Mathematics High School

What is the distance, in radians, between 0 and 0=pie , sin0=0

Answers

Answer 1
We are asked to find the distance (in radians) between 0 and pi, and sin 0 to 0. 

The value of pi in degrees is 180 degrees. In radians, its value is 3.1415. So from 0 to pi, the distance is simple 3.1415 rad. Since sin 0 is equal to 0, then its distance from 0 is also 0. 
Answer 2

Answer:

What is the distance, in radians, between 0 and the value you identified in part A? (PLATO QUESTION)      pi (PLATO ANSWER)

Step-by-step explanation:

pi is the answer for plato users

Related Questions

Describe the graph of y > mx, where m > 0.

Answers

Since the slope is positive, the graph is increasing.
The boundary line is dashed, and everything above it is shaded.

Answer:

The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.    

Sample Response

Step-by-step explanation:

Hope this helps any of you! :)

The radii of earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of Pluto does it take to have the same volume as earth?

Answers

Earth volume: (3/4).π.(6371)³ = 1,0832x10¹² km³

Pluto volume: (3/4).π.(1171)³ = 6,555,189,765 km³

How many spheres the size of Pluto does it take to have the same volume as earth?

volume Earth/ volume Pluto = 1,0832x10¹² / 6,555,189,765 = 165.25

Answer: the answer will be 165.2

Step-by-step explanation:

By selling a stool for rupees 67.50,a carpenter loses 10%.how much percent would he gain or lose by selling it for rupees 82.50.?

Answers

Let the actual value of the stool be x.

So if the carpenter sells the stool x rupees he neither loses, now wins anything.

67.50 is the value x - 10% of x, that is:

67.50=x-0.1x
67.50=0.9x

x=67.50/0.9=75      (rupees) is the actual value of the stool.


Selling the stool for 82.50 rupees, the carpenter clearly would make a profit, say of y% of that actual value, that is y%*75.

So using the same method:

82.50=75+y%*75

y%*75=82.50-75=7.5

we can make the calculations, but clearly 7.5 is 10% of 75


Answer: 10% gain.


Quadrilateral abcd has side lengths of ab = 13w 5, bc = 5z 2, cd = 13w 5, and ad = 3z + 5. find the value of z for which quadrilateral abcd is a parallelogram.

Answers

Final answer:

To find 'z', utilise the properties of a parallelogram where opposite sides are equal. Setting these sides equal to each other and solving for 'z' provides the answer, 'z' = 3.5.

Explanation:

In this problem, you're given a quadrilateral ABCD for which you are supposed to find the value of 'z' when the quadrilateral is a parallelogram. In a parallelogram, the opposite sides are equal. Therefore, we can set AB = CD and BC = AD, and then solve for 'z'. From AB = CD (13w + 5 = 13w + 5), no information is required as their lengths are already equal. From BC = AD (5z - 2 = 3z + 5), solving for 'z' would give us 'z' = 7/2 or 3.5.

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What is the y intercept of y=7?
A.(0,7)
B.(7,0)
C.(7,7)
D.(-7,7)

Answers

y int of y = 7 is (0,7)

The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?
{2, 4}
{-2, -4}
{12, 14}
{-12, -14}
{0, 5}

Answers

f(x) = x+5 is the same as y = x+5

Plug in y = 7 and solve for x
y = x+5
7 = x+5
7-5 = x+5-5
2 = x
x = 2
So x = 2 is part of the domain

Now plug in y = 9 and solve for x
y = x+5
9 = x+5
9-5 = x+5-5
4 = x
x = 4
and x = 4 is also part of the domain

Therefore the domain is {2,4}


Read the following statement: All real numbers have a reciprocal. Which of the following choices is a counterexample to the statement?

1/4
0
1
-7

Answers

0 as its reciprocal is 0.

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

All real numbers have a reciprocal.

But we know that 0 has no inverse, means there is no reciprocal exists for 0.

Because,

[tex]\dfrac{1}{0}=\infty[/tex]

So, 0 is a counter example to the statement.

Hence, Second option is correct.

Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.

Answers

To solve for the surface area of the pyramid, we make use of the formula:

A= l w + l [sqrt ((w / 2)^2 + h^2)] + w [sqrt ((l / 2)^2 + h^2))

where,

l and w are the base of the pyramid = 100 mm

h is the height of the pyramid = 75 mm

 

Substituting the given values into the equation:

A= 100 * 100 + 100 [sqrt ((100 / 2)^2 + 75^2)] + 100 [sqrt ((100 / 2)^2 + 75^2))

A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)

A = 20,148.90 mm^2

 

Therefore the surface area of the pyramid is about 20,149 mm^2.

What is the factorization?

-3x^3+15x^2+42x

A. 3(x+7)(x+2)
B. 3(x^2)(x+2)
C. -3x(x+7)(x-2)
D. -3x(x-7)(x+2)

Answers

First take out the GCF
-3x(x^2-5x-14)
-3x(x-7)(x+2)
-7+2=-5
-7*2=-14

Answer: D

How to write 310, 763, 136 in expandes forma

Answers

310:
Three hundred and ten
763:
Seven hundred and sixty three
136:
One hundred and thirty six

The expanded form of 310, 763, 136 is:

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

310, 763, 136

This can be written in expanded form as,

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

Thus,

The expanded form is:

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

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The rule T1, -4 RO, 180°(x, y) is applied to rectangle KLMN. Which rectangle shows the final image??

Answers

Let me help you!

Looking at the visual, we can see five figures: KLM, 1, 2, 3, and 4.
Applying the rule T1, -4 RO, 180°(x, y) to rectangle KLMN - without even solving - just by merely observing, we can say (without a doubt) that the rectangle KLMN will most likely fall in the negative axis.

First rotation: -4 to the left.
Second rotation: -4 to the left.
Last rotation: -4 to the left making the last figure 3. <----- What we are looking for!

Therefore, the rectangle which shows the final image is figure 3 or rectangle 3.

Answer:

Figure 3.

Step-by-step explanation:

We perform the rotation first.  A 180° rotation about the origin maps every point

(x, y)→(-x, -y).  This means it negates both the x- and y-coordinates.

The pre-image points are:

K(3, -4); L(3, -1); M(5, -1); N(5, -4).  Performing the rotation and negating the coordinates will give us:

K'(-3, 4); L'(-3, 1); M'(-5, 1); N'(-5, 4).

Now we perform the translation.  The translation rule is <1, -4>; this means we add 1 to each x-coordinate and subtract 4 from each y-coordinate.  This maps to our new points:

K''(-2, 0); L''(-2, -3); M''(-4, -3); N''(-4, 0)

These are the points of figure 3.


Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi.

C = 5π; A = 20π

C = 10π; A = 20π

C = 10π; A = 25π

C = 5π; A = 25π

Answers

Hello there!

First, let's take a look at what the formula for the circumference and area of a circle is.

The circumference is "2[tex] \pi [/tex]r", or "2 * 3.14 * r".
The area is "[tex] \pi [/tex]r^2", or "3.14 * r * r".

Let's establish what the radius is, as [tex] \pi [/tex] is equivalent to 3.14.
The radius is half of the diameter, and our diameter is 10.
Divide 10 by 2 to find our radius.
10 / 2 = 5
The radius is 5.

Now, let's plug in 5 for the radius for both formulas.
C = 2 * 3.14 * 5
10 * 3.14
31.4 is our Circumference.

Now, onto the area.
A = r * r * 3.14
5 * 5 * 3.14
25 * 3.14
78.5 is our Area.

I hope this helps!

Answer:

The answer by Equinimity is incorrect. On my test, those weren't even options. The answer is:

C = 10n; A = 25n

(the symbol that looks like 'n' anyway)

1. It's what the answer is on pretty much every other version of this question on brainly.

2. I did the math.

which choice is equal to the repeating decimal below? 0.6

a) 0.666
b) 6/10
c) 0.66666666

Answers

the answer is 6/10 my fren :) good luck.

Hello.

[tex]6/10 = 0.6 [/tex]

I am confused by the question though. 0.6 is not a repeating decimal. But either way, 6/10 = 0.6

Feel free to ask me more questions on my profile. I am more than happy to help. Don't forget Brainliest! :)

Kite PQRS is dilated to form LMNO. what corresponding angle is congruent to angle QRS? type the essay in the box below

Answers

MNO. When you dilate a figure the angles stay the same.

(1 point) solve the separable differential equation y′(x)=2y(x)+18−−−−−−−−−√, y′(x)=2y(x)+18, and find the particular solution satisfying the initial condition y(5)=9.

Answers

We write the equation in terms of dy/dx,
y'(x)=sqrt (2y(x)+18)
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9)) 

Separating the variables in the equation, we will have:
1/sqrt(y + 9) dy= sqrt(2) dx 

Integrating both sides, we will obtain
2sqrt(y+9) = x(sqrt(2)) + c 
where c is a constant and can be determined by using the boundary condition given 
y(5)=9 : x = 5, y = 9
sqrt(9+9) = 5/sqrt(2) + C 

C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2

Substituting to the original equation,
sqrt(y+9) = x/sqrt(2) + sqrt(2) / 2

sqrt(y+9) = (2x + 2) / 2sqrt(2) 

Squaring both sides, we will obtain,
y + 9 = ((2x+2)^2) / 8

y = ((2x+2)^2) / 8 - 9

find the exact value of tan75
This is a question from sum and differences of trigs so it must include that. I've tried multiple things and nothing has given me one of the options for answers.

Answers

[tex]\bf tan({{ \alpha}} + {{ \beta}}) = \cfrac{tan({{ \alpha}})+ tan({{ \beta}})}{1- tan({{ \alpha}})tan({{ \beta}})}\\\\ -------------------------------\\\\ tan(75^o)\implies tan(45^o+30^o)=\cfrac{tan(45^o)+tan(30^o)}{1-tan(45^o)tan(30^o)} \\\\\\ tan(45^o+30^o)=\cfrac{\frac{sin(45^o)}{cos(45^o)}+\frac{sin(30^o)}{cos(30^o)}}{1-\frac{sin(45^o)}{cos(45^o)}\cdot \frac{sin(30^o)}{cos(30^o)}}[/tex]

[tex]\bf tan(45^o+30^o)=\cfrac{\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}+\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}}{1-\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}\cdot \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}} \implies tan(45^o+30^o)=\cfrac{1+\frac{1}{\sqrt{3}}}{1-1\cdot \frac{1}{\sqrt{3}}}[/tex]

[tex]\bf tan(45^o+30^o)=\cfrac{\frac{\sqrt{3}+1}{\sqrt{3}}}{1-\frac{1}{\sqrt{3}}}\implies tan(45^o+30^o)=\cfrac{\frac{\sqrt{3}+1}{\sqrt{3}}}{\frac{\sqrt{3}-1}{\sqrt{3}}} \\\\\\ tan(45^o+30^o)=\cfrac{\sqrt{3}+1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}-1}\implies tan(45^o+30^o)=\cfrac{\sqrt{3}+1}{\sqrt{3}-1}[/tex]


so... let's rationalize the denominator.. now, the denominator is √(3) - 1, so, we'll use her conjugate, √(3) + 1, and multiply top and bottom by it, so we end up with a "difference of squares" at the bottom, so, let's do so.

[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{\sqrt{3}+1}{\sqrt{3}-1}\cdot \cfrac{\sqrt{3}+1}{\sqrt{3}+1}\implies \cfrac{(\sqrt{3}+1)(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}\implies \cfrac{(\sqrt{3}+1)^2}{(\sqrt{3})^2-(1)^2} \\\\\\ \cfrac{(\sqrt{3}+1)^2}{3-1}\implies \cfrac{(\sqrt{3})^2+2\sqrt{3}+1^2}{2}\implies \cfrac{3+2\sqrt{3}+1}{2} \\\\\\ \cfrac{4+2\sqrt{3}}{2}\implies \cfrac{\underline{2}(2+\sqrt{3})}{\underline{2}}\implies 2+\sqrt{3}[/tex]

Which of the following is a rational number?

Answers

The rational number would be 16

(5ab+2a-2)-(ab-3) find the difference.

Answers

Hey!

(5ab + 2a - 2) - (ab - 3)
(5ab + 2a - 2) - ab + 3
4ab + 2a +1  <------------- That's your answer!

Vote for me as Brainliest if there is a second answer, PLEASE!!!

What is the solution of the equation e^xe^2x = 4? Round your answer to the nearest hundredth.

Answers

The equation is:

[e^x] [e^(2x)] = 4

1) Applying property of multiplication of powers wiith same base =>

e ^ (x + 2x) = 4

=> e ^ (3x) = 4

2) Applying logarigth properties

3x = ln(4)

=> x = ln(4) / 3 ≈ 1.38629 / 3 ≈ 0.4621

Answer: x = ln(4) / 3 ≈ 0.4621

Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4)? a 180 (dagree) rotation about the origin a 90 (dagree) counterclockwise rotation about the origin and a translation down 4 units a 90 (dagree) clockwise rotation about the origin and a reflection over the y-axis a reflection over the y-axis and then a 90(dagree) clockwise rotation about the origin

Answers

The triangle ABC is mapped to A'B'C' through a 180-degree rotation about the origin, as all the points' x and y coordinates have changed signs, consistent with this transformation.

