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klemol [59]
3 years ago
7

An open box with a volume of 1500 cm cube is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of

side length x cm from each corner, and folding up the sides. Find the exact dimensions of the box.
Mathematics
1 answer:
Liula [17]3 years ago
7 0
The dimensions of the box formed will be:
width: 20 - 2x 
length: 40 - 2x
height: x

Volume = width x length x height
1500 = x(20 - 2x)(40 - 2x)
1500 = x(800 + 4x² - 120x)
1500 = 4x³ - 120x² + 800x
0 = 4x³ - 120x² + 800x - 1500
0 = x³ - 30x² + 200x - 375
Solving the cubic equation:
x = 5 (only integer root)

Length = 30 cm
Width = 10 cm
Height = 5 cm
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Please help! :)
Volgvan

Answer:

So the correct option is First one

i.e \dfrac{9\pi}{A}=\dfrac{90}{360}

Step-by-step explanation:

Given:

Area of Shaded part = 9 π square feet

To Find :

Area of Circle = ?

Solution:

90 degree center angle is equivalent to an area of 9 Π  square feet

So, 360 degree center is equivalent to area A which is the area of the complete circle.

So the Ratio will be

\dfrac{90}{9\pi} =\dfrac{360}{A}

Setting the given statements in proportion:

\dfrac{90}{9\pi} =\dfrac{360}{A}

On solving we get the required

\dfrac{9\pi}{A} =\dfrac{90}{360}

So the correct option is First one

i.e \dfrac{9\pi}{A}=\dfrac{90}{360}

Alternate Method:

Shaded part is of 90°

Area of Shaded part = 9 π square feet

And Full Circle is of 360° that is 4 sector of 90°

\textrm{Area of Circle}=4\times (Shaded\ part)

\textrm{Area of Circle}=4\times 9\pi

\textrm{Area of Circle}=36\pi

So the correct option is First one

i.e \dfrac{9\pi}{A}=\dfrac{90}{360}

On solving this we get

A=36\pi\ feet^{2}

8 0
3 years ago
Can Someone plz help? Thx
Andreyy89

Answer:

7. 2355 m

8. 1570 km

9. 157 cm

10. 40.82 m

Step-by-step explanation:

The circumference of a circle is pi * diameter or 2 * pi * radius.

If you are given the diameter, just multiply it by pi, 3.14.

If you are given the radius, then multiply the radius by 2 and then by pi, 3.14.

7. d = 750 m

circumference = pi * d = 3.14 * 750 m = 2355 m

8. d = 500 km

circumference = pi * d = 3.14 * 500 km = 1570 km

9. r = 25 cm

circumference = 2(pi)r = 2 * 3.14 * 25 cm = 157 cm

10. r = 6.5 m

circumference = 2(pi)r = 2 * 3.14 * 6.5 m = 40.82 m


8 0
3 years ago
Given P(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. Use synthetic division to find the quotient and the remainder.
katrin [286]
You can find the remainder right away by simply plugging in x=3. The polynomial remainder theorem guarantees that the value of p(3) is the remainder upon dividing p(x) by x-3, but I digress...

Synthetic division yields

3   |   2   -11   18   -15
.    |           6   -15     9
- - - - - - - - - - - - - - - - -
.    |   2     -5     3     -6

which translates to

\dfrac{2x^3-11x^2+18x-15}{x-3}=2x^2-5x+3-\dfrac6{x-3}

(and note that p(3)=2(3)^3-11(3)^2+18(3)-15=-6, as expected)
5 0
3 years ago
Robin and Meg are traveling from New York to Florida, and plan to stop at three different campgrounds along the way. After choos
matrenka [14]

You are correct. For each of the three possibilities for their second day, there are two possibilities for the third day.

The total number of possibilities is 3*2 = 6.

6 0
3 years ago
Which of the following statements is true?
Arada [10]

Answer:

its c i tink but im not completly sure

Step-by-step explanation:

5 0
2 years ago
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