Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have. Let x denote the length of the side of the square being cut out. Let y denote the length of the base.
(a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes of several such boxes. (Do this on paper. Your teacher may ask you to turn in this work.)

(b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols. (Do this on paper. Your teacher may ask you to turn in this work.)

(c) Write an expression for the volume V in terms of x and y.
V =


(d) Use the given information to write an equation that relates the variables. (Do this on paper. Your teacher may ask you to turn in this work.)

(e) Use part (d) to write the volume as a function of x.
V(x) =


(f) Finish solving the problem by finding the largest volume that such a box can have.
V = ft3

Answer:

865.08

Step-by-step explanation:

✯Hello✯

↪  The answer is 865.08

↪  Times both of them by 10 so they are whole numbers

↪  Then it will be 534 x 162 = 86508

↪  Then divide by 100

❤Gianna❤

To multiply 53.4 and 16.2, calculate 534 * 162, then adjust the result by placing the decimal point two places from the right to get 865.08. This gives the final product of 865.08.

To find the product of 53.4 and 16.2, follow these steps:

        Here, 53.4 has one decimal place and 16.2 also has one decimal place, making a total of two decimal places.

Therefore, 53.4 * 16.2 equals 865.08.

Answer: 15 cubic inches.

Step-by-step explanation:

The volume of rectangular prism is given by :-

[tex]V=l\times w\times h[/tex], where l is length , w is width and h is height.

Given :  Hamsta' snacks box has a width of 1.5 inches,a length of 2.5 inches,and a height of 4 inches.

Then, the volume of the box will be :-

[tex]V=2.5\times 1.5\times 4=15\text{ cubic inches}[/tex]

Hence, the  volume of this Hamsta' snacks box is 15 cubic inches.

Answer:

I'm pretty sure it'd be set {3,6}

Answer:

A

Step-by-step explanation:

Answer:

b.  secx

Step-by-step explanation:

We have given a trigonometric expression.

csc(x)/cot(x)

We have to simplify it.

Since we know that

csc(x) is reciprocal to sin(x).

cscx = 1/sinx

cot(x) is ratio of cos(x) and sin(x).

cotx = cosx/sinx

Then, given expression becomes,

[tex]\frac{1/sinx}{cosx/sinx}[/tex]

[tex]\frac{1}{sinx}[/tex] × [tex]\frac{sinx}{cosx}[/tex]

[tex]\frac{1}{cosx}[/tex]

csc(x)/cot(x)   = secx

The equation for the line of reflection is x = 0 if the polygon ABCDE is reflected to produce polygon A'B'C'D'E'

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have a polygon ABCDE is reflected to produce polygon A'B'C'D'E' in the picture.

As we know, the reflection is the geometric transformation which create a mirror image of the object, but size or shape does not change.

The y-axis is the axis of reflection in this case.

The equation for the y-axis is x = 0

Thus, the equation for the line of reflection is x = 0 if the polygon ABCDE is reflected to produce polygon A'B'C'D'E'

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ2

Answer:

The ratio of their surface areas is [tex]\frac{4}{49}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

In this problem the scale factor is equal to the ratio [tex]\frac{2}{7}[/tex]

and

Remember that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

therefore

In this problem the ratio of their surface areas is [tex](\frac{2}{7})^{2}=\frac{4}{49}[/tex]

Final answer:

The ratio of the surface areas of two similar solids with a linear dimension ratio of 2:7 is 4:49.

Explanation:

The question deals with the concept of geometric similarity and the ratio of surface areas for similar solids. When two solids are similar, the ratio of their surface areas is the square of the ratio of their corresponding linear dimensions. Therefore, if the ratio between the lengths of their edges is 2:7, then the ratio of their surface areas would be the square of this ratio, which is (22):(72) or 4:49.