To determine which transformations can map the original triangle ABC to the new triangle A'B'C', we must closely examine the coordinates given and analyze the possible transformations.

Looking at the coordinates:

A(2, 2) to A'(-2, -2) suggests a reflection over the origin, which can be considered as a 180-degree rotation around the origin.

B(4, 1) to B'(-1, -4) also suggests a similar transformation, as the x and y values are negated and swapped in position.

C(4, 5) to C'(-5, -4) follows the same pattern.

All these transformations indicate that the original triangle has been rotated 180 degrees about the origin. This can also be observed by noting that the x and y coordinates have simply changed their signs, an effect of 180-degree rotation about the origin. This satisfies the claim of the classical geometry theorem which states that such transformations can be expressed as either a translation or a rotation. In this case, it's purely a rotation as there's no translation component.

what is the equation of a line perpendicular to y=1/2x-1 through (0,6)

Answers

well, first off let's take a peek of what is the slope of "y" in this case hmmm

[tex]\bf \begin{array}{llll} y=&\frac{1}{2}x&-1\\ &\uparrow &~\uparrow \\ &slope&y-intercept \end{array}[/tex]   so, is 1/2 ok....

now, a line that is perpendicular to that equation, will have a slope that is negative reciprocal of that.

[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\ slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\ -------------------------------\\\\ slope=\cfrac{1}{2}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies -2[/tex]

so, what is the equation of a line whose slope is -2 and passes through (0,6)?

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 0}}\quad ,&{{ 6}})\quad \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -2 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-6=-2(x-0)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-6=-2x\implies y=-2x+6[/tex]

On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"? 4x + 8y < 50 4x + 8y ≤ 50 4x + 8y  > 50 4x + 8y ≥ 50

Answers

The answer is 4x + 8y ≥ 50 
Answer:

Hence, the inequality that will represent the marks he needs  is:

4x+8y≥50

Step-by-step explanation:

On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points.

Lorenzo needs at least 50 points on the final to earn a "B" in the class.

Let x be the number of correct multiple-choice questions, and y, the number of correct word problems.

Hence, the inequality that will represent the marks he needs  is:

4x+8y≥50

Which system of equations can be graphed to find the solution(s) to x^2 = 2x + 3?

Answers

It's the  4th choice.
The solutions will be the points of intersection of the 2 graphs.

URGENT

A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women?




A.
5/143


B.

7/143


C.

28/143


D.

30/143

Answers

5/13 * 4/12 * 3/11 is our representation, which yields 5/143, A. There is no replacement therefore the amount of available total candidates and available women shrink with each position filled.

Answer:

[tex]A. \frac{5}{143}[/tex]

Step-by-step explanation:

Given,

Number of women = 5,

Number of men = 8,

Total persons = 5 + 8 = 13,

∵ Ways of selecting any 3 persons = [tex]^{13}C_3[/tex]

Also, the ways of selecting 3 women = [tex]^5C_3[/tex]

Hence, the probability of selecting 3 women

[tex]=\frac{\text{Ways of selecting any 3 women}}{\text{ Ways of selecting any 3 persons}}[/tex]

[tex]=\frac{^5C_3}{^{13}C_3}[/tex]

[tex]=\frac{\frac{5!}{2!3!}}{\frac{13!}{3!10!}}[/tex]

[tex]=\frac{10}{\frac{13\times 12\times 11}{6}}[/tex]

[tex]=\frac{60}{13\times 12\times 11}[/tex]

[tex]=\frac{5}{143}[/tex]

Hence, OPTION A is correct.

H-79= -83 Solve the equation ?

Answers

Ok so take -79 and add it too -83 so -83 + 79 to get your answer of H= what ever answer you get
H-78=-83
Add 78 on both sides
H=-4
Check=
-4-79=-83
-83=-83
So h=-4.

wahts the quotient of 92 and 5

Answers

quotient is division

92/5 is 18.4


_18.4___
5) 92
-5
4 2
-40
20

Final answer: 18.4

the least common multiple of 2/3 5/6 and 9/4

Answers

multiply them together and simlify
2/5 times 5/6 times 9/4=90/120=9/12=3/4
lcm is 3/4 then

The least common multiple of 2/3 5/6 and 9/4 is 12.

