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attashe74 [19]
3 years ago
6

Statements :

Mathematics
1 answer:
3241004551 [841]3 years ago
4 0

Answer:

"e^x is irrational for every nonzero integer x"

Step-by-step explanation:

The original statement is

"e^x is rational for some nonzero integer x."

The negation is technically:

"It is NOT true that e^x is rational for some nonzero integer x."

So it's expressing that it's false that e^x can be rational for some nonzero integer x.

This just means that e^x is always irrational when x is a nonzero integer.

Which can be worded as

"e^x is irrational for every nonzero integer x"

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A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner
algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by  using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

V=x(216-24x-36x+4x^{2})

V=x(4x^{2}-60x+216)

V=4x^{3}-60x^{2}+216x

So now we can find the derivative of the volume:

V'=12x^{2}-120x+216

and set it equal to zero, so we get:

12x^{2}-120x+216=0

and now we can solve. We can start by factoring the left side of the equation, so we get:

12(x^{2}-10x+18)=0

which yields:

x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}

so we substitute the corresponding values:

x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

5 0
3 years ago
Leonardo da vinci took out A simple interest loan at 12.75% interest for 12 months. His previous balance is % 942.36. What is hi
makkiz [27]

Answer:

A = 2,384.1708

Step-by-step explanation:

A = P(1  + rt)

P = 942.36

r = 12.75%

t = 12 months

A = 942.36(1 + 12.75/100(12))

A = 942.36(2.53)

A = 2,384.1708

6 0
3 years ago
What is the equation in slope-intercept form of the line that passes through the points(-4,2) and (12,6)?
aleksandrvk [35]

Answer:

y=1/4x+3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(6-2)/(12-(-4))=4/(12+4)=4/16=1/4

y-y1=m(x-x1)

y-2=1/4(x-(-4))

y-2=1/4(x+4)

y=1/4x+4/4+2

y=1/4x+1+2

y=1/4x+3

3 0
2 years ago
In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x)
Tcecarenko [31]

Answer:

A

Step-by-step explanation:

6 0
3 years ago
5x-2y=2 slope intercept form?
Nata [24]

Answer:

y = \frac{5}{2}x-1  

Step-by-step explanation:

Slope-intercept form is represented by the formula y = mx  + b. So, to place the given equation in slope-intercept form, isolate the y on the left side and arrange the terms in that matching order. Remember, whatever you do to one side, do to the other:

5x-2y = 2\\-2y = -5x + 2\\\frac{-2}{-2}y = \frac{-5}{-2} x+\frac{2}{-2} \\y = \frac{5}{2} x-1

So, the slope-intercept form is y = \frac{5}{2}x-1.

6 0
3 years ago
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