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lesya692 [45]
3 years ago
7

List all positive factors for each 30-18

Mathematics
1 answer:
dangina [55]3 years ago
3 0

30 has 2, 3, 5, 6, 15

18 has 1, 2, 3, 6, 9, 18.

You might be interested in
A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi
mestny [16]

Answer:

  • Base Length of 84cm
  • Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, V=x^2h=296352

h=\dfrac{296352}{x^2}

Surface Area of the box = Base Area + Area of 4 sides

A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}

Step 2: Find the derivative of A(x)

If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}

Step 3: Set A'(x)=0 and solve for x

A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42

Therefore, the dimensions that minimizes the box surface area are:

  • Base Length of 84cm
  • Height of 42 cm.
5 0
3 years ago
Tanya is training a turtle for a race. For every 1/2 of an hour that the turtle is crawling, he can travel 3/20 of a mile. At wh
vazorg [7]

Answer:

\frac{6}{20} \ mile\ per\ hour

Step-by-step explanation:

Given:

For every 1/2 of an hour that the turtle is crawling, he can travel 3/20 of a mile

Question asked:

At what unit rate is the turtle crawling?

Solution:

As here<u> time taken is given</u> and the <u>distance traveled is also given </u>and hence we will apply speed and distance formula to find rate of crawling of turtle.

Time taken by turtle = \frac{1}{2} \ hour

Distance which can be traveled by turtle = \frac{3}{20} \ miles

Speed =\frac{Distance}{Time}

         =\frac{3}{20} \div\frac{1}{2} \\\\ =\frac{3}{20} \times\frac{2}{1} \\ \\ =\frac{6}{20}

Therefore, the rate at which the turtle is crawling is \frac{6}{20} \ mile\ per\ hour

4 0
3 years ago
The length of the rectangle is twice the width. Find the length of the rectangle if the perimeter is 42m.
kompoz [17]

Answer:

28m

Step-by-step explanation:

2x+x=42

3x=42

x=14

However, since the length of the rectangle is twice the width, we'll need to multiply it by 2.

So: 14 times 2=28

8 0
3 years ago
28.)Find the value of x.320(3x-10°A.) x = 22.67B.) x = 34.67C.) x = 21.6D.) x = 24.25
katen-ka-za [31]

Since the big triangle is an isosceles one, we conclude that the angles of the left triangle are: 32, 90 and 3x-10. Sinche the sum of this angles have to be 180° we have:

(3x-10)+32+90=180

Solving for x, we have:

\begin{gathered} (3x-10)+32+90=180 \\ 3x-10+32+90=180 \\ 3x=180+10-90-32 \\ 3x=68 \\ x=\frac{68}{3} \\ x=22.67 \end{gathered}

Therefore, x=22.67 and the answer is A.

7 0
1 year ago
The product of 5 and g
stich3 [128]

Answer:

5g

Step-by-step explanation:

6 0
3 years ago
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