What is a fraction?

A fraction represents a part of a number or any number of equal parts.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We are given that;

The numbers 2/3 5/6 and 9/4

Now,

To find the least common multiple of fractions, we need to find the least common multiple of their denominators and divide it by the greatest common factor of their numerators. The steps are:

Multiples of 3: 3, 6, 9, 12, 15, 18,

Multiples of 6: 6, 12, 18,

Multiples of 4: 4, 8, 12,

Find the greatest common factor of 2, 5 and 9. This is the largest number that can divide all three numbers without leaving a remainder. One way to do this is to list the factors of each number and find the largest one that they have in common. For example:

Factors of 2: 1 and 2

Factors of 5: 1 and 5

Factors of 9: 1,3 and9

The only common factor is 1, so this is the greatest common factor of the numerators.

Divide the least common multiple of the denominators by the greatest common factor of the numerators. This gives us:

12 /1 =12

Therefore, the LCM of given fraction will be 12.

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When determining the number of significant figures in a number, zeroes to the left of the decimal point are never counted.
a. True
b. False?

Answers

The number of significant figures in a number means the number of digits that actually have a meaning in the number and should be included in measurements.

Zeros are not counted in special cases, these cases are as follows:
1- When the zero is the first digit from the left followed by other digits before the decimal point 
Example: 02.5 , 009.3 (zeros are not counted here)
However, in a number as 30.3, the zero is definitely counted

2- When the zero is the last digit on the right after the decimal point
Example: 23.330 , 8.90 (zeros are not counted here)

Based on this, the above mentioned statement is false.
Since zeros are counted before the decimal point when they are not the leftmost digits 
counted in : 30.4
not counted in : 03.4

How long does it take a plane, traveling at a speed of 110 m/s, to fly once around a circle whose radius is 2850 m?

Answers

V=110, s= 2×π×r (circumference of a circle)
t=s/v=110/2×π×2850

Answer:

It takes to the plane [tex]162.792[/tex] seconds to fly once around a circle whose radius is 2850 m at a speed of [tex](110)\frac{m}{s}[/tex]

Step-by-step explanation:

The first step in this exercise is to find the total distance that the plane will fly.

This distance is equal to the perimeter of a circle whose radius is 2850 m.

Given a circle of radius R, the perimeter ''P'' can be calculated as :

[tex]P=\pi .d=\pi  .2.R[/tex]

Where ''d'' is the diameter of the circle that is equal to 2.R

The distance that the plane will fly in the exercise is :

[tex]P=\pi .2.R=\pi .2.(2850m)=17907.078m[/tex]

Now, the speed is equal to distance divided by time.

[tex]speed=\frac{distance}{time}[/tex]

We have the speed of the plane and the distance (that is the perimeter ''P'' of the circle). We only need to replace this values in the equation and find the time variable.

[tex](110)\frac{m}{s}=\frac{(17907.078)m}{t}[/tex]

[tex]t=\frac{(17907.078)m}{(110)\frac{m}{s}}=(162.792)s[/tex]

[tex]t=(162.792)s[/tex]

We find that the time is [tex]162.792[/tex] seconds.

A rectangular box has dimensions of length = 6, width = 4, and height = 5. the measure of the angle formed by a diagonal of the box with the base of the box is

Answers

Final answer:

To find the angle formed by a diagonal of a rectangular box with its base, calculate the base diagonal using the Pythagorean Theorem and then use the inverse tangent function with the height and base diagonal as arguments.

Explanation:

The angle formed by a diagonal of the rectangular box with the base of the box can be found using the Pythagorean Theorem. In this case, the box has a length of 6, a width of 4, and a height of 5. The diagonal of the base can be calculated as the hypotenuse of a right triangle formed by the length and the width. According to the Pythagorean theorem, this diagonal (D) is √(6² + 4²) which is √(36 + 16) or √52. To find the angle between the box's base diagonal and the body diagonal (which includes the height), we need to use trigonometry, specifically the inverse tangent function (tan-1). So we have the length of the box's base diagonal (D) and the height (H), forming a right triangle with the body diagonal as the hypotenuse. The angle θ can be calculated using tan-1(H/D), where H is the height of the box and D is the length of the diagonal on the base. This equates to tan-1(5/√52). Evaluating this expression with a calculator gives us the angle θ formed by the body diagonal with the base of the box.

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