Given log base 2 =1/6, what is log base 4

0.66 inches of material is needed to be cut off to make the volume maximum.

When the second derivative of a function is negative, the function has a maximum point and if the second derivative is positive, the function has a minimum point.

Analysis:

After cut and folded, length = 8-2x

Width = 3-2x

Thickness = x.

Volume of the folded shape = (8-2x)(3-2x)(x)

After expansion, V = 4[tex]x^{3}[/tex]-[tex]22x^{2}[/tex] +24x

for turning point of the function, dv/dx = 0

dv/dx = 12[tex]x^{2}[/tex] -44x + 24

lowest term = 3[tex]x^{2}[/tex] - 11x + 6

3[tex]x^{2}[/tex] - 11x + 6 = 0

3[tex]x^{2}[/tex] - 9x -2x +6 = 0

3x(x-3) -2(x-3) = 0

(3x-2)(x-3) = 0

x = 2/3 or x = 3

To test for maximum point, we differentiate dv/dx again

we have 6x - 11

for x = 3,  6(3) - 11 = 18 - 11 = 7 which is positive x= 3 is a minimum

for x = 2/3 6(2/3) - 11 = 4 - 11 = -7, x = 2/3 is a maximum.

Therefore for maximum volume, the length to be cut out is 2/3 which is 0.66 inches.

Learn more about maximum and minimum points: brainly.com/question/26913652

#SPJ1

Substitute [tex]y = \sqrt x[/tex], so that [tex]y^2 = x[/tex] and [tex]2y\,dy = dx[/tex]. Then the integral becomes

[tex]\displaystyle \int \frac{dx}{\sqrt{1 + \sqrt x}} = 2 \int \frac y{\sqrt{1+y}} \, dy[/tex]

Now substitute [tex]z=1+y[/tex], so [tex]dz=dy[/tex]. The integral transforms to

[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = 2 \int \frac{z-1}{\sqrt z} \, dz = 2 \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz[/tex]

The rest is trivial. By the power rule,

[tex]\displaystyle \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz = \frac23 z^{3/2} - 2z^{1/2} + C = \frac23 \sqrt z (z - 3) + C[/tex]

Put everything back in terms of [tex]y[/tex], then [tex]x[/tex] :

[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = \frac43 \sqrt{1+y} (y - 2) + C[/tex]

[tex]\displaystyle \int \frac{dx}{\sqrt{1+\sqrt x}} = \boxed{\frac43 \sqrt{1+\sqrt x} (\sqrt x - 2) + C}[/tex]

The maximum height of the object is 82.7034 from the ground

Velocity is the measure of movement of an object with respect to time.

It is measured in m/sec

h = -4.9t²+21.6t +58.9

dh/dt = -9.8t +21.6

At maximum height ,  velocity = 0

therefore

-9.8t +21.6 = 0

9.8t = 21.6

t = 2.204 sec

h = -4.9 (2.204)²+ 21.6 * 2.204 +58.9

h = -23.803  +47.606 +58.9

h = 82.7034 from the ground

h = 23.80 from the point it is launched.

The maximum height of the object is 82.7034 from the ground

To know more about Velocity

https://brainly.com/question/18084516

#SPJ1

a) Intercepts are the points on the x and y axis

In the graph:

x-int: (-2,0), (2,0)

y-int: (0,1)

b) Domain is the list of x-values and Range is the list of y-values that make this graph true

Interval notations of domain and range

(Square brackets because the circles are closed)

Domain: [3,3]

Range: [0,3]

c) Intervals of increase and decrease: where the graph is increasing and decreasing

Increasing: -2 to 0 & 2 to 3

Decreasing: -3 to -2 & 0 to 2

d)Even, odd or neither

It is an even degree as both of its hands are facing upwards

Hope it helps!

Total amount she paid to repay her loan was $17,687

Amount is the total sum  of money paid to the bank.It is basically the sum of interest and principal amount.

Principal is the sum of money taken from the bank

Interest is the sum of money charge by the bank during the period of loan repayment.

Rate of interest is the rate at which interest is charge in the principal sum

Time is the total period of the loan repayment.

Simple interest = (P x Rx T)/100

where, P=principal

           R=rate of interest

           T= time

Amount= Principal +Interest

As per question,

P=$17000

R=6.8%

I=$687

Amount=P+I

              =$17000+687

              =$17687

Therefore,Total amount she paid to repay her loan was $17,687

Learn more about simple interest,

https://brainly.com/question/2151013

#SPJ10

Step-by-step explanation:

You need to attach the table in order to get an answer.

Answer:

area of the circle

area=7.54

Answer:

4x+2h+5

Step-by-step explanation:

[tex]\frac{(2(x+h)^{2}+5(x+h)) - (2x^{2} +5x) }{h} \\[/tex]

For now I'm just going to ignore the denominator for simplicity

[tex](2(x^{2}+2xh+h^{2})+5x+5h) - (2x^{2} +5x)\\(2x^{2}+4xh+2h^{2}+5x+5h) - (2x^{2} +5x)\\(4xh+2h^{2}+5h)\\\\\frac{(4xh+2h^{2}+5h)}{h}\\ 4x+2h+5[/tex]

Final step just distributes the division

By critically observing the given graphs, we can logically deduce that "graph C" returns greatest integer that is less than or equal (≤) to x.

A greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graphs, we can logically deduce that y in "graph C" returns greatest integer that is less than or equal (≤) to x.

Read more on greatest integer function here: https://brainly.com/question/12165085

#SPJ1

Using it's concept, it is found that the percentage of his sales that area food costs is of 29.62%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, he has $1643 out of $5546 in food, hence the percentage is given by:

[tex]P = \frac{1643}{5546} \times 100\% = 29.62%[/tex]

More can be learned about percentages at https://brainly.com/question/10491646

#SPJ1

The x intercept of the linear equation is -4 and y intercept is 8.

The intercept of the linear equation is calculated as follows;

x - y/2 = -4

make y the subject of the formula;

y/2 = x + 4

y = 2x + 8

y = 0 + 8

y = 8

0 = 2x + 8

2x = -8

x = -4

Thus, the x intercept of the linear equation is -4 and y intercept is 8.

Learn more about x and y intercept here: https://brainly.com/question/24363347

#SPJ1

Answer:

The x intercept of the linear equation is -4 and y intercept is 8

Step-by-step explanation:

Answer:

1/27

Step-by-step explanation:

We can substitute x=0 into the function to get:

Answer:

1/1

Step-by-step explanation:

As the question is halfing by 2

So

2 divide 2 equals 1

Answer:

1

Step-by-step explanation:

it's fractions of divided half. next one will be number 1

========================================================

Explanation:

The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.

Similarly the smallest y value is y = -1 and the largest is y = 1.

----------

Plug in the smallest x and y value to get

f(x,y) = x+5y

f(-1,-1) = -1+5(-1)

f(-1,-1) = -6

Therefore, the absolute min is -6

----------

Now plug in the largest x and y values

f(x,y) = x+5y

f(1,1) = 1+5(1)

f(1,1) = 6

The absolute max is 6

u=-54

you have -54 because

-54(-2)=108/9=12

Answer:

u =-54

Step-by-step explanation:

-2/9u=12

To solve for u multiply each side by -9/2 to isolate u

-9/2 * -2/9 u= 12 * -9/2

u =-54

If the value of mean is 781.67, then the standard deviation will be 100. Then the correct option is C.

The complete question is given below.

Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan. The list represents the approximate number of megabytes of data Grace used each month.

700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750

What is the standard deviation of the data? Round to the nearest whole number.

65

75

100

130

It is a metric for statistical information dispersion. The degree of spread indicates how much the result varies.

Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan.

The list represents the approximate number of megabytes of data Grace used each month.

700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750

The mean of the data will be

Mean = (700 + 735 + 680 + ...... + 820 + 750) / 12

Mean = 781.67

Then the standard deviation will be

SD² = [(700 – 781.67)² + (735 – 781.67)² + ..... + (750 – 781.67)²] / 12

SD² = 10072.2222

SD = 100.36 ≈ 100

Then the correct option is C.

More about the standard deviation link is given below.

https://brainly.com/question/12402189

#SPJ1

Answer:

[tex]\frac{3}{32}[/tex]

Step-by-step explanation:

-> Simplify

[tex]\frac{6}{64} =\frac{6/2}{64/2} =\frac{3}{32}[/tex]

6/64 simplified.

Step-by-step explanation:

1) zeros of the given function:

6x²-3=0; ⇔ 6(x²-0.5)=0; ⇔ x²=0.5; ⇔

[tex]\left[\begin{array}{ccc}x=-\sqrt{0.5} \\x=\sqrt{0.5} \end{array}[/tex]

2) relationship:

if to see the equation x²-0.5=0 (ax²+bx+c=0 is standart form!), then the sum of the zeros is '0' (it is 'b' of the standart form), the product of equation roots is '-0.5' (it is 'c' of the standart form).

[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]

★ The polynomial

f(x) = 6x² - 3

[tex]{\large{\textsf{\textbf{\underline{\underline{To \: find :}}}}}}[/tex]

★ Zeroes of the polynomial f(x) = 6x² - 3

[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

We have,

[tex]f(x) = \tt 6 {x}^{2} - 3[/tex]

Which can also be written as

[tex] \implies f(x) = \tt {(\sqrt{6} x)}^{2} - { (\sqrt{3}) }^{2} [/tex]

Using a² - b² = (a - b) (a + b)

[tex] \implies f(x) = \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} )[/tex]

To find the zeroes, solve f(x) = 0

[tex] \longrightarrow \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} ) = 0[/tex]

either [tex] \tt \sqrt{6} x - \sqrt{3} = 0 \: or \: \sqrt{6} x + \sqrt{3} = 0[/tex]

[tex] \implies \tt \sqrt{6} x = \sqrt{3 \: } \: or \: \: \sqrt{6} x = - \sqrt{3}[/tex]

[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{6} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{6} }[/tex]

[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} }[/tex]

[tex]\implies \tt x = \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} } \: or \: x = - \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} }[/tex]

[tex]\implies \tt x = \dfrac{1}{ \sqrt{2} } \: \: or \: \: - \dfrac{1}{ \sqrt{2} }[/tex]

Hence, the zeroes of f(x) = 6x² - 3 are:

[tex] \tt \alpha =\sf \boxed {{ \red{ \dfrac{1}{ \sqrt{2} } } }}\: \: and \: \: \beta =\sf \boxed {{ \red{ - \dfrac{1}{ \sqrt{2} } } }}[/tex]

• Verification

Sum of zeroes = [tex] ( \alpha + \beta )[/tex]

[tex] = \tt \dfrac{1}{ \sqrt{2} } + \bigg(- \dfrac{1}{ \sqrt{2} } \bigg)[/tex]

[tex] = \tt \dfrac{1}{ \sqrt{2} } + - \dfrac{1}{ \sqrt{2} } [/tex]

[tex]= \tt 0[/tex]

and, [tex]\tt - \dfrac{Coefficient \: of \: x}{Coefficient \: of \: {x}^{2} }[/tex]

[tex] \tt = - \dfrac{0}{6} [/tex]

[tex] \tt = 0[/tex]

[tex] \therefore \tt \: Sum \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Coefficient \: of \: x}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]

Also,

Product of zeroes = [tex] \alpha \beta [/tex]

[tex] = \dfrac{1}{ \sqrt{2} } \times - \dfrac{1}{ \sqrt{2} } [/tex]

[tex] = - \dfrac{1}{ 2 } [/tex]

and, [tex]\tt - \dfrac{Constant \: term}{Coefficient \: of \: {x}^{2} }[/tex]

[tex] \tt = \dfrac{ - 3}{6} [/tex]

[tex] \tt = \dfrac{ - 1}{2} [/tex]

[tex] \therefore \tt \: Product \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Constant \: term}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]

[tex]\rule{280pt}{2pt}[/tex]

Answer:

A≈113.1

Step-by-step explanation:

A=4πr2=4·π·32≈113.09734

Answer:

No, the total is 43.5 which is below 50.

Step-by-step explanation:

English: 25% × 48 = 12

Mathematics: 50% × 35 = 17.5

Typing: 5% × 80 = 4

Accounting 20% × 50 = 10

12 + 17.5 + 4 + 10 = 43.5

Total: 43.5

Passing: 50

Answer: No. The total is too low.

Answer:

y = 2x + 6 and y + x = 51

Step-by-step explanation:

the first number is y

the second number is X

" 6 is more than" implying +

"6 is more than twice another" implying y = 6 + 2 multiples by the second number "X"

their sum is equal to 51

add first and the second number

that is

y+x = 51

so we have

y = 6+2x and y +x = 51

Answer:

404 cm³ Anyway... Look down here for my explanation.

Step-by-step explanation:

Let's Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth on your paper. A right-angled triangle is formed too. The Length of side to the water-surface is 5 cm, the hospot is 7 cm.

We Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area 88.8/360*area of circle - ½*7*788.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

Volume of water = cross-sectional area * length

13.5 * 30 cm³

404 cm³

Answer:

They are not parallel

Step-by-step explanation:

original equation

10x + 3y = -3

subtract 10x

3y = -10x - 3

divide by 3

y = -10/3x - 1

original equation

5x - 4y = -3

subtract 5x

-4y = -5x-3

divide by -4

y = 5/4x + 3/4

the slopes are not equal to each other (5/4x and -10/3x) so they are not parallel

Answer:

Step-by-step explanation:

The graph of the given f(x) shows you what you need to know. Nothing cancels. Two answers are going to be true: one for x<3 and one for x>6.

From the graph, you can see that for x>6 the graph is decreasing. That makes B incorrect.

You can also see that for x < 6 The bottom parabola shape is decreasing which makes A true.

Finally at least one of C or D has to be true. As you can see, they both are depending on which shape you look at.  

The correct answer is B: f(x) is increasing for all x > 6.

To determine the intervals of increase and decrease for the function f(x), we can analyze the critical points and the behavior of the derivative. The derivative of f(x) is given by:

f'(x) = [(x² - 9x + 18)'(x + 6) - (x + 6)'(x² - 9x + 18)] / (x² - 9x + 18)²

Simplifying the derivative and finding the critical points, we get:

f'(x) = (x² - 3x - 18) / (x² - 9x + 18)²

Setting the numerator equal to zero and solving for x, we find the critical points:

x² - 3x - 18 = 0

(x - 6)(x + 3) = 0

x = 6 or x = -3

Analyzing the intervals created by the critical points and using test points, we find that f(x) is increasing for all x > 6. Therefore, the correct answer is B: f(x) is increasing for all x > 6.

To know more about derivative:

https://brainly.com/question/32963989

#SPJ3

Answer:

x² + 6x + 9

Explanation:

[tex]\sf = \left(x+3\right)^2[/tex]

Use perfect square formula: (a + b)² = a² + 2ab + b²

[tex]= \sf x^2 + 2(x) (3) + 3^2[/tex]

simplify the following

[tex]= \sf x^2 + 6x +9[/tex]

Hence Maria is not correct. The correct answer is x² + 6x + 9.

Answer:

$165554

Step-by-step explanation: I  use the Law of Cosines to find one of the angles of the triangle.  Then use the formula for the area of the triangle: A = (1/2)absinC.

C= 92.856 degree

Area = (1/2)(112)(148)sin(92.856°) = 8277.7 ft^2

To find the price just need to take 8277.7 time 20 = 165554

So the answer is $165554

244x3+1474x2+63x/

x+6

Answer:

[tex]\textsf {0.08 miles per minute}[/tex]

Step-by-step explanation:

[tex]\textsf {Speed = Distance (Miles) / Time (Minute) }[/tex]

[tex]\textsf {Speed = 18 miles / 213 minutes }[/tex]

[tex]\textsf {Speed = 0.08 miles per minute }[/tex]

Answer:

The speed in miles per minute is 0.0845 mpm.

Step-by-step explanation:

The explanation above clearly states that a car travel a distance of 18 miles in a time of 213 minutes . And it is asking for speed in miles per minute. Keep this in mind that the symbol for miles per minute is mpm. Speed formula is distance ÷ time.

Speed = Distance ÷ Time

Speed = 18 m / 213 min

18 divided by 213 = 0.0845

speed = 0.0845 mpm

Therefore the speed in miles per minute is 0.0845 mpm.