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3 years ago

Simplify the following rational expression and state for what values they are undefined.

Mathematics

2 answers:

Svetllana [295]3 years ago

8 0

<em>Answer: </em>d - 2 and d cannot equal 8

<em>Step-by-step explanation:</em> To simplify this rational expression, start by factoring both the numerator and the denominator.

So factoring the numerator in this problem, we have a

trinomial that factors as the product of two binomials.

So we are looking for factors of +16 that add to -10 which are -8 and -2.

So we have (d - 8)(d - 2) in the numerator.

The denominator doesn't factor however.

So we have $\frac{(d - 8)(d - 2)}{(d - 8)}$ and the d - 8's cancel leaving us with d - 2.

The values d cannot be happen when the denominator is set equal to 0.

So we have d - 8 = 0 which means d = 8.

This means d = 8 wouldn't work!

QveST [7]3 years ago

3 0

Answer:

d-2 and d cannot = 8

Step-by-step explanation:

d^2 -10d+16

-----------------------

d-8

Factor the numerator

( d-8)(d-2)

-------------------

d-8

The undefined values occur when the denominator is equal to zero

d-8 = 0

d= 8

This means d cannot equal 8

Now cancel like terms in the equation ( d-8)

This yields d-2

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Researchers at a lake have determined that the percentage of fish in the lake that are intolerant to pollution can be estimated

dusya [7]

Answer:

a. 23.02 %

b. 49%

c. W

Step-by-step explanation:

Solution:-

- A multi-variable function for the percentage of fish in the lake that are intolerant to the pollution is given as:

$P ( W , R , A ) = 49 - 1.61W - 1.41R - 1.38A$

Where,

W: percentage of wetland

R: percentage of residential area

A: percentage of agriculture

- We are to evaluate the percentage of fish intolerant to pollution in the case where W = 3 , R = 15 , A = 0. We will plug in the values in the modeled function P ( W , R , A ) as follows:

$P ( 3 , 15 , 0 ) = 49 - 1.61*3 - 1.41*15 -1.38*0\\\\P ( 3 , 15 , 0 ) = 23.02\\$

- To determine the maximum percentage of fish that will be intolerant to pollution we will employ the use of critical points. The critical point that is defined by the linear relationship between P and all other parameters ( W, R , A ). The maximum value occurs when W = R = A = 0.

$P ( 0 , 0 , 0 ) = 49 - 1.61*0 -1.41*0 - 1.38*0 = 49$

- Hence, the maximum value of the function is 49%.

- The linear relationship between each induvidual parameter ( R, W , A ) and the function ( P ) is proportional in influence. The extent of influence can be quantized by the constant multiplied by each parameter.

- We see that that ( 1.61*W ) > ( 1.41R ) > ( 1.38A ). The greatest influence is by parameter ( W ) i.e the influence of percentage of wetlands .

6 0

3 years ago

g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the sh

Maslowich

Answer:

0.3537 feet per minute.

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=10$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10$

We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.

$When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute$