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zhannawk [14.2K]
3 years ago
10

Rewrite the radical exponent as a radical

Mathematics
1 answer:
shepuryov [24]3 years ago
3 0
\bf a^{\frac{ n}{ m}} \implies  \sqrt[ m]{a^ n} 
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
-------------------------------\\\\
\left( 5^{\frac{3}{4}} \right)^{\frac{2}{3}}\implies 5^{\frac{3}{4}\cdot \frac{2}{3}}\implies 5^{\frac{1}{2}}\implies \sqrt[2]{5^1}\implies \sqrt{5}
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A cone has a volume of 942 in.³ and a height of 9 inches what is the radius of the cone use 3.14 for pie
bija089 [108]

Answer:

r = 51.96 inches

Step-by-step explanation:

V_{cone} = \pi {r}^{2} h  \\  \\  \implies \: r^{2}  =  \frac{V_{cone}}{\pi h } \\  \\  \implies \:  r^{2} =  \frac{942}{3.14 {(9) } }\\  \\  \implies \:  r^{2} =  \frac{942}{3.14 {(9) } } \\  \\  \implies \:  r^{2} =2700 \\  \\  \implies \:  r= \sqrt{2700}  \\  \\  \implies \:  r=51.96 \: inches

8 0
2 years ago
Which of the following situations could be modeled by an exponential function?
Sauron [17]

Answer: Option D.

Step-by-step explanation:

An exponential function is something like:

f(x) = A*(r)^x

Where:

A = initial amount.

r = rate of growth

x = variable.

This type of function is used to describe situations like "you have A dollars, and it increases by 30% each week"

or:

"There is a population of A animals, and it doubles each year"

Let's analyze briefly all the given options and see which one is an exponential function.

A) The water level of a tank decreases by 5 gallons every day.

This is a linear relation, if W is the initial amount of water, and x is the number of days, then the water level of the tank after x days is:

y = W - 5 gal*x

B) The amount of money collected by a charity increases by $5,000 each year.

The amount collected increases $5000 each year.

Then if in year 1 they collected A.

in year 2 they collected A + $5000

in year 3 they collected A + 2*$5000

We already can see the pattern, this is a linear relation:

in year X they colected A + (X - 1)*$5000

C) A tree was 10 feet tall when purchased and grows at a rate of 2 feet per year.

if y is the height of the tree, and x is the number of years, this can be written as:

y = 10ft + x*2ft

Again, a linear relation.

D) The number of people in a stadium is decreasing at a rate of 45% every 10 minutes.

Let's define x as each "lapse" of 10 minutes that passes.

If N is the initial number of people in te stadium, then after 10 minutes the number of people is = N*(1 - 45%/100%) = N*(1 - 0.45) = N*0.55

After another 10 minutes, the population decreases again.

N*0.55*(1 - 45%/100%) = N*0.55*0.55 = N*0.55^2

We can see the pattern here, this can be written as

People(x) = N*(0.55)^x

This is an exponential function.

3 0
2 years ago
The playing surfaces of two foosball tables are similar. The ratio of the corresponding side lengths is 10:7. What is the ratio
Dvinal [7]

Let's write this proportion of equivalent ratios in equation form and then plug in our two known values to determine our two unknown values:

    (s1)2 : (s2)2 = A1 : A2

    (10)2 : (7)2 = 100 : 49

 

Ratio of the Areas = 100 : 49

 

5 0
3 years ago
What triangle does the pythagorean theorem relate to
Vesna [10]

Answer:

Right Triangle

Step-by-step explanation:

I hope this helps!

6 0
2 years ago
Help! Please Geometry
maria [59]

Answer:

The answer is 60

Step-by-step explanation:

Every triangle is 180 degrees. You have 30+90=120. (The square represents 90 degrees because it is a right angle) So to have 180 total you would subtract 180 from 120(180-120) which gives you 60. 60+120=180

5 0
3 years ago
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