Answer:

  [tex]\log_{9}{\dfrac{13}{x}}=\log_{9}{\boxed{13}}-\log_{9}{x}[/tex]

Step-by-step explanation:

The rule is ...

  log(a/b) = log(a) -log(b) . . . . all logs to the same base

Then for a/b = 13/x, this becomes ...

  log(13/x) = log(13) -log(x)

If the base of logarithms is 9, then this is ...

  log9(13/x) = log9(13) -log9(x)

Answer:

30.9 ft

Step-by-step explanation:

Answer:

dx/dy =  (x^4 -  2x^5y -  6xy^2) /  (5x^4y^2 - 4x^3y +  2y^3).

Step-by-step explanation:

x^5y^2 − x^4y + 2xy^3 = 0

Applying the Product and Chain Rules:

y^2*5x^4*dx/dy + 2y*x^5 - (y*4x^3*dx/dy + x^4) + (y^3* 2*dx/dy + 3y^2*2x) =0

Separating the terms with derivatives:

y^2*5x^4*dx/dy - y*4x^3*dx/dy + y^3* 2*dx/dy =  x^4 -  2y*x^5 -  3y^2*2x

dx/dy =  (x^4 -  2x^5y -  6xy^2) /  (5x^4y^2 - 4x^3y +  2y^3)

Answer:

[tex]\frac{dx}{dy}=\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex]

Step-by-step explanation:

The given equation is

[tex]x^5y^2-x^4y+2xy^3=0[/tex]

Differentiate with respect to y.

[tex]\frac{d}{dy}(x^5y^2)-\frac{d}{dy}(x^4y)+\frac{d}{dy}(2xy^3)=0[/tex]

Using product rule we get

[tex]x^5\frac{d}{dy}(y^2)+y^2\frac{d}{dy}(x^5)-x^4\frac{d}{dy}(y)-y\frac{d}{dy}(x^4)+2x\frac{d}{dy}(y^3)+2y^3\frac{d}{dy}(x)=0[/tex]           [tex](fg)'=fg'+gf'[/tex]

[tex]x^5(2y)+y^2(5x^4\frac{dx}{dy})-x^4(1)-y(4x^3\frac{dx}{dy})+2x(3y^2)+2y^3\frac{dx}{dy}=0[/tex]

[tex]2x^5y+5x^4y^2\frac{dx}{dy}-x^4-4x^3y\frac{dx}{dy}+6xy^2+2y^3\frac{dx}{dy}=0[/tex]

Isolate [tex]\frac{dx}{dy}[/tex] terms on left side.

[tex]5x^4y^2\frac{dx}{dy}-4x^3y\frac{dx}{dy}+2y^3\frac{dx}{dy}=-2x^5y+x^4-6xy^2[/tex]

[tex](5x^4y^2-4x^3y+2y^3)\frac{dx}{dy}=-2x^5y+x^4-6xy^2[/tex]

Isolate [tex]\frac{dx}{dy}[/tex] term.

[tex]\frac{dx}{dy}=\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex]

Therefore the value of [tex]\frac{dx}{dy}[/tex] is [tex]\frac{-2x^5y+x^4-6xy^2}{5x^4y^2-4x^3y+2y^3}[/tex].

Answer:

2/4

Step-by-step explanation:

1/4 = 0.25

3/4 = 0.75

0.75 - 25 = 0.50

0.50 is your answer

ANSWER

1.

[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]

2.

[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]

3.

[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) [/tex]

EXPLANATION

1. The given logarithmic expression is

[tex] log_{4}(3x) [/tex]

Use the product rule:

[tex] log_{a}(mn) = log_{a}(m) + log_{a}(n) [/tex]

We apply this rule to obtain:

[tex]log_{4}(3x) = log_{4}(3) + log_{4}(x)[/tex]

2. The given logarithmic expression is

[tex] log_{3}( \frac{27}{x} ) [/tex]

We apply the quotient rule:

[tex]log_{a}( \frac{m}{n} ) = log_{a}(m) - log_{a}(n) [/tex]

This implies that;

[tex]log_{3}( \frac{27}{x} ) = log_{3}(27) - log_{3}(x) [/tex]

We simplify to get;

[tex]log_{3}( \frac{27}{x} ) = log_{3}( {3}^{3} ) - log_{3}(x) [/tex]

Apply the power rule:

[tex] log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]

[tex]log_{3}( \frac{27}{x} ) = 3 log_{3}( {3}) - log_{3}(x) [/tex]

simplify;

[tex]log_{3}( \frac{27}{x} ) = 3 (1) - log_{3}(x) [/tex]

[tex]log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)[/tex]

3. The given logarithmic expression is;

[tex] log_{4}( {x}^{5} ) [/tex]

Apply the power rule of logarithms.

