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4 years ago

8.) A linear equation has more than one y-intercept. What can you conclude about the graph of the equation??

2 answers:

5 0

I'm not sure if this is a trick question, but the definition of a linear function prevents the function from having more than one y-intercept. x-values can't be shared in a function; there is a unique x value for every y value. at the y-axis, the value of x is 0. two y-intercepts would mean that x would be 0 for TWO points on the linear function, which doesn't pass the vertical line test and, therefore, isn't a function.

a graph CAN, however, have more than one x-intercept. the line y = 0, which passes the vertical line test and sits directly on top of the x-axis, has infinitely many x-intercepts and it is still a linear function.

Vladimir [108]4 years ago

4 0

Answer:

Step-by-step explanation:

A straight line can either have 1 y-intercept or infinitely many y intercepts. The only case in which there are infinitely many y-intercepts is when the line represents the y-axis itself. On y-axis, x is always 0. So the line that represents the y-axis is the line x=0. However, it is not a linear equation. In short, only the line representing y-axis has more than 1 y-intercepts. There cannot be such a linear equation(function).

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Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the

m_a_m_a [10]

Answer:

Required volume is $\frac{4864\pi}{3}$ unit.

Step-by-step explanation:

Given equations of curves,

$y=32-x^2$ , $y=x^2$

substitute second in first we will get,

$x^2=36-x^2\implies x^2=16\implies x=\pm 4$

When $x=4, y=16$ and $x=-4, y=16$ . Thus both curves intersect at the points (4,16),(-4,16). And thus $-4$ .

Considering width of the representative rectangle as $\Delta x$ which is parallel to x-axis because of considering cylindrical shell. Therefore volume of the shell is given by,

$V_{Shell}=(\textit{Length of box})\times (\textit{Width of box})\times (\textit{Thikness of box})$

Now,

Length of generating box=Length of $\Delta x$ from line x=4(axis of revolution)=circumference of the shell=(4-x)

Width of box= $(36-x^2)-x^2$

Hence,

$V_{Shell}$

$=\int_{-4}^{4}2\pi (4-x)(36-2x^2)dx$

$=2\pi\int_{-4}^{4}(144-36x-8x^2+2x^3)dx$

$=2\pi\{144\big[x\big]_{-4}^{4}-18\big[x^2\big]_{-4}^{4}-\frac{8}{3}\big[x^3\big]_{-4}^{4}+\frac{1}{2}\big[x^4\big]_{-4}^{4}\}$

$=\frac{4864\pi}{3}$

which is required volume of generating area.

3 0

3 years ago

Find the median the first and third quartiles the interquartile range and my outliers for set of data 81,69,90,79,59,125,95,116,

JulsSmile [24]

Answer:

Step-by-step explanation:

Find the median of the first and third quartiles

81, 69 ,90, 79, 59, 125, 95, 116, 183, 97, 92, 50, 122, 55, 92

50, 55, 59, 69, 79, 81, 90, 92, 92, 95, 97, 116, 122, 125, 183.

The first quartile: 50, 55, 59, 69, 79, 81, 90: median of the first quartile is 69

The third quartile: 92, 95, 97, 116, 122, 125, 183: median of the third quartile is 116.

The interquartile range is the difference between the median of both the first and third quartile: which is 116 - 69 = 47.

There are no outliers in this set of data

5 0

3 years ago

Jimmy's cedar trunk is in the shape of a rectangular prism and has a volume of cubic yard. How many cubic blocks with a side len

vagabundo [1.1K]

The answer is 6 }{}{}{{}

4 0

3 years ago

Read 2 more answers

(4) use the method of lagrange multipliers to determine the maximum value of f(x, y) = x a y b (the a and b are two fixed positi

wlad13 [49]

Assuming $f(x,y)=x^ay^b$ . We have Lagrangian

$L(x,y,\lambda)=x^ay^b+\lambda(x+y-1)$

with partial derivatives (set to 0)[/tex]

$L_x=ax^{a-1}y^b+\lambda=0\implies ax^{a-1}y^b=-\lambda$
$L_y=bx^ay^{b-1}+\lambda=0\implies bx^ay^{b-1}=-\lambda$
$L_\lambda=x+y-1=0$

$\implies ax^{a-1}y^b=bx^ay^{b-1}\implies -bx+ay=0$
$x+y-1=0\implies x+y=1$

Solving this system of linear equations yields $x=\dfrac a{a+b}$ and $y=\dfrac b{a+b}$ as the sole critical point, which in turn gives a maximum value of $f\left(\dfrac a{a+b},\dfrac b{a+b}\right)=\dfrac{a^ab^b}{(a+b)^{a+b}}$ .

8 0

3 years ago

Help plz I will mark brainliest

bearhunter [10]

Answer:

Angle 2= 127

Angle 3= 23

The measure of angle 4 is 90° because the 90° is marked

4 0

3 years ago