help me i will give brainlest

If the area of the area of the base increases at rate of 2 cm²/sec then the rate at which the height of the box is decreasing is 0.11 cm/sec .

In the question ,

it is given that ,

the volume of the rectangular box having square base is 1100 cm³ ;

the rate of decrease of the area is (dA/dt) is = 2 cm²/sec ;

we know that ; Volume = Area × Height ;

the area of the square base of side 12 cm is = 12 × 12 = 144 ;

So , height = Volume/Area ;

= 1100/144 ;

Now , V = A × h ;

differentiating the above equation w.r.t. "t" ,

we get ;

dV/dt = A×(dh/dt) + h×(dA/dt)

0 = 144×(dh/dt) + (1100/144)×(2)

dh/dt = -2200/(144 × 144)

= -0.106095

≈ -0.11

Therefore , the rate of change of height is = 0.11 cm/sec .

Learn more about Rate Of Change here

https://brainly.com/question/18648394

#SPJ4

Answer:

11[tex]\frac{5}{8}[/tex]

Step-by-step explanation:

15-1/2 = 31/2

(31/2)(3/4) = 93/8 = 11[tex]\frac{5}{8}[/tex]

The solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.

The given steps are-

x² - 4x = 15.

(b/2)² = (-2)²

x² - 4x + (-2)² = 15 +(-2)²

x² - 4x + 4 = 19

There are various ways to display the outcome.

(x - 2)² = 19

x = ±√19 + 2

Thus, the solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.

To know more about the completing square, here

https://brainly.com/question/10449635

#SPJ4

The equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].

What is perpendicular lines?

When two geometric objects intersect at a right angle, they are considered to be perpendicular in elementary geometry. By using the perpendicular symbol,, the condition of perpendicularity can be graphically represented. Between two lines, a line and a plane, or between two planes can be used to define it.

Consider the given equation of line

5x + 4y = 10

Convert it into the form y = mx + c

⇒ 4y = -5x + 10

y = -5/4x + 10/4

y = -5/4x + 5/2

Here the slope of line is, -5/4.

The slope of perpendicular line is negative reciprocal of the slope of given line.

So, the slope of perpendicular line is,

[tex]-\frac{1}{(-5/4)} = \frac{4}{5}[/tex]

Also the line passes through the point (5, -4).

By using the point slope form to find the equation of line

[tex]y-y_1 = m(x-x_1)\\y-(-4) = \frac{4}{5}(x-5)\\ y+4=\frac{4}{5}x - 4\\ y = \frac{4}{5}x - 4 - 4\\ y = \frac{4}{5}x - 8[/tex]

Hence, the equation of the perpendicular line to the given line is, [tex]y = \frac{4}{5}x - 8[/tex].

To know more about perpendicular lines, click on the link

https://brainly.com/question/17683061

#SPJ1

The vector <8,-5> when expressed in coordinate notation is (8, -5)

From the question, we have the following parameters that can be used in our computation:

Notation = <8, -5>

The above expression is in vector notation

To express the vector notation in a coordinate notation, we simply express the <> as ()

So, we have the following representation

(8, -5)

Hence, the coordinate notation is (8, -5)

Read more about coordinates at

https://brainly.com/question/11337174

#SPJ1

Answer:13.77 cm.

Step-by-step explanation:

r = sqrt((3V)/(pih))

= sqrt((31758)/(pi29))

= sqrt((5274)/(pi*29))

= sqrt(182.16)/(pi/29)

= 13.77 cm

Step-by-step explanation:

a finite decimal number into a fraction is very easy.

remember what the different positions after the decimal point are worth :

tenths, hundredths, thousandths, tenthousandths, hundredthousandths, ...

0.225 covers thousandths.

how many ?

well, 225, of course.

so,

0.225 = 225/1000 = 9/40 × 25/25 = 9/40

Answer 3.8 x 104

Step-by-step explanation:

Answer:0.038

Step-by-step explanation:

The ordinary number equivalent of 3.8x10⁻² is expressed as 0.038.

To express the number 3.8x10⁻² as an ordinary number, we need to understand scientific notation. In scientific notation, numbers are written in the form of a coefficient (a decimal number greater than or equal to 1 but less than 10) multiplied by 10 raised to a certain power (positive or negative). This notation is commonly used to represent very large or very small numbers in a concise and standardized way.

Let's break down 3.8x10⁻² step by step:

The coefficient: 3.8

The coefficient is the decimal part of the number, which should be greater than or equal to 1 but less than 10. In this case, the coefficient is 3.8.

The exponent: -2

The exponent indicates the power of 10 to which the coefficient is raised. If the exponent is negative, it means the number is less than 1. In this case, the exponent is -2, which means we are dividing the coefficient by 100 (10 raised to the power of -2 is 1/100).

Now, to express 3.8x10⁻² as an ordinary number, we simply perform the calculation:

3.8 × 10⁻² = 3.8 ÷ 100 = 0.038

So, the ordinary number equivalent of 3.8x10⁻² is 0.038.

To know more about ordinary number click here :

https://brainly.com/question/31645095

#SPJ2

The first and fourth quadrant of a coordinate grid should be used to display the given data .

In the question ,

it is given that ,

from the time the storm has started the temperature change is from 0° to - 20° .

we know that time cannot be in negative , and temperature can be both negative and positive .So only quadrant 1 and 4 can be used for representation .

Y = temperature

X = time

Quadrant 1 = (+x , +y) this can be used because x can only be positive and y is also positive.

Quadrant II = (-x , +y) this cannot be used because x cannot be negative

Quadrant III = (-x , -y) this cannot be used because x cannot be negative

Quadrant IV = (+x , -y) this can be used because x can only be positive and y can be negative.

Therefore , only 1 and 4 quadrants can be used .

The given question is incomplete , the complete question is

An equation is written to represent the relationship between the temperature in Alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. if the storm lasted five hours and the temperature saw a drop from 0° to - 20°, which quadrant(s) of a coordinate grid should be used to display this data ?

Learn more about Quadrants here

https://brainly.com/question/1960547

#SPJ4

Answer:

X=1

Step-by-step explanation:

For step one you have to Distribute

2x-1(4x+3)=-7x+2 --> 2x-4x-3=-7x+2

For step two you have to Combine Like Terms

2x-4x-3=-7x+2 --> -2x-3=-7x+2

For step three you have to Add Three To Both Sides

-2x-3=-7x+2 --> -2x=-7x+5

For step four you have to Add 7x To Both Sides

-2x=-7x+5 --> 5x=5

For step 5 you have to Divide Both Sides By The Same Factor (5)

5x=5 --> x=1

Hope This Helps!

Answer:

its 3

Step-by-step explanation:

the rate is 3

By simplifying the above equation i.e 27^(3/4) we get, 9 x (3)^(1/4).

Simplification is the process of substituting a mathematical expression with a simpler (typically shorter) counterpart. A fraction is simplified to an irreducible fraction. In computer algebra, expressions are simplified.

In order to simplify the given equation we need to factorize the bases. You can see that in the following steps :

(a^b)^c=a^(bc)

a^(b+c)=a^b x a^c

By using this above equation, we can factorize the bases.

So, factorization would be equal to :

27 ^(3/4) = ((3^3) )^ (3/4)

       = 3^(9/4)

      = 3^ (2+1/4)

       = 3^2 x 3^(1/4)

      = 9 x 3^(1/4)

That’s how we simplified the given equation.

To know more about Simplification,  click here :

https://brainly.com/question/1280754

#SPJ4

The number of apples obtained from the product of the fraction represented by the apples and the total number of fruits is 5 apples.

A fraction is a representation of the proportion or part of a whole quantity.

The fraction of the fruit that are apples = One quarter = 1/4

The fraction of the fruit that are oranges = One quarter of the number of fruits

The number of bananas = 4

Number of pear = 3

Number of plums = 3

The fraction of the whole fruit are represented by  apples and oranges = (1/4) + (1/4) = 1/2

The fraction of the total number of fruits represented by the bananas, pear and plum = 1 - (1/4 + 1/4)) = 1/2

Therefore;

Half of the total number of fruits = 4 + 3 + 3 = 10 fruits

Half of the fruits = 10

The total number of fruits is therefore, n = 2 × 10 = 20

The number of fruits that are apples = (1/4) × The total number of fruits

Therefore, the number of apples = (1/4) × 20 = 5

The number of fruits that are apples are 5 fruits

Learn more about fractions here:

https://brainly.com/question/78672

#SPJ1

The probability that the two pets selected are of the same species  is 0.2426   .

In the question ,

it is given that ,

the number of puppies in the pet store = 6

the number of kittens in the pet store = 9

the number of lizards in the pet store = 4

the number of snakes in the pet store = 5

total animals = 24

the probability of selecting 2 puppies = ⁶C₂/²⁴C₂

the probability of selecting 2 kittens = ⁹C₂/²⁴C₂

the probability of selecting 2 lizards = ⁴C₂/²⁴C₂

the probability of selecting 2 snakes = ⁵C₂/²⁴C₂

So , the required probability is

= ⁶C₂/²⁴C₂  + ⁹C₂/²⁴C₂ + ⁴C₂/²⁴C₂  + ⁵C₂/²⁴C₂  

Simplifying further ,

we get ,

= 5/92 + 3/23 + 1/46 + 5/138

= 0.0543 + 0.1304 + 0.0217 + 0.0362

= 0.2426

Therefore , the required probability is 0.2426   .

The given question is incomplete , the complete question is

The pet store has 6 puppies , 9 kittens , 4 lizards and 5 snakes . if you select two pets from the store randomly, what is the probability that they are both the same species ?

Learn more about Probability here

https://brainly.com/question/14570375

#SPJ4

The numbers are 10 and 10. And the sum of their squares will be 200.

For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.

The maximum and minimum value of the function is at f'(x) = 0.

The sum of the two numbers is 20.

Let the first number be 'x'. Then the other number is (20 - x). Then the equation is given as,

y = x² + (20 - x)²

Differentiate the function, then we have

y' = 0

2x + 2(20 - x)(-1) = 0

x - 20 + x = 0

2x = 20

x = 10

Then the other number is given as,

⇒ 20 - 10

⇒ 10

The sum of their squares is given as,

⇒ 10² + 10²

⇒ 100 + 100

⇒ 200

The numbers are 10 and 10. And the sum of their squares will be 200.

More about the maxima and minima links are given below.

https://brainly.com/question/12870695

#SPJ1

The integration of 1/ln(x) is not possible as We permit y = lnx, we then recognize that x = ey.

By differentiating each aspects of this equation with admire to y we get:dx/dy = ey, because the exponential characteristic differentiates to itself whilst differentiated with admire to its power.

In mathematics, the logarithmic quintessential characteristic or quintessential logarithm li(x) is a unique characteristic. It is applicable in issues of physics and has variety theoretic significance. In particular, in keeping with the high variety theorem, it's far a excellent approximation to the high-counting characteristic, that is described because the variety of high numbers much less than or same to a given value x.

Read more about integrate:

https://brainly.com/question/20163609

#SPJ4

Answer:

Step-by-step explanation:

The correct option is A 6

×

4 = 24

Closure property of multiplication for whole numbers states that product of two whole numbers a and b is always a whole number c.

Only options B and C have a multiplication sign. Of them, option B is of the form a

×

b = b

×

a

So 6

×

4 = 24 is an example for closure property of multiplication.

Generally speaking, a S corporation is put up to reduce the tax obligations. It is Option (3).

A business form known as a S corporation is one that is allowed by the tax code to distribute its taxable income, credits, deductions, and losses to its shareholders directly. This provides it certain advantages over the more popular C corp. The S corp, an alternative to the limited liability company, is only available to small firms with 100 or fewer stockholders (LLC). S corporations and LLCs are both referred to as "pass-through entities" since they don't pay corporate taxes, instead, they pay their owners, who are then in charge of paying the necessary taxes.

One sort of legal corporate structure that is popular among small businesses is the S corporation, commonly referred to as a S corp or S corp or S subchapter. Another is a limited liability company (LLC). A corporation with 100 shareholders or fewer can profit from incorporation while still being taxed as a partnership thanks to the requirements of a S corp. S corporations and LLCs are both pass-through companies, which means they don't pay corporate taxes and provide their owners and principals with limited liability protection. LLCs, however, offer more flexibility.

To learn more about S corporation visit : brainly.com/question/13570969

#SPJ4

Correct Question:

An S corporation is generally set up to:

1. implement an expansion strategy

2. attract capital

3. reduce tax burdens

4. easy entry into an industry

5. take advantage of limited liability

The value of (1 + i)^5 is -2 * 2^1.5 * (1 + i). De Moivre's describes how the power of a complex number can be calculated using the properties of its modulus and argument.

De Moivre's theorem states that for any complex number z and any integer n, we have (z^n) = (r^n)(cos(nθ) + i * sin(nθ)), where r is the magnitude of z and θ is the angle that z makes with the positive real axis in the complex plane. Using this theorem, we can easily find the fifth power of 1+i as follows:

First, we need to express 1+i in polar form, which is given by z = r * cis(θ), where r is the magnitude of z and cis(θ) is the complex number with magnitude 1 and angle θ in the complex plane. In this case, we have z = 1+i = sqrt(2) * cis(π/4), where sqrt(2) is the magnitude of 1+i and cis(π/4) is the complex number with magnitude 1 and angle π/4 in the complex plane.

Next, we substitute this expression for z into the formula for (z^n) given by De Moivre's theorem, which gives us

(1 + i)^5 = √2^5 * (cos(5 * 45) + i * sin(5 * 45))

        = 2^2.5 * (cos(225) + i * sin(225))

(1 + i)^5 = 2^2.5 * (-cos(45) + i * -sin(45))

        = 2^2.5 * (-1 + i * -1)

        = -2 * 2^1.5 * (1 + i)

Therefore, the value of (1 + i)^5 is -2 * 2^1.5 * (1 + i).

Learn more about DeMoivre's theorem, here https://brainly.com/question/28035659

#SPJ4

The exponential generating function is,

G(x) = (x¹/1! + x²/2! + ...)(x¹/1! + x³/3! + x⁵/5! +...)(x°/0! + x¹/1! + x²/2! + ...)²

where the first factor describes the pennies, the second describes the quarters, and the last describes nickles and dimes.

We want the coefficient of [tex]x^{r}[/tex]/r!.

Using exponential identities we get,

G(x) = ([tex]e^{x}[/tex] - 1)([tex]\frac{e^{x}-e^{-x} }{2}[/tex]) ([tex]e^{x}[/tex])² = [tex]\frac{1}{2}[/tex] ([tex]e^{4x} - e^{2x} - e^{3x} + e^{x}[/tex]),

and the coefficient is

[tex]\frac{1}{2} (4^{r} - 2^{r}- 3^{r} + 1 )[/tex]

The generating function is

G(x) = (x¹/1! + x²/2! + ...)⁴(x°/0! + x¹/1! + x²/2!+...)²² = ([tex]e^{x}-1[/tex])⁴[tex]e^{22x}[/tex],

and we again want the coefficient of [tex]x^{10}[/tex]/10!.

Multiplying we get,

G(x) = ([tex]e^{4x}-4e^{3x}+2e^{2x}+1[/tex])[tex]e^{22x}[/tex] = [tex]e^{26x}-4e^{25x}+2e^{24x}+e^{22x}[/tex]

so the coefficient of [tex]x^{10}[/tex]/10! is

26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰

To know more about arrangements here

https://brainly.com/question/17583653

#SPJ4

(A) cylindrical coordinate = (r, θ, z) = (√2, -π/4, 1)

(B) cylindrical coordinate = (r, θ, z) = (14, -π/3, 7)

In the given question, we have to change from rectangular to cylindrical coordinates. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A) (-1,1,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

So we find the value of r and θ one by one.

r = √x^2+y^2

r = √(-1)^2+(1)^2

r = √1+1

r = √2

θ = [tex]\tan^{-1}[/tex](y/x)

θ = [tex]\tan^{-1}[/tex](1/-1)

θ = [tex]\tan^{-1}[/tex](-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√2, -π/4, 1)

B) (-7,7√3,7)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

So we find the value of r and θ one by one.

r = √x^2+y^2

r = √(-7)^2+(7√3)^2

r = √49+147

r = √196

r = 14

θ = [tex]\tan^{-1}[/tex](y/x)

θ = [tex]\tan^{-1}[/tex](7√3/-7)

θ = [tex]\tan^{-1}[/tex](-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 7)

To learn more about change from rectangular to cylindrical coordinates link is here

brainly.com/question/17185505

#SPJ4

Answer:

3h - 3k

Step-by-step explanation:

I hope that this answer will help

You have to distribute

The value of natural logarithm, ln(1/0.32) where base "e" or e =2.7182 is 1.13943..

Logarithm, an exponent or power that must be raised to obtain a particular number. Expressed mathematically, x is the logarithm of n in base a, where x = logₐ n.

Basic Rules:

Wehave given that,

ln(1/0.32) here , a = 1 , b = 0.32

using formula, ln(1/0.32) = ln(1) - ln(0.32)

Now, from logarithm table , log(1) = 0

log(0.32)= ln(0.32) = - 1.13943

ln(1/0.32) = ln(1) - ln(0.32) = 0-(- 1.13943)

=> ln(1/0.32) = 1.13943

Hence, the value of ln(1/0.32) is 1.13943.

To learn more about Logarithm function, refer:

https://brainly.com/question/19513407

#SPJ4

The stated inequality, x < 9 or x >=14, indicates that the two potential values for x are $8 and $14.

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >,,, or are used to denote an inequality, when the two expressions aren't always equal.

x < 9 or x ≥ 14

This indicates that x must be more than 9 but not equal to 14.

In the choices

All values below nine are

$8

There are no values larger than or equal to 14.

$14

The stated inequality, x < 9 or x >=14, indicates that the two potential values for x are $8 and $14.

To know more about inequality in equation visit:-

https://brainly.com/question/11897796

#SPJ1

Oliver travelled the distance of 21.5 ft

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

As shown in the figure, we need to find the perimeter of the triangle ABC.

Perimeter = g + h +f ............(1)

g=f = 6.3 ft

Finding h using pythogoras theorem formula:

h² = g² + f²  

    = 6.3² +  6.3²

   =  79.38

h =√79.38  = 8.909 ≈ 8.9 ft  

So, (1) => Perimeter = 6.3 + 6.3 + 8.9 = 21.5 ft

Thus, Oliver travelled the distance of 21.5 ft

To learn more about the perimeter form the link:

https://brainly.com/question/19819849

#SPJ1

180 people would the elevator carry than if all the passengers were​ adults.

What is the meaning of times?

The mathematical symbol is used to represent the multiplication operation and the consequent product. It is often referred to as the times sign or the dimension sign.

Given an elevator can carry 25 adults or 30 children at one time.

One day the elevator carries a full passenger load 36 times.

If the elevator carries all adults, then it carries (25 × 36) = 900 adults.

If the elevator carries all children, then it carries (30 × 36) = 1080 adults.

If all the passengers were​ children, then the elevator carry more than (1080 - 900) = 180 people if all the passengers were​ adults.

To learn more about times, click on below link:

https://brainly.com/question/28532873

#SPJ1

(a) The rectangles represent a left sum, as the rectangles are drawn starting from the left endpoints of the intervals.

