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2 years ago

If the cube shown is 7 centimeters on all sides what is the length of the diagonal x.

Mathematics

2 answers:

Volgvan2 years ago

7 0

Answer:

9.899

Step-by-step explanation:

7²+7²=98

$\sqrt{98} =9.899$

Marina86 [1]2 years ago

3 0

There's no cube shown but we can guess the diagonal is the long diagonal.

In a rectangular parallelpiped (aka a box) with dimensions a × b × c the long diagonal x satifies a 3D version of the Pythagorean Theorem,

x² = a² + b² + c²

In a cube a=b=c

x² = 3a²

x = a√3

Answer: 7√3

You might be interested in

Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible cho

yaroslaw [1]

Answer:

a) attached below

b) ( T,T )

c) The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

d) The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 )

Step-by-step explanation:

A) write down the game in matrix form

let: E = exit at the industry immediately

T = exit at the end of the quarter

N = exit at the end of the next quarter

matrix is attached below

B) weakly dominated strategies is ( T,T )

C) Find the pure-strategy Nash equilibria

The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

D ) Find the unique mixed-strategy Nash equilibrium

The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 ) since T is weakly dominated then the mixed strategy will be NE

Assume that P is the probability of firm 1 exiting immediately ( E )

and q is the probability of firm 1 staying till next term ( N ) ∴ q = 1 - P.

hence the expected utility of firm 2 choosing E = 0 while the expected utility of choosing N = 4p - 2q .

The expected utilities of E and N to firm 2 =

0 = 4p - 2q = 4p - 2 ( 1-p) = 6p -2 which means : p = 1/3 , q = 2/3

4 0

2 years ago

The time a projectile spends in the air can be modeled by the equation t² -t - 8 = 0, in which t represents the amount of time t

s2008m [1.1K]

Answer:

(t - 4)(t + 2) = 0

Step-by-step explanation:

The general formula for a quadratic expression is

y = ax² + bx + c

Your expression is

y = t² - 2t - 8 = 0

By comparison, we see that

a = 1; b = -2; c = -8

1. Find two numbers that multiply to give ac and add to give b.

In this case, find two numbers that multiply to give -8 and add to give -2.

It helps to list the factors of -8.

They are ±1, ±2, ±4, and ±8

After a little trial and error, you should find the numbers -4 and +2.

-4 × 2 = -8, and -4 + 2 = -2)

2. Rewrite the middle term with those numbers

t² -4t + 2t - 8 = 0

3. Factor the first and last pairs of terms separately

t(t - 4) +2(t - 4) = 0

4. Separate the common factor

The common factor is t - 4.

(t - 4)(t + 2) = 0

8 0

2 years ago

A translation is applied to the rectangle formed by the points A(−2, 6) , B(2, 6) , C(2, 4) , and D(−2, 4) . The image is the re

Alexxx [7]

A(−2, 6) ⇒⇒⇒ A′(1, 6)
B(2, 6) ⇒⇒⇒ B′(5, 6)
C(2, 4) ⇒⇒⇒ C′(5, 4)
D(−2, 4) ⇒⇒⇒ D′(1, 4)

By comparing the coordinates of points and its images we can deduce the rule of the transformation which is :
(x , y ) ⇒⇒⇒ ( x + 3 , y )

So, the rectangle is transformed 3 units to the right.

3 0

3 years ago

What is the equation of a circle with center (-3, -1) that contains the point (1, 2)?

Leno4ka [110]

So, we know the center is at -3,-1, ok

hmmm what's the radius anyway? well, we know that there's a point at 1,2 that is on the circle's path...hmmmm what's the distance from the center to that point? well, is the radius, let's check then.

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -3}}\quad ,&{{ -1}})\quad 
% (c,d)
&({{ 1}}\quad ,&{{ 2}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
r=\sqrt{[1-(-3)]^2+[2-(-1)]^2}\implies r=\sqrt{(1+3)^2+(2+1)^2}
\\\\\\
r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5$

so, what's the equation of a circle with center at -3, -1 and a radius of 5?

$\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{\quad k}})\qquad 
radius=&{{ r}}\\
&-3&-1&5
\end{array} 
\\\\\\\
[x-(-3)]^2+[y-(-1)]^2=5^2\implies (x+3)^2+(y+1)^2=25$

7 0

2 years ago

Solve the system.

liraira [26]

Answer:

Option D is right,.

Step-by-step explanation:

-a+4b+2c=-8 ... i

3a+b-4c=9 ... ii

b=-1 ... iii

Substitute the value of b, in i and ii

-a-4+2c =-8 or -a+2c = -4

and 3a-1-4c = 9 or 3a -4c =8

Now we have two equations in two variables

-a+2c =-4 and 3a-4c =8

a = 2c+4: substitute this in the other equatin.

3(2c+4)-4c =8 Or 2c +12 =8

2c =-4 or c = -2

Substitute in -a+2c =12

-a-2 = -4

a = -2+4 =2

a=2, b=-1 and c =-1 is the solution.

6 0

3 years ago