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4 years ago

I need help on this pleasssee!!

Mathematics

1 answer:

aev [14]4 years ago

8 0

Answer:

Option D. $x=-3$

Step-by-step explanation:

we have

$f(x)=\frac{5x^{4}-7}{x+3}$

we know that

The denominator cannot be equal to zero

therefore

To find the equation of the vertical asymptote equate the denominator to zero

$(x+3)=0$

$x=-3$ -----> equation of the vertical asymptote

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Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = x^3 – 3x^2 + 2x

castortr0y [4]

Answer: The correct option is second, i.e. ,"2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".

Explanation:

The given equation is,

$y=x^3-3x^2+2x$

It can be written as,

$f(x)=x^3-3x^2+2x$

Find the zeros of the equation. Equation the function equal to 0.

$0=x^3-3x^2+2x$

$x(x^2-3x+2)=0$

$x(x^2-2x-x+2)=0$

$x(x-2)(x-1)=0$

So, the three zeros are 0, 1 and 2.

The graph of the equation is shown below.

From the given graph it is noticed that the enclosed by the curve and x- axis is lies between 0 to 2, but the area from 0 to 1 lies above the x-axis and area from 1 to 2 lies below the x-axis. So the function will be negative from 1 to 2.

The area enclosed by curve and x-axis is,

$A=\int_{0}^{1}f(x)dx+\int_{1}^{2}[-f(x)]dx$

$A=\int_{0}^{1}f(x)dx-\int_{1}^{2}f(x)dx$

From the graph it is noticed that the area from 0 to 1 is symmetric or same as area from 1 to 2. So the total area is the twice of area from 0 to 1.

$A=2\int_{0}^{1}f(x)dx$

$A=2\int_{0}^{1}[x^3-3x^2+2x]dx$

Therefore, The correct option is "2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".

3 0

3 years ago

Find the missing symbol: 1/6 ? 1/2<br><<br>><br>=<br>please help

Amanda [17]

Answer:

1/6 < 1/2

Step-by-step explanation:

The larger the denominator, the smaller that fraction would be. Both of the numerators are equal, so we don't have to worry about that. Since 6 is larger than 2, we know that 1/2 is larger than 1/6. hope I helped:))

8 0

3 years ago

Read 2 more answers

Melcher used 24% if the memory card on his digital camera while taking pictures at a family reunion. If melcher took 96 pictures

Leya [2.2K]

24/100 X = 96

24x = 9600

X= 9600/24 = 400 pics is the full memory

3 0

4 years ago

Can I please get some help

Aleksandr [31]

Answer:

a. $1.76$

b. $2.5$

Step-by-step explanation:

You have the following formula given in the exercise:

$t=\frac{\sqrt{100-h}}{4}$

a. If the object is 50 feet above the ground, you can identify that the value of the variable "h" would be the following:

$h=50$

Then, knowing that value, you can substitute it into the given formula and then evaluate in order to calculate the time in seconds for the object to be 50 feet above the ground.

This is:

$t=\frac{\sqrt{100-50}}{4}\\\\t=1.76$