(b) The rectangles lead to a lower estimate of the integral, as the rectangles are drawn underneath the curve of the function.

(c) The value of n is 5, as there are 5 rectangles drawn.

(d) The value of Δx is 1, as the interval between the limits 0 to 6 is divided into 5 equal parts.

(e) The approximate value of the integral g(x)dx between the limits 0 to 6 is 22.5.

left-end points:

[tex]g(0)[/tex]Δ[tex]x[/tex] [tex]+ g(2)[/tex]Δ[tex]x + g(4)[/tex]Δ[tex]x[/tex]

Right-end points:

[tex]g(2)[/tex]Δ[tex]x + g(4)[/tex]Δ[tex]x + g(6)[/tex]Δ[tex]x[/tex]

[tex](g(2)+g(4)+g(6))^{2}[/tex]

Δ[tex]x=\frac{b-a}{n}[/tex]

   [tex]2=\frac{6-0}{n} \\\\2=\frac{6}{n}\\\\n=\frac{6}{2}=3 \\\\n=3[/tex]

Δ[tex]x=2-0=2[/tex] (each sub-interval length)

[tex]g(x)=x^{2} \\\\\int\limits^6_0{g(x)} \, dx = \int\limits^6_0 {x^{2} } \, dx[/tex]

              [tex]=[\frac{x^3}{3} ]^6_0\\\\=\frac{6^3}{3} -0\\\\=72[/tex]

The integral can be evaluated using the Fundamental Theorem of Calculus, which states that the integral of a function [tex]f(x)[/tex] with respect to [tex]x[/tex]from [tex]a[/tex] to [tex]b[/tex] is equal to the difference between the values of the antiderivative of [tex]f(x)[/tex] evaluated at [tex]b[/tex] and at [tex]a[/tex].

Therefore, the integral of [tex]f(x)[/tex] from [tex]a[/tex] to [tex]b[/tex] is given by:

[tex]\int\limits f{(x)} \, dx =f(b)-f(a)[/tex]

where[tex]F(x)[/tex] is the antiderivative of [tex]f(x)[/tex].

In this case, the antiderivative of f(x) is given by [tex]F(x) = \frac{x2}2 + c[/tex], where [tex]c[/tex] is the constant of integration. Therefore, the integral of f(x) from [tex]a[/tex] to [tex]b[/tex] is given by:

[tex]\int\limits f(x)dx = F(b) - F(a)\\\\= (\frac {b2}{2} + c) - (\frac{a2}{2} + c)\\\\= \frac{(b2 - a2)}{2}[/tex]

To learn more about Integration, visit:

brainly.com/question/18125359

#SPJ4

The new coordinates after a reduced scale factor of 0.77 with the origin will be equal to (−10, 10), (20, 40), (30, 30). Hence, option B is correct.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the data given in the question,

We will combine the x and y dimensions even by scale factors to shrink the picture by a multiplier of 0.77 with both the origins as that of the center of dilatation because the figure's vertices are (-13, 13), (26, 52), and (39, 39).

So, the first point is (-13, 13)

-13 × 0.77 = -10 and,

13 × 0.77 = 10

So, the new point is (-10, 10).

The second point is (26, 52).

26 × 0.77 = 20

52 × 0.77 = 40

So, the new point is (20, 40)

The third point is (39, 39)

39 × 0.77 = 30

39 × 0.77 = 30

So, the new point is (30, 30).

To know more about Graph:

https://brainly.com/question/17267403

#SPJ1

The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.

Given that,

We have to find the system of linear equation in which (2,-1) is a solution of the first equation but not for the second equation and (5,5) is a solution for system of equation.

We know that,

To find the system of equation we have a formula that is

y=mx-mx₁+y₂

Here m is slope

m=-1-5/2-5

m=-6/-3

m=2

The equation is

y=2x-2(5)+5

y=2x-10+5

y=2x-5

Therefore, The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.

To learn more about equation visit: https://brainly.com/question/29657983

#SPJ4