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Answer:

11.08 cm/s

Step-by-step explanation:

Here it is given that the edges of a cube are increasing at a rate of 6.4 cm/s . And we need to find out the rate at which the diagonals are increasing . If we assume each side of the cube to be x , then ;

[tex]\longrightarrow \dfrac{da}{dt}= 6.4 \ cm/s\dots (i) [/tex]

Now we can find diagonal as ,

[tex]\longrightarrow d = \sqrt{ length^2+breadth^2+height^2} [/tex]

Here l = b = h = a ; so ,

[tex]\longrightarrow d =\sqrt{ a^2+a^2+a^2} [/tex]

Simplify,

[tex]\longrightarrow d =\sqrt{3a^2} [/tex]

Take out a from square root,

[tex]\longrightarrow d =\sqrt3 a[/tex]

Now , we can find the rate of change of diagonal as ;

[tex]\longrightarrow r =\dfrac{d\sqrt3 a}{dt} [/tex]

Take out the constant,

[tex]\longrightarrow r = \sqrt3\dfrac{da}{dt} [/tex]

From equation (i),

[tex]\longrightarrow r = 1.732 \times 6.4 \ cm/s [/tex]

Multiply ,

[tex]\longrightarrow \underline{\underline{ rate_{of\ change \ of \ diagonals}= 11.08\ cm/s}}[/tex]

This is the required answer!

If the side length increases at a rate of 6.4 cm/s, then the diagonal increases at a rate of 11.1 cm/s

The diagonal of a cube of side length S is given by:

d = S*√3

In this case, we know that the side length increases at a rate of 6.4 cm/s, then we can write:

S = S₀ + 6.4cm/s*t

Where S₀ is the initial side length, replacing that on the diagonal formula we get:

d = (S₀ + 6.4cm/s*t)*√3

Now if we differentiate it with respect to the time t, we get:

d' = 6.4cm/s*√3 = 11.1 cm/s

So, if the side length increases at a rate of 6.4 cm/s, then the diagonal increases at a rate of 11.1 cm/s.

If you want to learn more about rates of change, you can read:

https://brainly.com/question/8728504

Answer:

-6x+12

Step-by-step explanation:

-3(2x-4)

First, -3 distributes to 2x to make it -6x.

Then -3 distributes to -4. A negative times a negative is a positive so it will equal 12.

Sure

Answer:

x = -2

If the steps aren't belong to the lesson that you want, just tell me the lesson title so I can get the answer for you !!!!

...

The steps

Multiply all terms by (x-3)(x+3) and cancel:

x(x+3)+2x(x−3)=18

3x2−3x=18(Simplify both sides of the equation)

3x2−3x−18=18−18(Subtract 18 from both sides)

3x2−3x−18=0

3(x+2)(x−3)=0(Factor left side of equation)

x+2=0 or x−3=0(Set factors equal to 0)

x=−2 or x=3

Check answers. (Plug them in to make sure they work.)

x=−2 (Works in original equation)

x=3 (Doesn't work in original equation)

The solution set for the number line of inequality can be represented as,

{x | x ≤ 4. 5}

The number line is the way of representation of number and digits in a arranged form to understand the data batter.

The meaning of circle in number line,

The number line going from negative 5 to positive 5 and a solid circle appears between positive 4 and positive 5. The middle point of 4 and 5 is 4.5.

The solid or closed circle means that the value has less than or equal to 4.5. Thus, the solution set for the number line of inequality can be represented as,

{x | x ≤ 4. 5}

Learn more about the number line here;

https://brainly.com/question/24644930

Answer:

20 student who have a screen time of 12 or more hours have a grade below 80

Answer:

14

I hope it works for you

Answer:

The answer is below.

Step-by-step explanation:

Answer:

H(2,-6)

Step-by-step explanation:

reflection over the x-axis results in the y-coordinate getting the opposite sign

Answer:  132-5=127

Step-by-step explanation:

22 ounces in teaspoons is 132 -5=127

Answer:

5x-3

Step-by-step explanation:

x= "a number"

5 times x= 5x

3 less that 5x=

5x-3

Hope this helps!

