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13 days ago

A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.

Mathematics

2 answers:

tester [3.9K]13 days ago

7 0

Answer:

The accurate statements are:

The sphere has a diameter of 32 inches.

The length of the radius is half that of the diameter.

The sphere's volume totals StartFraction 16,384 Over 3 EndFraction pi cubic inches.

Step-by-step explanation:

The sphere has a diameter of 8 in. False

This is incorrect because the radius is always half the diameter. Half of 8 in gives 4 in, whereas the stated radius is 16 in.

The sphere’s volume is StartFraction 2,048 Over 3 EndFraction pi cubic inches. False

This is incorrect since the formula for a sphere's volume is 4πr³/3 = (16,384/3) π cubic inches.

The sphere has a diameter of 32 in. True

This is correct as the radius is half the diameter. Half of 32 in is 16 in, aligning with the given radius.

The length of the radius is half that of the diameter. True

This is accurate because the radius, by definition, is half of the diameter.

The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi cubic inches. True

This is correct based on the volume calculation of 4πr³/3 = (16,384/3) π cubic inches.

The diameter is half the radius's length. False

Instead, it is the radius that measures half the diameter’s length.

lawyer [4K]13 days ago

6 0

Answer:

The sphere has a 32 in. diameter. CORRECT: A sphere's diameter equals twice its radius; therefore, if the radius is 16, then the diameter is 32.
The radius measures half the diameter's length. CORRECT: According to the definition, the diameter represents the greatest distance across the sphere, and its length is twice the radius since the radius extends from the center to the surface (imagining that distance across the sphere can connect two radii, which create the diameter).
The sphere's volume (V) can be computed as $\frac{4\pi r^3}{3}$ , where r is the radius. In this instance, the sphere's volume equals $\frac{4\pi\times16^3}{3}=\frac{4\pi\times4096}{3}$ , which can also be expressed as $\frac{16384\times\pi}{3}$ .

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Two planes A and B can each fly through still air at 550 mph. The distance from Paris to Los Angeles is 5000 miles. Wind blows f

PIT_PIT [3919]

Answer:2688.63 miles

Step-by-step explanation:

Given

The distance from Paris to Los Angeles $d=5000 miles$

Wind traveling at 100 mph from Los Angeles to Paris

The velocity of the plane through still air is $v=550 mph$

Relative velocity of Plane A is $v_a=550-100 =450 mph$ since Plane A is heading against the wind

Relative velocity of Plane B is $v_b=550+100=650 mph$

Plane A departs at noon

Distance covered by Plane A in 1 hour $=450\times 1=450 miles$

The total separation distance between the planes is $5000-450=4550 miles$

Assuming they meet after t hours

Distance covered by Plane B in that time frame $=v_b\times t=650\times t$

Distance traveled by Plane A in t hours is $=v_a\times t=450 t$

The total distance equals 4550 miles

$4550=650t+450t$

$t=\frac{4550}{1100}$

$t=4.13 hr$

Distance traveled by B is $=650\times 4.136=2688.63 miles$

thus, they meet at a point 2688.63 miles away from Los Angeles.

5 0

11 days ago

Explain two ways you could solve 20 = 5(-3 + x)

Leona [4166]

Answer:

The solution to your inquiry can be found below

Step-by-step explanation:

First method

20 = 5(-3 + x) expanding this equation

20 = -15 + 5x combine like terms

5x = 20 + 15

5x = 35 dividing by 5

5x/5 = 35/5

x = 7

Second method

20/5 = 5/5 (-3 + x) divide both sides by 5

4 = -3 + x adding 3 to both sides

4 + 3 = -3 + 3 + x simplifying

7 = x

3 0

12 days ago

Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth. From the least to the greatest, the

zzz [4022]

Response:

Refer to the attached graph

x₁ ≈ - 2.1

x₂ ≈ 0.2

Clarification:

To analyze log (−5.6x + 1.3) = −1 − x visually, graph these equations on the same coordinate system:

Equation 1: y = log (5.6x + 1.3)

Equation 2: y = - 1 - x

The first equation can be graphed using these characteristics of logarithmic functions:

Domain: values must be positive ⇒ -5.6x + 1.3 > 0 ⇒ x < 13/56 (≈ 0.23)

Range: all real values (- ∞, ∞)

x-intercept:

log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒ x = 0.3/5.6 ≈ 0.054

y-intercept:

x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11

Choose additional values to create a table:

x log (-5.6x + 1.3)

-1 0.8

-2 1.1

-3 1.3

This graph is shown in the attached image: it's represented by the red curve.

Graphing the second equation is simpler as it forms a straight line: y = - 1 - x

slope, m = - 1 (the coefficient of x)

y-intercept, b = - 1 (the constant term)

x-intercept: y = 0 = - 1 - x ⇒ x = - 1

This graph is indicated by the blue line in the image.

The resolution to the equations corresponds to the points where the two graphs intersect. The graphing method thus allows you to determine the x coordinates of these intersection points. Ordered from smallest to largest, rounded to the nearest tenth, we have: