If a sphere’s volume is doubled, what is the corresponding change in its radius?

Answers

Answer 1

Answer: The answer is the radius is increased ∛2 (≈ 1.26) times.

The sphere's volume formula is:
V = 4/3 π r³
where:
V - the sphere's volume,
r - radius of the sphere.

If sphere's volume is doubled, we have:
V₁ = 4/3 π r₁³
We need to know what is the ratio of r₁ and r.

V₁ = 2 × V = 2 × 4/3 π r³
⇒ 2 × 4/3 π r³ = 4/3 π r₁³
We can remove the same parts of the left and right sides of the equation:
2 × r³ = r₁³
r₁ = ∛(2 × r³)
r₁ = ∛2 × ∛r³
r₁ =∛2 × r
r₁ ≈ 1.26 r
Or: r₁/r = 1.26

Therefore, the radius is increased ∛2 (≈ 1.26) times.

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Consider the logarithmic equation f(x) = ln (x + 2) – 1. Round all values to the tenths place.(a) Determine any x- and y-intercepts.
(b) Determine the domain and the equation of the vertical asymptote.
(c) Make a table of values to find three other points on the graph.
(d) Graph the function. Label the three points you found in Part (c).

Answers

Hello,

A) x=0==> f(0)=ln(2)-1=-0,30685281944005469058276787854182
y=0==>ln(x+2)-1=0
==>ln(x+2)=1
==>e^ln(x+2)=e^0
==>x+2=0
==>x=-2

B)
dom f(x)={x∈IR | x>2}
x=-2 is the vertical asymptote

c)
A=(-1,-1)
B=(0,ln(2)-1=-0,30685281944005469058276787854182 )
C=(1,ln(3)-1=0,09861228866810969139524523692253)
D=(2,ln(4)-1)=0,38629436111989061883446424291635)

d) see picture

What is the solution to the following equation?

5(2x –6) + 20 = 10 (4 points)

Answers

5(2x-6)+20=10

Distribute

(5)(2x)+(5)(-6)+20=10

10x-30+20=10

Combine like terms (10x)+(-30+20)=10

10x-10=10

Add 10 to both sides

10x-10+10=10+10

10x=20

x = 20/10

x= 2

I hope that's help !

Book is 24 dollars. Ben pays 25.02. what is sales tax rate.

Answers

$25.02-24.00=x$
$1.02=x$
$24.00(x)=1.02$
$24x=1.02$
$(24x)/(24) = (1.02)/(24)$
$x=0.0425$
Sales tax rate is 4.25&

Answer:

he paid $1.02 tax. i think that based on this, the tax rate would be 1.025%, but i might be wrong

Step-by-step explanation:

A broker takes 2% as commission for the sale of property of value up to rupees 3,00,000. If the sale price is more than this, the broker changes 1.5% for the remaining amount. If a property was sold for rupees 4,50,000.What was the broker's commission.