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Svetllana [295]
2 years ago
14

10) If two angles in a triangle measure 53 degrees and 45 degrees, what is the value of the

Mathematics
1 answer:
pshichka [43]2 years ago
8 0

Answer:

d

Step-by-step explanation:

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A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six
kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

V = Length \times Width \times Height \\\\

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

Width = 3 - 2x \\\\

The length of the shaded region is given by

Length = \frac{1}{2} (5 - 3x) \\\\

So, the volume of the box becomes,

V =  \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V =  \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V =  \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V =  \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

a = 18 \\\\b = -38 \\\\c = 15 \\\\

x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 +  19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\

Volume of the box at x= 1.59:

V =  \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\

Volume of the box at x= 0.53:

V =  \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0
3 years ago
How do i solve this?
ss7ja [257]

Answer:

O

Step-by-step explanation:

8 0
3 years ago
What is the factor of 2k^2-25k+12
denpristay [2]

Answer:(2k-1)(k-12)

Step-by-step explanation:

8 0
2 years ago
When Sarah invests $4000 in a money market
gogolik [260]

Answer:

$4,224

Step-by-step explanation:

P(principal)=$4,000

R(rate)=1.4%

T(Time): 4 years

A=4,000×(1+(0.014×4))=$4,224

A=$4,224.00

So, Sarah will have $4,224 of interest in 4 years.

7 0
3 years ago
Please show work and thank youuu
Papessa [141]

Answer:

<u>x = 8√2</u>

Step-by-step explanation:

As the opposing side of the angle and the hypotenuse are given, take the sine ratio of the angle.

  • sin 45° = x/16
  • 1/√2 = x/16
  • x = 16 / √2
  • x = 16√2 / 2
  • <u>x = 8√2</u>
8 0
1 year ago
Read 2 more answers
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