Tomas drew a rectangle with an area of 6 square cintemeters. What is the greatest possible perimeter for this rectangle

Answer:

b) local minimum at [tex]x=\frac{1}{e}[/tex]

c) Graph of the function is convex

Step-by-step explanation:

We are told that [tex]f'(\frac{1}{e})=0[/tex], which implies there is a turning/stationary point at [tex]x=\frac{1}{e}[/tex].

Substituting [tex]x=\frac{1}{e}[/tex] into [tex]f''(x)[/tex] will tell us if the turning point is a minimum or a maximum:

[tex]f''(\frac{1}{e})=\frac{1}{\frac{1}{e} } =e>0 \implies \textsf{local minimum}[/tex]

Therefore, statement a) is false and statement b) is true.

If the function has a minimum turning point, then this implies that the curve is convex.  Therefore, statement c) is true.

Extremum = local min and max points.

We have already established that there is a local minimum at [tex]x=\frac{1}{e}[/tex], therefore statement d) is false.

I know this is not needed for this question, but here are the workings to detemine the equation of the function (I've also attached a graph).  This supports the answers above.

[tex]\textsf{if} \ f''(x)=\frac{1}{x}\\\\\implies f'(x)=\int f''(x) \ dx \\\\\implies f'(x)=ln|x|+C\\[/tex]

[tex]\textsf{if} \ f'(\frac{1}{e})=0\\\\\implies ln|\frac{1}{e}|+C=0\\\\\implies -1+C=0\\\\\implies C=1\\\\[/tex]

[tex]\implies f'(x)=ln|x|+1\\[/tex]

[tex]\textsf{if} \ f'(x)=ln|x|+1\\\\\implies f(x)=\int f'(x) \ dx\\\\\implies f(x)=xln(x)-x+x+C\\\\\implies f(x)=xln(x)+C[/tex]

Answer:

7 movie tickets 59.5

Step-by-step explanation:

divide 34 by 4 and then you get 8.5 then multiply that by 7

Answer:

It's not possible to determine the perimeter of a rectangle given only the area. The area of a rectangle depends on two unknowns, the length and the width, so you must be given at least one side of the rectangle along with the area to determine the other side and, thus, the perimeter

Step-by-step explanation:

Answer:

It is not possible to determine the perimeter of a figure given its area.

Answer:

Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.

Exact Form:

x=1/2,−5

Decimal Form:

x=0.5,−5

Step-by-step explanation:

branliest

Answer:

A and B both equal -6c - 2c

Since you requested for only the answer, here you go:

the slope is 0

The y int is none

the equation is

x=-7

Step-by-step explanation:

Slope formula:

[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]

Substitute the points into the formula format:

[tex] \frac{4}{ - 5} - \frac{8}{ - 5} = m[/tex]

Solve:

[tex] \frac{ - 4}{0} = m[/tex]

When a slope has a run (x) of 0, the slope is undefined.

Answer:

-4 / 0

Step-by-step explanation:

Given the following question:

(-5, 8), (-5, 4)

In order to find the answer to this question we will use rise over run, substitute the values, and then solve.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]
(-5, 8), (x1, y1)
(-5, 4), (x2, y2)
4 - 8 = -4
-5 - -5 = 0
m = -4 / 0

Hope this helps.

Step-by-step explanation:

Hope it will helps you..

Your photo is so unclear ..but i try my best to understand...

Answer:

Ask yourself what a percentage means. It means out of a hundred.

20 percent is basicallly 20/100
20/100 is 0.2

So 20 percent of 58 is asking-

0.2*58 = ?

Solve and you’ll get

$11.60

Answer:

Option B is the correct answer.

Step-by-step explanation:

[tex]f(x)=27\bigg(\frac{1}{3}\bigg)^x[/tex] matches the table.

