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2 years ago

Prove that this equation have no solutions

Mathematics

2 answers:

melomori [17]2 years ago

7 0

Answer:

Step-by-step explanation:

(x - 4)² = -1/(x+3)³

(x - 4)²(x + 3)² = -1

[(x - 4)(x + 3)]² = -1

This has no solution since a perfect square (on the left) is never negative.

12345 [234]2 years ago

6 0

Answer:It doesn't

Step-by-step explanation:

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All of the following are equivalent, except _____.

puteri [66]

Everything except 11x2

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2 years ago

Read 2 more answers

H(x)={(-7,-1),(0,0),(5,8)} domain and range

Bingel [31]

Answer:

The domain is -7, 0, and 5

The range is -1, 0, and 8

Step-by-step explanation:

The domain of a set of points is the x-value. In this case the x-values are -7, 0, and 5 respectively. The range of a set of points is the y-value so in this case the range is -1, 0, and 8.

7 0

2 years ago

A marketing researcher wants to find a 96% confidence interval for the mean amount those visitors spend per person per day while

ki77a [65]

Answer:

$n=(\frac{2.054(12)}{4})^2 =37.97 \approx 38$

So then the minimum sample to ensure the condition given is n= 38

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=12$ represent the population standard deviation

n represent the sample size

ME = 4 the margin of error desired

Solution to the problem

When we create a confidence interval for the mean the margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =4 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 96% of confidence interval now can be founded using the normal distribution. The significance is $\alpha=1-0.96 =0.04$ . And in excel we can use this formula to find it:"=-NORM.INV(0.02;0;1)", and we got $z_{\alpha/2}=2.054$ , replacing into formula (b) we got:

$n=(\frac{2.054(12)}{4})^2 =37.97 \approx 38$

So then the minimum sample to ensure the condition given is n= 38

5 0

3 years ago

Find the volume of the wedge cut from the first octant by the cylinder z=12-3y^2 and the plane x+y=2.

LuckyWell [14K]

Answer:

The wedge cut from the first octant ⟹ z ≥ 0 and y ≥ 0 ⟹ 12−3y^2 ≥ 0 ⟹ 0 ≤ y ≤ 2

0 ≤ y ≤ 2 and x = 2-y ⟹ 0 ≤ x ≤ 2

V = ∫∫∫ dzdydx

dz has changed from zero to 12−3y^2

dy has changed from zero to 2-x

dx has changed from zero to 2

V = ∫∫∫ dzdydx = ∫∫ (12−3y^2) dydx = ∫ 12(2-x)-(2-x)^3 dx =

24(2)-6(2)^2+(2-2)^4/4 -(2-0)^4/4 = 20

Step-by-step explanation:

8 0

3 years ago

What is the y-intercept of the line perpendicular to (1,1) and (-3,-1) and passes through (-3,-2)

marin [14]

Answer:

-8

Step-by-step explanation:

Let's first establish the reference line (the one that the second line will be perpendicular to). We are told that this line passes through two points:

(1,1) and (-3,-1).

We'll find a line equation using the point slope form format to start:

(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.

(x,y) = (1,1)

(x1,y1) = (-3,-1)

Rearrange the equation:

(y - y1) = m * (x - x1)

m = (y - y1)/ (x - x1)

m = (1-(-1))/(1-(-3))

m = 2/4, or 1/2: The slope is 1/2. [<u>This is "m."]</u>

We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:

y = (1/2)x + b

Use either of the two given points. I'll use (1,1) since I have memorized the "1" math tables.

y = (1/2)x + b

1 = (1/2)(1) + b for (1,1)

b = 1/2

This makes the reference line: y = (1/2)x+(1/2)

===

The line perpendicular must have a slope that is the negative inverse of (1/2). This would be -(2/1), or -2.

We can then write y = -2x + b

To find be, enter the one given point for this line: (-3,-2)

y = -2x + b

-2 = -2(-3) + b

-2 = 6 + b

b = -8

The perpendicular line is thus:

y = -2x - 8

It has a y-intercept of -8

5 0

2 years ago