[tex]log_{a}( {m}^{n} ) = n log_{a}(m) [/tex]

This implies that,

[tex]log_{4}( {x}^{5} ) = 5 log_{4}(x) .[/tex]

Answer:

[tex]\large\boxed{\tan x(\cot x-\cos x)=1-\sin x}[/tex]

Step-by-step explanation:

[tex]Use\\\\(\tan x)(\cot x)=1\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\text{distributive property:}\ a(b-c)=ab-ac\\======================\\\\\tan x(\cot x-\cos x)=(\tan x)(\cot x)-(\tan x)(\cos x)\\\\=1-\left(\dfrac{\sin x}{\cos x}\right)(\cos x)=1-\sin x[/tex]

Answer:

Step-by-step explanation:

To prove that Circle X is similar to Circle Y, we need to show that their corresponding angles are equal and their corresponding sides are proportional. We can compare the ratios of the circumference to the diameter for both circles, which are equal, implying that the angles in the two circles are equal and Circle X is similar to Circle Y.

To prove that Circle X is similar to Circle Y, we need to show that their corresponding angles are equal and their corresponding sides are proportional. Since the radii of the two circles are different (r for Circle X and s for Circle Y), we cannot directly compare their sides. However, we can compare their ratios. If we divide the circumference of Circle X by its diameter, we get the value of pi (π), which is approximately 3.14. Similarly, if we divide the circumference of Circle Y by its diameter, we would also get pi (π). This means that the ratios of the circumference to the diameter for both circles are equal, which implies that the angles in the two circles are equal and therefore, Circle X is similar to Circle Y.

Answer:

The height of the second box is [tex]6\ in[/tex]

Step-by-step explanation:

we know that

If the two boxes are congruent

then

The volume of the first box is equal to the volume of the second box

The length of the first box is equal to the length of the second box

The width of the first box is equal to the width of the second box

The height of the first box is equal to the height of the second box

so

Find the height of the first box

Remember that

The volume of the box is equal to

[tex]V=LWH[/tex]

substitute the values and solve for H

[tex]72=(3)(4)H[/tex]

[tex]H=72/(12)=6\ in[/tex]

domain and range are both infinite

Answer:

See attached picture.

Step-by-step explanation:

Graph the function as (x,y) points.

(-3,5)

(4,6)

(6,-9)

(9,-10)

These are graphed in black on the picture.

To graph the inverse, switch the points from (x,y) to (y,x).

(5,-3)

(6,4)

(-9,6)

(-10,9)

These are graphed in red on the picture.

Answer:

The measure of the angle A is [tex]53.13\°[/tex]

Step-by-step explanation:

we know that

In the right triangle ABC

The tangent of angle A is equal to the opposite side to the angle A divided by the adjacent side to angle A

so

[tex]tan(A)=\frac{BC}{AB}[/tex]

substitute

[tex]tan(A)=\frac{4}{3}[/tex]

[tex]<A=arctan(\frac{4}{3})=53.13\°[/tex]

Answer: 2.94 ft²

Step-by-step explanation:

Observe the figure attached:

The line LM divide the triangle into two right triangles.

Find the heigh "h" as following:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\sin(40\°)=\frac{h}{2.7}\\\\h=(2.7)(sin(40\°))\\h=1.73ft[/tex]

Apply the formula for calculte the area of a triangle:

[tex]A=\frac{Bh}{2}[/tex]

Where B (B=3.4 ft) is the base and h is the height (h=1.73ft)

Then:

[tex]A=\frac{(3.4ft)(1.73ft)}{2}=2.94ft^2[/tex]

Answer: 9 feet.

Step-by-step explanation: The formula to convert inches to feet is to divide the amount in inches by 12. 108/12 = 9.

Answer:

a) R = 3.6

b) A = 2

Step-by-step explanation:

To find the value, start by modeling the inverse proportionality by using the base equations with the original givens.

y = k/x

12 = k/1.5

18 = k

Now we use that to model the equation

R = 18/A

And we can now use that to solve parts a) and b)

a)

R = 18/A

R = 18/5

R = 3.6

b)

R = 18/A

9 = 18/A

2 = A

Answer:

1/4.

Step-by-step explanation:

I am assuming that there are 3 even and 3 odd tiles in each bag.

Probability( drawing an even tile form one bag) = 3/6 = 1/2.

The probability  of drawing  an even from the first and an even from the second = 1/2 * 1/2 = 1/4 (answer).

The individual probabilities  are multiplied because the 2 events are independent.

Answer:

9/36

Step-by-step explanation:

Answer:

The 10! means 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

- Factorial number means a number which is multiply itself to its

 decreasing numbers

- In mathematics, the factorial of a non-negative integer n, denoted by

 n! is the product of all positive integers less than or equal to n

- That means n! = n × (n-1) × (n-2) × (n-3) × ...........× 1

- Ex: 5 ! = 5 × 4 × 3 × 2 × 1 = 120

* Lets solve the problem

- There was 10 factorial 10! possible different orders

- The meaning of 10! is the multiplication of all the numbers from

 10 to 1

∴ 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

* The 10! means 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

The correct choice is C, 10(9)(8)(7)(6)(5)(4)(3)(2)(1). The expression 10! (ten factorial) means the product of all integers from 1 to 10, which is calculated as 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.

Therefore, the correct choice is C. For example, 4! equals 4 × 3 × 2 × 1 = 24.

The expression 10!, read as 'ten factorial', represents the product of all integers from 1 to 10. It is calculated as follows:

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

So, the correct choice for what 10! means is:

C- 10(9)(8)(7)(6)(5)(4)(3)(2)(1)

For example, the factorial of 4 is calculated as 4! which equals 4 × 3 × 2 × 1 = 24.

Similarly, for 10!, you multiply all integers from 10 down to 1.

Answer:

105

Step-by-step explanation:

to get this you must first divide 17.5 by 2.5 to see how many times to multiply 15 by 2.5

sorry if it does not make scence

Answer:

9 servings of meat.

Step-by-step explanation:

The first ratio you are given is 8:36. You are trying to figure out what 2:__ is.

8/36 x  2/X

Multiply 2 x 36 and get 72. Now divide 72 by 8 to get 9.

Answer:

The answer really is 9 servings of meat.

Step-by-step explanation:

I had the same question and I got it right...but mine said: Write a proportion that could be used to solve this problem. Do not solve it.

Answer:15

Step-by-step explanation:he has 3 packs of model cars. 15 is in each pack if he gave away four he would have 11 left.

[tex]GT=\frac{HF.TS}{SF}=\frac{4.8\times 21}{12}=8.4 [/tex]

The point-slope form of the line with slope 6 that contains the point (1, 2) is y - 2 = 6(x - 1).

The point-slope form of a line is given by:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where m is the slope of the line and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.

Given that the slope m = 6 and the point [tex]\( (x_1, y_1) = (1, 2) \)[/tex], we can substitute these values into the point-slope form:

y - 2 = 6(x - 1)

So, the point-slope form of the line with slope 6 that contains the point (1, 2) is y - 2 = 6(x - 1).

Answer:

$77,380

Step-by-step explanation:

If she gets a 6% raise next year she will make 106% of what she makes this year.  

106% is 1.06 as a decimal.  Multiply her salary by 1.06 to find out how much she will make next year...

$73,000(1.06) = $77,380

Answer:

77,380

Step-by-step explanation:

divide 73000 by 100% and you get 730, then you multiply it by 6 since you need a 6% raise. once you get this value, you simply add it to the 73000 and you get the answer

I think you're answer is five hundred seventy six