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goldfiish [28.3K]

3 years ago

14

What is the value of

alt="\frac{81^4}{3^5}" align="absmiddle" class="latex-formula">? (Express your answer in exponential form.)

1 answer:

IRISSAK [1]3 years ago

5 0

Answer: $3^1^1\\$

Step-by-step explanation:

$\frac{81^4}{3^5}$

$\frac{3^1^6}{3^5}$

The base is same power can be add or subtract

$3^1^6^-^5$

$3^1^1$

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A lake polluted by bacteria is treated with an antibacterial chemical. Aftertdays, thenumber N of bacteria per milliliter of wat

jeyben [28]

Answer:

N(1)=50 is a minimum

N(15)=4391.7 is a maximum

Step-by-step explanation:

<u>Extrema values of functions </u>

If the first and second derivative of a function f exists, then f'(a)=0 will produce values for a called critical points. If a is a critical point and f''(a) is negative, then x=a is a local maximum, if f''(a) is positive, then x=a is a local minimum.

We are given a function (corrected)

$N(t) = 20(t^2-lnt^2)+ 30$

$N(t) = 20(t^2-2lnt)+ 30$

(a)

First, we take its derivative

$N'(t) = 20(2t-\frac{2}{t})$

Solve N'(t)=0

$20(2t-\frac{2}{t})=0$

Simplifying

$2t^2-2=0$

Solving for t

$t=1\ ,t=-1$

Only t=1 belongs to the valid interval $1\leqslant t\leqslant 15$

Taking the second derivative

$N''(t) = 20(2+\frac{2}{t^2})$

Which is always positive, so t=1 is a minimum

(b)

$N(1)=20(1^2-2ln1)+ 30$

N(1)=50 is a minimum

(c) Since no local maximum can be found, we test for the endpoints. t=1 was already determined as a minimum, we take t=15

(d)

$N(15)=20(15^2-2ln15)+ 30$

N(15)=4391.7 is a maximum

7 0

3 years ago

Please please please hellllllppp meeeeee !!!!!!!!!

Nezavi [6.7K]

ANSWER: 77
Explanation: Making 88 in 8 minutes means that the machine is making 11 per minute thus being said if the machine worked for 7 minutes it would make 77 pens.
88/8=11
11*7=77

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3 years ago

2. A local baseball stadium has a total of 2,414 seats, with 221 seats reserved for season ticket holders.

kogti [31]

2414 total seats.......221 reserved.....x = non-reserved.....y = remaining seats

y = 2414 - (x + 221)
y = 2414 - x - 221
y = 2193 - x <=====

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The radius of a cylindrical gift box is (2x+3) in. The height of the gift box is twice the radius. What is the surface area of t

inessss [21]

SA=2pir^2+2hpir=2pir(r+h)
h=2r=2(2x+3)=4x+6

SA=2pi(2x+3)(2x+3+4x+6)
SA=(4x+6)(pi)(6x+9)
SA=24πx²+27πx+54π

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3 years ago

5. Solve the following inequality –1 + 6(-1 - 3x) > -39 - 2x.

Stells [14]

Answer:

Step-by-step explanation:

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3 years ago