x^{3}[4ln(x) + 1]

Now, find the critical points: f'(x) = 0

x^{3}[4ln(x) + 1] = 0

x^{3} = 0

x = 0

and

4ln(x) + 1 = 0

ln(x) = \frac{-1}{4}

x = e^{\frac{-1}{4} }

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

  • Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;
  • After 0.78, it increase (has a change of sign) and f is also defined;

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = x^{4}ln(x)

f(0.78) = 0.78^{4}ln(0.78)

f(0.78) = - 0.092

The point of <u>minimum</u> is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = \frac{d^{2}}{dx^{2}} [x^{3}[4ln(x) + 1]]

f"(x) = 3x^{2}[4ln(x) + 1] + 4x^{2}

f"(x) = x^{2}[12ln(x) + 7]

x^{2}[12ln(x) + 7] = 0

x^{2} = 0\\x = 0

and

12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56

Substituing x in the function:

f(x) = x^{4}ln(x)

f(0.56) = 0.56^{4} ln(0.56)

f(0.56) = - 0.06

The <u>inflection point</u> will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  x^{2}[12ln(x) + 7]

f"(0.1) = 0.1^{2}[12ln(0.1)+7]

f"(0.1) = - 0.21, i.e. <u>Concave</u> is <u>DOWN.</u>

f"(0.7) = 0.7^{2}[12ln(0.7)+7]

f"(0.7) = + 1.33, i.e. <u>Concave</u> is <u>UP.</u>

4 0
3 years ago
What is the constant proportionality of y=32x-4
alexira [117]
32 is the constant because it doesn’t have a letter
4 0
3 years ago
Read 2 more answers
What is the volume of a cube with an edge length of 3.2 meters?
klemol [59]
Volume of a cube is Side to the third power ( S^3)

S = 3.2 meters

Volume = 3.2^3

Volume = 32.768 cubic meters (cm^3)

You may need to round the answer.. The problem doesn't say how many decimal places are needed.
8 0
3 years ago
Read 2 more answers
The first jumbo jet was the Boeing 747, which is 70.5 meters long. The wingspan of a 747 is 60 meters. A model 747 has a wingspa
nydimaria [60]

Answer:

94 cm

Step-by-step explanation:

Set up and solve an equation of ratios:

wingspan         length

60 meters        70.5 m

----------------- = ----------------

80 cm                   x

Cross multiplying:

(60 m)x = (70.5 m)(80 cm)

Solve for x by dividing both sides of this equation by 60 m:

x = (70.5 m)(80 cm) / (60 m) = 94 cm

The length of the model should be 94 cm.

6 0
3 years ago
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