Answer:

5x-3

Step-by-step explanation:

less than means it comes after

5 times a number

5x

3 less than

5x-3

Answer:

Step-by-step explanation:

a, compares to 50 beacuse a means the staying point ; slope, so that’s why it starts at 50.

b, compares to 3 beacuse that is the y-intercept

Answer:

9/20  also 45%

Step-by-step explanation:

well if 20 of them 9 are brown so 9 out of 20 of them are brown/45% of them because out of 20 each thing right or each person is 5%

Answer:

45/100 out of the 20 chickens are brown

Step-by-step explanation:

9/20 = 45/100

9/20 x 5 = 45/100

Answer:

If you want to know laps per minute it is 5 laps / 6 min = 0.83 laps per min

Step-by-step explanation:

Answer:

The first multiple-choice doesn't represent a function  

Step-by-step explanation:

(-4,3),(1,-6),(-8,-1),(1,9)

because a function has two pairs with the same x value

*hope that makes sense*

Answer:

what triangle where is the triangle?

Answer:

x = 7 5/8

Step-by-step explanation:

Given:

x - 2 5/8 = 6 1/4

first, let's find a common denominator so we can deal with the fractions easier.

The smallest number 8 and 4 is divisible by, is 8.

so we just multiply everything in the equation by 8 now, this helps get rid of the fractions.

x - 2 5/8 = 6 1/4

8 (x -2 5/8) = 8 (6 1/4)

simplifies into

8x -16 + 5 = 48 + 2

simplify some more

8x -11 = 50

solve for x

8x = 11 + 50

8x = 61

x = 61/8

or

x = 7 5/8

Answer:

Decimal: x=8.87

Improper fraction: x=71/8

Mixed number: x=8 7/8

Step-by-step explanation:

[tex]x-2\frac{5}{8}=6\frac{1}{4}[/tex]

First, let's convert mixed numbers to improper fraction

[tex]x-\frac{21}{8}=\frac{25}{4}[/tex]

Now, we can add 21/8 to both sides

[tex]x-\frac{21}{8}+\frac{21}{8}=\frac{25}{4}+\frac{21}{8}[/tex]

[tex]x=\frac{71}{8}[/tex]

We can convert 71/8 to a mixed number

[tex]x=8\frac{7}{8}[/tex]

Hope this helps!

Answer:

D) 1.23

Step-by-step explanation:

There are infinitely many numbers that are between 1.2 and 1.3 really, but given the answer choices, D is the correct one.

Answer:

2.5

Step-by-step explanation:

By the angle bisector theorem, [tex]\frac{AC}{BC}=\frac{CD}{DB}[/tex]. Plugging in the known side lengths gives [tex]\frac{5.8}{6.2}=\frac{?}{2.7}[/tex]. Solving gives:

[tex]?=(5.8\cdot 2.7)/6.2[/tex]

[tex]\approx 2.5[/tex], rounded to one decimal place.

Answer:

Learn PEMDAS on YT

Step-by-step explanation:

Check the picture below.

Answer:

70.8

Step-by-step explanation:

You have a total of 3 bills ( 2 one dollar and 1 five dollar)

There are two chances out of the three of getting a one dollar bill.

This is written as 2/3 probability

Answer: 2/3

Answer:

(2x4 + 11x2 - 5)

Step-by-step explanation:

((2•(x5))+(7•(x3)))-(5x-22x3)

((2 • (x5)) +  7x3) -  (5x - 4x3)

(2x5 +  7x3) -  (5x - 4x3)

2x5 + 11x3 - 5x  =   x • (2x4 + 11x2 - 5) 

Factoring  2x4 + 11x2 - 5 

Multiply the coefficient of the first term by the constant  2 • -5 = -10  

Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   
10   +   1   =   -9   
-5   +   2   =   -3
-2   +   5   =   3     
-1   +   10   =   9

Hope this helps!

Answer:

Step-by-step explanation:

m∠e = m∠a ( Corresponding Angles)

Answer:

6/5

Step-by-step explanation:

Answer:

5/6

the lowest number from 30 is 5x6 which is 30.

6x6 = 36

therefore,

5/6