Suppose a spider was able to create one thread that would extend from the top-right back corner of its tank to the bottom-left front corner. Approximately how long would that thread need to be for the tank below? The path of the spider's thread is shown with a red dotted line. Round your answer to the nearest tenth of an inch. Show your work.

Answer 1

To calculate the length of the spider's thread, we will need the dimensions of the tank. Let's denote the dimensions of the tank as follows:

• Length (L): the distance along the x-axis
• Width (W): the distance along the y-axis
• Height (H): the distance along the z-axis

The spider's thread extends from the top-right back corner (which we'll denote as point A) to the bottom-left front corner (which we'll denote as point B) of the tank. The coordinates of these two points can be expressed as:

• Point A (top-right back corner) = (L, W, H)
• Point B (bottom-left front corner) = (0, 0, 0)

To find the length of the thread, we can use the distance formula in three-dimensional space:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

In our case:

• \((x_1, y_1, z_1) = (L, W, H)\)
• \((x_2, y_2, z_2) = (0, 0, 0)\)

Plugging these coordinates into the distance formula gives:

\[ d = \sqrt{(0 - L)^2 + (0 - W)^2 + (0 - H)^2} \] \[ d = \sqrt{L^2 + W^2 + H^2} \]

Now, you need to provide the dimensions (L, W, and H) of the tank in order to calculate the exact length of the thread. Please give me those values so I can calculate the length for you!

Answer 2

ok the top says 35in and the bottem says 12in and the midel says 16in

Answer 3

Given the dimensions of the tank:

• Length (L) = 35 inches
• Width (W) = 12 inches
• Height (H) = 16 inches

We can use the formula for the distance \(d\) that we derived earlier:

\[ d = \sqrt{L^2 + W^2 + H^2} \]

Plugging in the values:

\[ d = \sqrt{(35)^2 + (12)^2 + (16)^2} \]

Calculating each squared term:

\[ (35)^2 = 1225 \] \[ (12)^2 = 144 \] \[ (16)^2 = 256 \]

Now, add these values together:

\[ d = \sqrt{1225 + 144 + 256} \] \[ d = \sqrt{1625} \]

Next, we need to calculate the square root of 1625.

\[ d \approx 40.311 \]

Rounding this to the nearest tenth:

\[ d \approx 40.3 \text{ inches} \]

Therefore, the length of the spider's thread would need to be approximately 40.3 inches.

Answer 4

The diagonal of the bottom of the tank is blank inches. To the nearest tenth of an inch, the length of the spider's thread is blank inches.

Answer 5

To find the diagonal of the bottom of the tank, we will consider the length and width of the tank. Using the dimensions:

• Length (L) = 35 inches
• Width (W) = 12 inches

The formula for the diagonal \(d\) of a rectangle (which in this case is the bottom of the tank) is given by:

\[ d = \sqrt{L^2 + W^2} \]

Plugging in the values:

\[ d = \sqrt{(35)^2 + (12)^2} \]

Calculating each squared term:

\[ (35)^2 = 1225 \] \[ (12)^2 = 144 \]

Now, add these values together:

\[ d = \sqrt{1225 + 144} = \sqrt{1369} \]

Now we calculate the square root:

\[ d = 37 \text{ inches} \]

Thus, the diagonal of the bottom of the tank is 37 inches.

Now, referring back to the length of the spider's thread (which was previously calculated):

• The length of the spider's thread is approximately 40.3 inches.

To summarize:

• The diagonal of the bottom of the tank is 37 inches.
• The length of the spider's thread is 40.3 inches.

Filling in the blanks:

• The diagonal of the bottom of the tank is 37 inches.
• To the nearest tenth of an inch, the length of the spider's thread is 40.3 inches.