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timofeeve [1]
3 years ago
11

(20 points)

Mathematics
2 answers:
chubhunter [2.5K]3 years ago
8 0
V = (1/4)(π* d² * h) 
<span>V = (1/4)(π * 10² * 12) </span>
<span>V = (1/4)(1200π) </span>
<span>V = 300π </span>
<span>[ V ≈ 942 cubic units . . . . . to 3 s.f. ] </span>
<span>V ≈ 942 cubic units 
</span>
Papessa [141]3 years ago
5 0

Answer:

Step-by-step explanation:

It is given that a cylinder has a base diameter of 10, then the radius of the cylinder will be 5.

Also, it is given that the height of the cylinder is 12, then

Volume of cylinder is given as:

V={\pi}r^2h

V=3.14{\times}(5)^2{\times}12

V=3.14{\times}25{\times}12

V=78.5{\times}12

V=942.0 cubic units

Therefore, the volume of the cylinder is 942 cubic units.

You might be interested in
A bacteria population experiences continuous growth. If there were 2,000 bacteria present at the start of an experiment, how lon
allochka39001 [22]

Answer:

D. About 15.69 hours.

Step-by-step explanation:

Let x be the number of hours.

We have been given that there  were 2,000 bacteria present at the start of an experiment and the growth rate was 7% per hour.

Since number of bacteria is growing exponentially, so we will use exponential growth function to solve our given problem.

The continuous exponential growth formula is in form: y=e^{kx}, where,

e= mathematical constant,

k = Growth rate in decimal form.

Let us convert our given rate in decimal form.

7\%=\frac{7}{100}=0.07

Upon substituting our given values we will get exponential function for bacteria growth as: y=2,000*e^{0.07x}, where, y represents number of bacteria after x hours.

Since we need to figure out the number of hours it will take for there to be 6,000 bacteria, so we will substitute y= 6,000 in our function.

6,000=2,000*e^{0.07x}

Let us divide both sides of our equation by 2,000.

\frac{6,000}{2,000}=\frac{2,000*e^{0.07x}}{2,000}

3=e^{0.07x}

Let us take natural log of both sides of our equation.

\text{ln}(3)=ln(e^{0.07x})

\text{ln}(3)=0.07x

1.0986122=0.07x  

x=\frac{1.0986122}{0.07}  

x=15.69446\approx 15.69  

Therefore, it will take about 15.69 hours to be 6,000 bacteria and option D is the correct choice.




3 0
3 years ago
This months rainfall is 30% less than last months total of 3.5 inches.
Afina-wow [57]

Answer:

1.05

Step-by-step explanation:

3.5x.30=1.05

6 0
3 years ago
Read 2 more answers
What is the 109th term of the arithmetic sequence {963, 936, 909, 882, …}?
tatyana61 [14]

Answer:

D. a109=-1,953

8 0
3 years ago
What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?
astra-53 [7]

x³ - 3x² + 4x - 2

complex roots occur in conjugate pairs

1 + i is a root then so is 1 - i

the factors of the polynomial are therefore

f(x) = (x - 1 )(x - (1 + i))(x - (1 - i))

     = (x - 1 )(x² - 2x + 2 ) ( expand factors and simplify )

     = x³ - 3x² + 4x - 2



4 0
3 years ago
Read 2 more answers
What is the value of z in the equation 2(4z − 3 − 21) = 166 − 46? 21 24 30 36
Nataly_w [17]
2(4z-3-21)=166-46

Combine like terms
2(4z-24)= 120

Distribute
8z-48= 120

Add 48 to both sides
8z= 168

Divide both sides by 8
z=21

Final answer: z=21
5 0
3 years ago
Read 2 more answers
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