∠RQT is a straight angle. What are m∠RQS and m∠TQS?

Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphin's clicking sounds using computer

lina2011 [118]

Step-by-step explanation:

The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:

(y - k)^2 = 4 * f * (x - h)

In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:

y^2 = 4 * f * x

= 4 * (-1.3) * x

= -5.2x

The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.

4 0

1 year ago

Find the dimensions of an open rectangular box with a square base that holds 2000 cubic cm and is constructed with the least bui

Vesnalui [34]

<h3>The dimensions of the given rectangular box are:</h3><h3>L = 15.874 cm , B = 15.874 cm , H = 7.8937 cm</h3>

Step-by-step explanation:

Let us assume that the dimension of the square base = S x S

Let us assume the height of the rectangular base = H

So, the total area of the open rectangular box

= Area of the base + 4 x ( Area of the adjacent faces)

= S x S + 4 ( S x H) = S² + 4 SH ..... (1)

Also, Area of the box = S x S x H = S²H

⇒ S²H = 2000

$\implies H = \frac{2000}{S^2}$

Substituting the value of H in (1), we get:

$A = S^2 + 4 SH = S^2 + 4 S(\frac{2000}{S^2}) = S^2 + (\frac{8000}{S})\\\implies A = S^2 + (\frac{8000}{S})$

Now, to minimize the area put :

$(\frac{dA}{dS} ) = 0 \implies 2S - \frac{8000}{S^2} = 0\\\implies S^3 = 4000\\\implies S = 15.874 \approx 16 cm$

Putting the value of S = 15.874 cm in the value of H , we get:

$\implies H = \frac{2000}{S^2} = \frac{2000}{(15.874)^2} = 7.8937 cm$

Hence, the dimensions of the given rectangular box are:

L = 15.874 cm

B = 15.874 cm

H = 7.8937 cm

3 0

3 years ago

Duke has a spinner that is divided into six equal-sized sections. Each section is a different color. He spun the spinner multipl

N76 [4]

Answer:

C. 1/6

Step-by-step explanation:

The experimental probability is the probability that is obtained by dividing the number of times the required outcome has occurred by the total number of trials.

In the experiment given the color red is one of the six possible outcomes and the next time the experiment is performed the number of trials would be 1

so the experimental probability would be 1/6

If the previous number of trials were given then the probability would have been different.

6 0

3 years ago

Read 2 more answers

"Calculate the volume of the cylinder if the diameter is 42 cm and height of cylinder is 8 cm"

olga55 [171]

To find the answer of this problem you need the formula for a cylinder.

V= pi* r^2 * h just plug in your numbers and you have the answer.

You also need to remember that diameter is just twice the radius.

6 0

2 years ago

The regular price of an item is $65. The item is on sale with a discount of $8.What is the discount rate

amid [387]

The discount rate is the discount amount ($8) divided by the regular price, as a percentage.65/8=8.125 rounded to 8 so 8%.

6 0

2 years ago