• When x = 0

[tex]\implies f(x)=27\bigg(\frac{1}{3}\bigg)^0= 27*1=27[/tex]

•When x = 1

[tex]\implies f(x)=27\bigg(\frac{1}{3}\bigg)^1= 27*\frac{1}{3}=9[/tex]

•When x = 2

[tex]\implies f(x)=27\bigg(\frac{1}{3}\bigg)^2= 27*\frac{1}{9}=3[/tex]

•When x = 3

[tex]\implies f(x)=27\bigg(\frac{1}{3}\bigg)^3= 27*\frac{1}{27}=1[/tex]

•When x = 4

[tex]\implies f(x)=27\bigg(\frac{1}{3}\bigg)^4= 27*\frac{1}{81}=\frac{1}{3}[/tex]

1/8 x 5 = 5/8

5/8 of the passengers were adults :)

Answer:

-5w - 5/2

Step-by-step explanation:

hope it helps

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7300\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=7300\left(1+\frac{0.042}{4}\right)^{4\cdot 5}\implies A=7300(1.0105)^{20}\implies A\approx 8996[/tex]

Answer:

Step-by-step explanation:

f(t)=t²-5t , t≤-10

f(-10)=(-10)²-5(-10)=100+50=150

Answer:

The answer is 6 pounds Which is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter of a rectangle  =  52 cm

2(length + width)  =  52 ==>  l + w  =  26

Let x be the length

width  =  (x/3) + 2

x + (x/3) + 2  =  26

[(3x + x)/3]  + 2 =  26

4x / 3  =  24

4x  =  24 (3)

x  =  6(3) ==>  18 cm

Width  =  (18/3) + 2

=  6 + 2  =  8 cm

So, the required dimension is 18 cm x 8 cm.

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Thank You!

Answered by: ms115

Answer:

Step-by-step explanation:

Let the perimeter be:

Find the numbers for the perimeter:

For A:

That means A is incorrect.

For B:

That means B is correct.

For C:

That means C is incorrect.

Correct choice is B.

Answer:

This doesn't make sense?

Step-by-step explanation:

What is the question?

࿐αɴѕωєя࿐

m = 93 - h / b

Step-by-step explanation:

bm + h = 93

bm = 93 - h

m = 93 - h / b

Hope it helps ⚜

Answer:

[tex]f(x)=x(x-9)(x-6)(x+8)(x-7)[/tex]

Step-by-step explanation:

If [tex]9=x[/tex]  then [tex]x-9=0[/tex]

If [tex]6=x[/tex]  then [tex]x-6=0[/tex]

etc.

So  [tex]f(x)=x(x-9)(x-6)(x+8)(x-7)[/tex]

Step-by-step explanation:

27 = 3×3×3

logb(m×n) = logb(m) + logb(n)

logb(27) = logb(3×3×3) = logb(3)+logb(3)+logb(3) =

= 3×logb(3) = 3×1.10 = 3.30

Answer:

Yes

Step-by-step explanation:

Non members - 8*6 = $48

Members - 20+(4*6) = $46

She should become a member of the gym because she will pay $2 less overall.

Answer:

Sarah should become a member. She would be paying a lot less money and be able to take more classes for cheaper

Step-by-step explanation:

Non member amount for 6 classes-   $8*6= $48

Member amount for 6 classes-  $4*6= 24  ($20 fee) = $44

As you can see above, the cost for 6 classes with a membership is cheaper than without a membership

Answer:

3; 5; 35

Step-by-step explanation:

Sorry can’t help

Answer:

sodas sold = 138

hot dogs sold = 79

Step-by-step explanation:

let s = number of sodas sold

let h = number of hot dogs sold

equation 1:    h + s = 217

equation 2:    h + 59 = s

Substitute equation 2 into equation 1 and solve for h:

⇒ h + (h + 59) = 217

⇒ 2h + 59= 217

⇒ 2h =158

⇒ h = 79

Substitute found value of h into equation 2 and solve for s:

⇒ 79 + 59 = s

⇒ s = 138

answer:

number of hot dogs is 79

number of sodas is 138

explanation:

solve:

Therefore:

x + x + 59 = 217

2x = 158

x = 79

79 hot dogs

79 + 59

138 sodas

Answer:

I think its B

Step-by-step explanation:

Answer: 10

Step-by-step explanation:

3 = $1.80

1 = $0.60

$6 = 10 pens