Calculate the radius of the sphere with the given volume.

Volume=4/81π ft^3

Answers

Answer 1

Answer:

Answer:

(∛3)/2 ft = r

Step-by-step explanation:

Start with the formula for the volume of a sphere: V = (4/3)πr³. Solve this for r³ and then take the cube root of the result:

V = (4/3)πr³ => (3/4)V = πr³ => (------- = r³

4π

3 · 4/81π ft^3 3 · 4π ft³ 3 ft³

Here we have r³ = -------------------- = ---------------- = -------------

4π 8(4π) 8

and so the radius is r = ∛[ (3/8) ft³] = (∛3)/2 ft = r

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Given: x + 3.8 > -10.02. Choose the solution set. {x | x R, x > -6.22} {x | x R, x > -10.40} {x | x R, x > -13.82}
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How do you divide can someone plz tell me

Answers

Just divide
Like 4:2=2

Its pretty easy lets say 2:4 How many times does 2 go into 4 two times see easy

A Geometry textbook has a mass of 48 grams.The textbook is in the shape of a rectangular prism with dimensions show below.

To find density use: density

mass

volume

5 cm

16 cm

10 cm

Determine the density of the Geometry textbook in g/cm3.

Round your answer to the nearest hundredths place.

Answers

The density of the Geometry textbook is 0.06 g/cm^3.

To find the density of the Geometry textbook in g/cm^3, we need to find its volume first. The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.

In this case, the length is 16 cm, the width is 10 cm, and the height is 5 cm. Therefore, the volume of the Geometry textbook is:

V = l x w x h = 16 cm x 10 cm x 5 cm = 800 cm^3

Now, we can find the density of the textbook using the formula:

$density = mass / volume$

Plugging in the given mass of 48 grams and the calculated volume of 800 cm^3, we get:

density = 48 g / 800 cm^3 = 0.06 g/cm^3

Therefore, the density of the Geometry textbook is 0.06 g/cm^3. We rounded our answer to two decimal places as the original mass was given in grams to two decimal places.

Learn more about Geometry here:

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Two numbers multiply to be -40 and add to be 3. What are the numbers?

Answers

Answer:

The numbers are (x,y)=(-5,8) or (8,-5)

Step-by-step explanation:

Let two numbers be x and y,

We have,

x+y=3

x=3-y---(i)

Now,

xy=-40

(3-y)y=-40 [From (i)]

3y-y^2=-40

y^2-3y-40=0

Factoring,

(y + 5) (y - 8)=0

Either,

y+5=0 or, y-8=0

y=-5 y=8

When y=-5,

x=3-y

3--5

3+5

When y=8,

x=3-y

3-8

-5

PLEASE HELP ME WITH THESE QUESTIONS

Answers

Answer: 8

Step-by-step explanation:

log₃ (x² - 32) = log₃ (4x) restrictions: x² - 32 > 0 and 4x > 0 ⇒ x > 4√2

x² - 32 = 4x

x² - 4x - 32 = 0

(x - 8)(x + 4) = 0

x - 8 = 0 or x + 4 = 0

x = 8 or x = -4

-4 does not meet the restriction so not valid

********************************************************************************************

Answer: y = 7x - 6

Step-by-step explanation:

7x -6

x² + 0x + 4 ) 7x³ - 6x² + 0x + 7

-7x³ + 0x² - 28x

-6x² - 28x + 7

6x² + 0x + 24

-28x + 31

********************************************************************************************

Answer: x = $(6)/(5)$

Step-by-step explanation:

ln 3 + ln x = ln 6 + ln (3x - 3) restrictions: x > 0 and 3x - 3 > 0 ⇒ x > 1

ln (3 * x) = ln (6*(3x - 3))

ln (3x) = ln (18x - 18)

3x = 18x - 18

-18x -18x

-15x = -18

$(-15x)/(-15) = (-18)/(-15)$

x = $(6)/(5)$

$(6)/(5)$ > 1 so answer is valid

********************************************************************************************

Answer: -5.9761

Step-by-step explanation:

log ₁₎₂ 63

= $(log (63))/(log((1)/(2)))$

= $(1.7993)/(-0.3010)$

= -5.9761

The diameter of a quarter is about 2.4 centimeters. a. What is the circumference of a quarter ? (Use 3.14 for pie) b. What is the ratio of the radius of the quarter to the diameter of the quarter?

Answers

radius=1.2
circuimsantece=2*3.14*1.2=76.36
circuimsantece of quarter=76,36/4=19.09
ratio=1/2

The terminal side of an angle θ in standard position passes through the point (3, 1). Calculate the exact values of the six trig functions for angle θ.

Answers

Answer:

sin α = $(y)/(r)$ = $(1)/(√(10) )$

cos α = $(x)/(r)$ = $(3)/(√(10) )$

tan α = $(y)/(x)$ = $(1)/(3)$

cot α = $(x)/(y)$ = $(3)/(1)$

sec α = $(r)/(x)$ = $(√(10) )/(3)$

csc α = $(r)/(y)$ = $(√(10) )/(1)$

Step-by-step explanation:

If the point is given on the terminal side of an angle, then:

Calculate the distance between the point given and the origin:

r = $√(x^2+y^2)$

Here it is: $√(3^2+1^2)$ = $√(9+1)$ = $√(10)$

So we have:

x = 3

y = 1

r = $√(10)$

Now we can calculate all 6 trig, functions:

sin α = $(y)/(r)$ = $(1)/(√(10) )$

cos α = $(x)/(r)$ = $(3)/(√(10) )$

tan α = $(y)/(x)$ = $(1)/(3)$

cot α = $(x)/(y)$ = $(3)/(1)$

sec α = $(r)/(x)$ = $(√(10) )/(3)$

csc α = $(r)/(y)$ = $(√(10) )/(1)$

Final answer:

The question involves calculating the six trigonometric functions (Sin, Cos, Tan, Csc, Sec, Cot) for an angle in standard position with its terminal side passing through point (3,1). We find opposite and adjacent sides from the point's coordinates, the hypotenuse from Pythagoras' theorem, and calculate each ratio accordingly.

Explanation:

In the context of the problem, the point (3,1) specifies the terminal side of angle θ in standard position. This point is effectively the definition of your right triangle's opposite (y) and adjacent (x) sides in the trigonometric calculation, with the hypotenuse (h) obtained from Pythagoras' Theorem (h² = y² + x²). In this case, we get h = sqrt(3² + 1²) = sqrt(10).

The six trigonometric functions are defined as follows for this scenario: