Directions: Complete each proof using the properties of equality. Not all rows be used.

olganol [36]

Answer:

see below

Step-by-step explanation:

All of the given data sets have x-values that are sequential with a difference of 1. That makes it easy to determine the sort of sequence the y-values make.

first choice: the y-values have a common difference of -2. This will be matched by a linear model.

second choice: the y-values have a common difference of +2. Again, this will be matched by a linear model.

third choice: the y-values have a common ratio of -2. This will be matched by an exponential model.

fourth choice: the y-value differences are 3, 5, 7, increasing by a constant amount (2). This is characteristic of a sequence that has a quadratic model.

5 0

3 years ago

According to the rational root theorem, what are all the potential rational roots of f(x)=5x^3-7x+11

Genrish500 [490]

Answer:

$\pm11,\pm1,\pm\frac{11}{5},\pm\frac{1}{5}$

Step-by-step explanation:

The given polynomial function is

$f(x)=5x^3-7x+11$

According to the Rational Roots Theorem, the ratio of all factors of the constant term expressed over the factors of the leading coefficient.

The potential rational roots are

$\pm\frac{11}{1}=\pm11$

$\pm\frac{1}{1}=\pm1$

$\pm\frac{11}{5}$

$\pm\frac{1}{5}$

4 0

4 years ago

Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3

Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

$\frac{dV}{dt} = -kA$

Using Euler's method

$\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i} \\$

Where initial droplet volume is:

$V(0) = \frac{4pi}{3} * r(0)^3 = \frac{4pi}{3} * 2.5^3 = 65.45 mm^3$

Hence, the iterative solution will be as next:

i = 1, ti = 0, Vi = 65.45

$V'_{i} = -k *4pi*(\frac{3*65.45}{4pi})^(2/3) = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88$

i = 2, ti = 0.5, Vi = 63.88

$V'_{i} = -k *4pi*(\frac{3*63.88}{4pi})^(2/3) = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33$

i = 3, ti = 1, Vi = 62.33

$V'_{i} = -k *4pi*(\frac{3*62.33}{4pi})^(2/3) = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813$

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

$r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\$

The average change of droplet radius with time is:

Δr/Δt = $\frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min$

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0

3 years ago

Graph a line with a slope of 2/5 that contains the point(-2,4)

fomenos

Answer:

(-2, 4) (3, 6)

Step-by-step explanation:

I think this would be correct? haha

y2-y1/x2-x1

6-4=2,3--2(or 3+2 because 2 negatives make a positive)=5, so 2/5.

I hope this helps :)

7 0

3 years ago

The degree of a polynomial is

scoundrel [369]

The degree of a polynomial is the highest degree of its terms when the polynomial is expressed in its canonical form consisting of a linear combination of monomials.The degree of a term is the sum of the exponents of the variables that appear in it.

5 0

3 years ago