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Xelga [282]
3 years ago
15

-6+x/x^4 limit at x →0

Mathematics
1 answer:
Jlenok [28]3 years ago
7 0

Answer:

not existing

Step-by-step explanation:

\frac{ - 6 + x}{ {x}^{4} }

lim x goes to 0 is

\frac{ - 6 + 0}{ {0}^{4} }  =   \frac{ - 6}{0}

so not exist

I'm not sure if u mean that or this

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E - 867 = 108; E = need help
lina2011 [118]
To solve for E you'll add 867 to 108.

E - 867 = 108
E = 108 + 867
E = 975

Hope this helps :)

7 0
3 years ago
Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola
mote1985 [20]

ANSWER

This is an ellipse. The equation is:

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

(a+b)^2=a^2+2ab+b^2

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

16x^2-32x=16(x^2-2x)

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

(x-1)^2=x^2-2x+1

To maintain the equation, we have to subtract 1,

16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

16(x-1)^2-16+9y^2+72y+16=0

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

9y^2+72y=9(y^2+8y)

Following the same reasoning as before, we have that the perfect binomial squared is,

(y+4)^2=y^2+8y+16

Remember to subtract the independent term to maintain the equation,

9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

16(x-1)^2-16+9(y+4)^2-144+16=0

Add like terms,

\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}

Add 144 to both sides,

\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}

As we can see, this is the equation of an ellipse. Its standard form is,

\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\  \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1

Note that we can simplify a and b,

\frac{12}{4}=3\text{ and }\frac{12}{3}=4

Hence, the equation of the ellipse is,

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

3 0
1 year ago
For your friend's birthday, you have 3 presents to wrap. Find the combined surface area of these 3 gifts so you know how much wr
omeli [17]

The answer is: 5,614 square inches.

The explanation is shown below:

1. The gift on the bottom is a rectangular prism. To calculate its surface area, you must apply the following formula:

 SA=2[(l)(w)+(l)(h)+(h)(w)]

Where l is the length (20 inches), w is the width (42 inches) and h is the heigth (16 inches).

2. Substitute values:

SA1=2[(20in)(42in)+(20in)(16in)+(16in)(42in)]=3,664in^{2

3. The surface area of the other gifts can be calculated with the formula for calculate the surface area of a cube:

SA=6s^{2}

Where s is the side.

4. The surface area of the bigger cube is:

SA2=6(15in^{2})=1,350in^{2}

5. The surface area of the smaller cube is:

SA3=6(10in^{2})=600in^{2}

6. The total surface area (the combined surface area of the three gifts) is:

SAt=SA1+SA2+SA3\\SAt=3,664in^{2}+1,350in^{2}+600in^{2}\\SAt=5,614in^{2}

7 0
3 years ago
Car is going at speed 40mph and travelled in 2 hours, what is the distance?
dalvyx [7]
Distance = speed * time
d = 40(2)
d = 80 miles
4 0
3 years ago
Read 2 more answers
Two more than the product of a number and 6 is equal to 5.
8090 [49]

Answer:

b = 1/2

Step-by-step explanation:

6x + 2 = 5

6x = 3

x = 1/2

8 0
3 years ago
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