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My name is Ann [436]
3 years ago
11

Rewrite the following problems using exponent rules. Then, solve using logarithms.

Mathematics
1 answer:
Anna35 [415]3 years ago
3 0

9514 1404 393

Answer:

  1. 3(0.96059601^t) = 15; t = -40.03

  2. 4.121204(1.01^t) = 8; t = 66.66

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

The solution for an exponential problem using logarithms is ...

  a·b^x = c   ⇒   log(c/a)/log(b) = x

_____

1. Rewrite: (3)(0.99^4)^t = 15  ⇒  3(0.96059601^t) = 15

Solution: t = log(15/3)/log(0.96059601) ≈ -40.03

__

2. Rewrite: 4(1.01^3)(1.01^t) = 8  ⇒  4.121204(1.01^t) = 8

Solution: t = log(8/4.121204)/log(1.01) ≈ 66.66

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Anika is 7 years older than Kit. If Kit is k years old, how old is Anika?
zaharov [31]

Answer:

k+7

Step-by-step explanation:

because k is the age of kit so Anika is 7 years older, so u have to add

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7 0
3 years ago
33% of what number is 1.45? Round to the nearest tenth.
tatuchka [14]

Take the unknown number as 'y'.

=》33% = 33/100

=》1.45 = 145/100

33/100 × y = 1.45

33/100 × y = 145/100

33y = 145/100 × 100/1

33y = 145

y = 145/33

y = 4.39

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RainbowSalt2222 ☔

3 0
2 years ago
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The graph shows the plans for a fence that Macy is building around her vegetable garden. Each unit on the graph represents 5 fee
ipn [44]

Answer:

70

Step-by-step explanation:

5*4=70

3 0
2 years ago
Ayuda con mates por favor
QveST [7]

Answer:

a) x = -1 and  y = 5, b) x = 2 and y = -1, c) x = -2 and y = 1, d) x = 2 and y = -9, e) x = 2 and y = -2, f) x = 2 and y = -1, g) x = 2 and y = -1, h) x = 1 and y = 2.

Step-by-step explanation:

Each system is solved as follows (Cada sistema es resuelto como sigue):

a) 2\cdot x + y = 3 and 3\cdot x - y = -8

y = 3 - 2\cdot x

3\cdot x - 3 + 2\cdot x = -8

5\cdot x = -5

x = -1

y = 5

b) x - 2\cdot y = 4 and -x+3\cdot y = -5

x = 4 + 2\cdot y

-4-2\cdot y+3\cdot y = - 5

-4+y = -5

y = -1

x = 2

c) -2\cdot x + 5\cdot y = 9 and x - y = -3

x = y-3

-2\cdot y +6 +5\cdot y = 9

3\cdot y = 3

y = 1

x = -2

d) 5\cdot x - 4\cdot y = 2 and 3\cdot x + 2\cdot y = -12

3\cdot x + 2\cdot y = -12

6\cdot x + 4\cdot y = -24

4\cdot y = -6\cdot x -24

5\cdot x +6\cdot x +24 = 2

11\cdot x = -22

x = 2

y = -9

e) x + y = 0 and 2\cdot x +3\cdot y = -2

y = -x

2\cdot x -3\cdot x = -2

-x = -2

x = 2

y = -2

f) 3\cdot x + 5\cdot y = 1 and x + y = 1

y = 1 - x

3\cdot x + 5 - 5\cdot x = 1

-2\cdot x = -4

x = 2

y = -1

g) 5\cdot x - 2\cdot y = 12 and 4\cdot x + 3\cdot y = 5

x = \frac{12+2\cdot y}{5}

x = \frac{5-3\cdot y}{4}

\frac{12+2\cdot y}{5} = \frac{5-3\cdot y}{4}

4\cdot (12+2\cdot y) = 5\cdot (5-3\cdot y)

48 + 8\cdot y = 25 - 15\cdot y

23\cdot y = -23

y = -1

x = 2

h) 7\cdot x + 8\cdot y = 23 and 3\cdot x + 2\cdot y = 7

3\cdot x + 2\cdot y = 7

12\cdot x + 8\cdot y = 28

8\cdot y = 28 - 12\cdot x

7\cdot x +28-12\cdot x = 23

-5\cdot x = -5

x = 1

y = 2

8 0
3 years ago
-9r<br> r=7<br> Please help I'm tired and can't think
Bas_tet [7]

Answer:

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Step-by-step explanation:

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8 0
2 years ago
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