3 in.

36 feet rounded to the nearest tenth of a foot

jek_recluse [69]

I don't exactly understand what you're asking, 36 feet does not need to be rounded to the nearest tenth as it is a whole number. Do you mean rounded to 40? (As that would be the nearsest multiple of 10) I'm a bit lost, but hopefully that helps

4 0

4 years ago

The manufacturing engineers of a renowned pizza brand reduced the manufacturing cost of a pizza delivery box by optimising the s

jekas [21]

Given: A pizza box's volume has been reduced by 25% by flattening the curved side of the box. The dimensions of the box are given.

Required: To determine the angle, the area of the sector of the top surface of the old box design, the area of the top surface of the newly designed box, and the volume, V, of the newly designed box. Also, determine the height of the box, h.

Explanation: The given box is-

If we draw a perpendicular as shown in the figure, the angle is bisected, and the side 24 cm is also bisected as the triangle on the top is an isosceles triangle. This can be easily proved by showing that the smaller triangles on the top face are congruent.

Next, we can use the trigonometric ratio sine to determine the angle as follows-

$\begin{gathered} sin\theta=\frac{12}{36} \\ \theta=sin^{-1}(\frac{1}{3}) \\ \theta=19.47\degree \end{gathered}$

Thus,

$2\theta=38.94\degree$

Next, the top of the new box is now a triangle with a base of 24 cm and a height-

$\begin{gathered} \text{ Height of triangle}=36cos\theta \\ =36cos(19.47\degree) \\ =33.94\text{ cm} \end{gathered}$

Hence, the area is-

$\begin{gathered} A=\frac{1}{2}\times24\times33.94 \\ =407.30\text{ cm}^2 \end{gathered}$

Now, the old box is a sector with a central angle of 38.94 degrees and a radius of 36 cm. Hence the area of the old box is-

$\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ \end{gathered}$

Substituting the values as-

$\begin{gathered} A=\frac{38.94}{360}\times3.14\times36\times36 \\ =440.18\text{ cm}^2 \end{gathered}$

Lastly, the volume of the new box is 25% less than the old box. Hence the volume of the new box is-

$\begin{gathered} V=\frac{25}{100}\times3277 \\ =819.25\text{ cm}^3 \end{gathered}$

We can determine the height as follows-

$\begin{gathered} Vol=Area\times h \\ \Rightarrow h=\frac{Vol}{Area} \end{gathered}$

Hence,

$\begin{gathered} h=\frac{819.25}{407.30} \\ =2.011\text{ cm} \end{gathered}$

Final Answer: A)

$2\theta=38.94\degree$

B) i) The area of the top of the old box=440.18 sq centimeters.

ii) The area of the top of the new box=407.30 sq centimeters.

C) i) The volume of the new box is 819 cubic centimeters.

ii) h=2.01 cm

8 0

2 years ago

The graph of which function has an axis of symmetry at x = 3?

xz_007 [3.2K]

f(x) = x² - 6x - 1

To find the axis of symmetry, use the axis of symmetry formula: -b\2a, according to the Quadratic Equation y = Ax² + Bx + C. You understand?

5 0

4 years ago

Read 2 more answers

Find slope ! Help:)!

Svet_ta [14]

Answer:

The slope is negative

Step-by-step explanation:

If the line is pointing down then the slope is negative. And if the line is pointing up then the slope is positive.

3 0

3 years ago

PLEASE HELP! SO CONFUSED! 25 POINTS!!

MrRa [10]

Answer:

D

Step-by-step explanation:

(f • g)(x)

= f(x) × g(x)

= (x + 4)(3x² - 7)

each term in the second factor is multiplied by each term in the first factor , that is

x(3x² - 7) + 4(3x² - 7) ← distribute both parenthesis

= 3x³ - 7x + 12x² - 28

= 3x³ + 12x² - 7x - 28 ← in standard form

7 0

2 years ago