All categories

2 months ago

What is the length of side PQ in this figure?

Mathematics

2 answers:

Svet_ta [12.7K]2 months ago

7 0

Response:

Option: C

Detailed explanation:

To determine the length of side PQ, we must first calculate the length of the vertical line segment that is perpendicular to side PR, which we shall call QS.

Since ΔQSR is a right triangle, and we know the lengths of sides QR and SR, we can apply the Pythagorean theorem:

$QR^{2}=SR^{2}+QS^{2}$

$5^{2}=3^{2}+QS^{2}\\ \\QS^{2}=5^{2}-3^{2}\\\\QS^{2}=25-3=16=4^2$

Thus, QS=4.

Next, we analyze ΔQSP, which is also a right triangle, and again utilize the Pythagorean theorem:

$PQ^{2}=QS^{2}+PS^{2}\\ \\PQ^{2}=4^{2}+6^{2}=16+36=52$

This implies $QS=\sqrt{52}=2\sqrt{13}$

Consequently, side PQ measures $\sqrt{52}=2\sqrt{13}$ .

Therefore, option C is the correct choice.

lawyer [12.5K]2 months ago

5 0

I trust this will assist you.

You might be interested in

What teacher exhibited the most consistent performance over this 5 year span

lawyer [12517]

Is there meant to be an image?

4 0

2 months ago

Drainage tubing comes in large rolls. At your hardware store, you cut tubing to the lengths the customers want. You also provide

Leona [12618]

Answer: $\frac{1}{36}\pi L$

Step-by-step explanation:

The volume of a cylinder is calculated using the formula:

$V=\pi r^2h$

In which "r" represents the radius and "h" is the height.

Convert inches to feet. Given that $1\ ft=12\ in$ , the result is:

$(2\ in)(\frac{1\ ft}{12\ in})=\frac{1}{6}\ ft$

Therefore, you can determine:

$r=\frac{1}{6}\\\\h=L$

After substituting these values into the formula and simplifying, the result is:

$V=\pi(\frac{1}{6})^2L\\\\V=\frac{1}{36}\pi L$

Consequently, the equation representing the volume of L feet of drainage tubing, in cubic feet, is:

$\frac{1}{36}\pi L$

4 0

2 months ago

Read 2 more answers

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. Which expression represents the h

babunello [11817]

Answer:

The height of the triangular pyramid base is represented by s√3/2 units.

Step-by-step explanation:

This question focuses on calculating the height of the equilateral triangle at the base of the oblique pyramid.

According to the question, the equilateral triangle side has a length of a units.

Let’s review some properties of equilateral triangles:

a. All sides are identical in length, in this case, side s represents all sides.

b. All angles measure the same, at 60 degrees each.

c. Drawing a perpendicular line from the top vertex to the base divides the triangle into two right triangles, which have angles of 60 and 30 degrees, respectively.

To find the height of this triangular base, we can utilize either of the two right-angled triangles.

Recall the angles of 30, 60 and the side length s.

For height h calculation, trigonometric functions will assist us.

The relevant trigonometric relationship involves the sine of the angle (where side length s is the hypotenuse and height h is the opposite side relative to the 60-degree angle).

Thus, we can express this as:

Sine of an angle = opposite side length/hypotenuse length

sin 60 = h/s

Consequently, h = s sin 60.

In surd form, this yields:

sin 60 = √3/2.

Therefore, we find:

h = s * √3/2 = s√3/2 units.

3 0

2 months ago

A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. Find the volume of the foam.

Leona [12618]

Answer:

V-foam = 4r³( 2 - ----- )

Step-by-step explanation:

Let r denote the radius of the sphere. The volume of the sphere is expressed as

V = (4/3)(π)(r³).

Next, understand that the cube's side length is 2r, hence the cube's volume is

V = (2r)³, which equals 8r³.

The volume of the foam is derived from the cube's volume subtracting that of the sphere:

V-foam = 8r³ - (4/3)(π)(r³). This can be simplified to

V-foam = 4r³( 2 - ----- )

5 0

2 months ago

Trevor is training for a race he swims 1/2 lap in 4/5 minute at that race how many minutes does it take for Trevor to swim each

Svet_ta [12734]

8/5 minutes is the solution.

7 0

2 months ago