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tia_tia [17]
3 years ago
15

Look at triangle STU:

Mathematics
1 answer:
kirza4 [7]3 years ago
8 0

Answer:

70 cm

Step-by-step explanation:

42^2 + 56^2 = c^2

1764 + 3136 = c^2

4900 = c^2

70 = c

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Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large
Debora [2.8K]

Answer:

x = 1,6 in   ( the side of the corner squares )

V(max) = 67,58 in³

Step-by-step explanation:

The cardboard is:

L = 12 in          w  =  8 in

Let´s call "x" the side of the square from the corner:

Then the sides of the base of the open box are:

( L - 2*x )    and    ( w - 2*x )     and   x is the height

( 12  -  2*x )  and  ( w  - 2*x )

V(ob) = (L - 2*x ) * (  - 2*x ) * x

Wich is a function of x

V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x

V(x) = ( 96 - 24*x - 16*x + 4*x²) * x

V(x) = 96*x - 40*x² + 4*x³

Tacking derivatives on both sides of the equation

V´(x) = 12*x² - 80*x + 96

V´(x) = 0     12*x² - 80*x + 96 = 0

Solving for x

x₁,₂ = 80 ± √ 6400 - 4608 / 24

x₁,₂ = 80 ± 42,33 / 24

x₁ = 5,10       We dismiss this solution since 2*x  becomes 2*5,10 = 10,20

ant this value is bigger than 8 inches

x₂ = 1,60 in

Therefore dimensions of the box

a = 12 - 2*x     ;  a =  12 - 3,20  ;  a = 8,8 in

b = 8 - 2*x   ; b = 8 - 3,20  ; b =  4,80  in

And the volume of the open box is:

V(max) = 8,8*4,8*1,6

V(max)  =  67,58 in³

How do we Know that is the maximun value for V?

We find  V´´(x)  = 24*x - 80     for  x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has  a local maximun for a value of x = 1,6

3 0
3 years ago
Write the following in ascending order a)4/10,49/100,357/10,1/1001 plz fast ,correct and plzz with explanation
suter [353]

Answer:

1/1001 < 4/10 < 49/100 < 357/10

Step-by-step explanation:

4/10 => 0.4

49/100 => 0.49

357/10 => 35.7

1/1001 => 0.0009

Ascending order is from smallest to the greatest.

5 0
3 years ago
Read 2 more answers
If Dave drives at a steady speed of 50 mph, how long will it take him to drive 10 miles?
ira [324]
50 miles = 1 hour
10 miles = 1/50 x 10
= 1/5 hours
= 12 minutes

It will take him 12 minutes to drive 10 miles.
5 0
3 years ago
What is the interval notation for y&lt;5?
Ilia_Sergeevich [38]

Hey there!☺

Answer: (-∞, 5)

Explanation:

You need to convert the inequality as an interval notation.

y as interval notation would be written like this:

(-∞, 5)

Hope this helps!

7 0
3 years ago
What is 3(x^2+2x-3)-4(4x^2-7x+5) equal to show step by step explanation
Lelu [443]

Step-by-step explanation:

\huge{\underbrace{\overbrace{\mathfrak{\pink{Answer:}}}}}

3(x2+2x-3)-4(4x2-7x+5)

3x2 + 6x - 9 - 16x2 + 28x - 20

-13x2 + 34x - 29

7 0
3 years ago
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