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4 years ago

12

Find the limit of the function by using direct substitution. limit as x approaches one of quantity x squared plus three x minus

one.

1 answer:

ivann1987 [24]4 years ago

6 0

<u>Answer:</u>

Limit = -1

<u>Step-by-step explanation:</u>

We are given the following function:

$x^2 + 3x -1$

We are to calculate the limit of this function as x approaches zero.

For that, we will use direct substitution method and substitute the x with 0 in the given function to calculate its limit as follows:

$x ^ 2 + 3 x - 1$

$( 0 ) ^ 2 + 3 ( 0 ) - 1 = - 1$

Therefore, the limit is -1.

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If x2=18x+y and y2=18y+x, then find the value of root

mezya [45]

Answer:

$\sqrt{x^2+y^2+1}=18$

Step-by-step explanation:

We are given:

$x^2=18x+y\qquad\qquad[1]$

$y^2=18y+x\qquad\qquad[2]$

Subtracting [1] and [2]:

$x^2-y^2=18x+y-(18y+x)$

Operating:

$x^2-y^2=18x+y-18y-x$

Recall:

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

Substituting:

$(x-y)(x+y)=18x+y-18y-x$

Rearranging:

$(x-y)(x+y)=18x-18y-(x-y)$

$(x-y)(x+y)=18(x-y)-(x-y)$

Dividing by x-y (recall x≠y):

$x+y=18-1=17$

$x+y=17\qquad[3]$

Now we add [1] and [2]:

$x^2+y^2=18x+y+18y+x$

Rearranging:

$x^2+y^2=18x+18y+x+y$

$x^2+y^2=18(x+y)+(x+y)$

$x^2+y^2=19(x+y)$

Substituting from [3]

$x^2+y^2=19*17=323$

Adding 1:

$x^2+y^2+1=324$

Taking the square root:

$\sqrt{x^2+y^2+1}=\sqrt{324}=18$

Thus:

$\mathbf{\sqrt{x^2+y^2+1}=18}$

3 0

3 years ago

PLEASE HELP THIS IS A MULTIPLE CHOICE QUESTION !!!!

SOVA2 [1]

Answer:

c) subtraction property of order

Step-by-step explanation:

To get from line 1 to line 2, 3 was subtracted from both sides of the inequality. The "subtraction property of order" says you can do that without changing the order or the solution.

It should not be a surprise that when subtraction is involved, the associated property has "subtraction" in its name.

8 0

4 years ago

X squared +14x+2 = 0

Naya [18.7K]

Answer:

x = -2/14

Step-by-step explanation:

+14x +2 = 0

+14x = 0 -2

14x = -2

x = -2/14

7 0

3 years ago

A circle is centered at $O$ and has an area of $48 \pi.$ Let $Q$ and $R$ be points on the circle, and let $P$ be the circumcente

nikklg [1K]

Answer:

Area of Triangle QRP = 3 $\sqrt{3}$

Step-by-step explanation:

According to Question , We have a circle With Centre 'O' & Area 48 $\pi$ .

Area Of Circle = 48 $\pi$

$\pi$ $r^{2}$ = 48 $\pi$

r = $\sqrt{48}$

Now We Have Two Points Given On Circle Q & R , P Is Circumcentre Of Triangle QRO .

Thus A Circle Can Also Be Formed with Centre P . ( See attachment For Diagram )

Now The Diameter of Circle With Centre P = Radius Of Circle with Centre O

so Radius Of Circle With Centre P( $r_{2}$ ) = $\frac{\sqrt{48}}{2}$

Now We Have To Find Area Of Equilateral Triangle .

A = $\frac{\sqrt{3}}{4} r_{2} ^{2}$

A= $\frac{\sqrt{3} }{4} * \frac{\sqrt{48} }{2}*\frac{\sqrt{48} }{2}$

The Area Of PQR is = 3 $\sqrt{3}$

For Diagram , Please Find In Attachment

7 0

3 years ago

a recycling bin is in the shape of a rectangular box. find the height of the box if its length is 16ft, its width is 6 ft, and i

Andre45 [30]

Answer:

Height 4 ft

Step-by-step explanation:

Surface area= 2(lw + lh + wh) =

2(16)16)+2(16h)+2(6h) =

2(16)(6)+32h+12h=368

192 + 44h = 368

44h = 368 - 192

44h = 176

h = 176/44

6 0

3 years ago