(Absolute value of 12 - 20) - (27/3 + 11) ^2

Mathematics

1 answer:

rodikova [14]3 years ago

6 0

Answer:

the answer is 400-8=394.

Step-by-step explanation:

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At time t=0 water begins to drip out of a pipe into an empty bucket. After 56 minutes 8 inches of water are in the bucket. What

oksano4ka [1.4K]

Answer:

The linear function of the bucket is $y = \frac{1}{7}\cdot x$ , where $y$ represents the amount of water, measured in inches, and $x$ is the time, measured in minutes.

Step-by-step explanation:

According to the Euclidean and Analytical Geometries, we can construct a line by knowing two distinct points on a plane. Besides, we know two different conditions for the bucket:

Initial condition of the bucket

$A(x,y) = (0\,min, 0\,in)$

Final condition of the bucket

$B(x,y) = (56\,min, 8 in)$

The equation of the line is defined by the following model:

$y = m\cdot x + b$ (1)

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$b$ - y-Intercept, dimensionless.

$m$ - Slope, dimensionless.

Based on the known conditions of the bucket, we obtain the following system of linear equations:

$b = 0$ (2)

$56\cdot m +b = 8$ (3)

The solution of the system of equations is:

$m = \frac{1}{7}$ and $b = 0$

Then, the linear function of the bucket is $y = \frac{1}{7}\cdot x$ , where $y$ represents the amount of water, measured in inches, and $x$ is the time, measured in minutes.

7 0

3 years ago

Identify each expression and value that represents the area under the curve y=x^2+4 on the interval [-3,2]

Alina [70]

The area under a graph is given by the integral of that function, evaluated in the interval of interest:

$\displaystyle \int_{-3}^2 x^2+4\;dx = \left[\dfrac{x^3}{3}+4x\right]_{-3}^2 = \left[\dfrac{2^3}{3}+4\cdot 2\right]-\left[\dfrac{(-3)^3}{3}+4\cdot(-3)\right] = \left[\dfrac{8}{3}+8\right]-\left[-9-12\right] = \dfrac{32}{3}+21 = \dfrac{95}{3}$