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ad-work [718]
2 years ago
14

Which of the following expressions is equivalent to the one shown below? (4^3)^5

Mathematics
1 answer:
Effectus [21]2 years ago
6 0
Answer: 262,144
explanation: (4^3) = 64
64^5 = 262,144
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Find two possible factors for the estimated product 2,800
CaHeK987 [17]
28 x 100 and 280 x 10
5 0
3 years ago
The wildflowers at a national park have been decreasing in numbers. There were 1200 wildflowers in the first year that the park
bonufazy [111]

Year      New flowers

1                 1200

2                 300

3                   75

There were 1200 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year

Initially there are 1200 flowers and start decreasing by \frac{1}{4}

So first term is 1200 and common ratio is \frac{1}{4}.

Its a geometric sequence so summation becomes

i =1∑ ∞ 1200(\frac{1}{4})^{i-1}

Now we find the sum

We use sum formula

Sum = \frac{a}{1-r}

Where a is the first term , a= 1200

r is the common ratio , r= 1/4

Sum = \frac{1200}{1-(\frac{1}{4})}

Sum = \frac{1200}{\frac{3}{4}}

Sum = 1600 wildflowers

4 0
3 years ago
........................​
shtirl [24]

Answer:

Step-by-step explanation:

Figure (1)

x° = 107° [Vertically opposite angles]

Since, vertical angles are equal in measure.

Figure (2)

x + 71° = 90° [Given, complementary angles]

x = 90° - 71°

x = 19°

Figure (3)

x + 21° = 180° [Given as supplementary angles]

x = 180° - 21°

x = 159°

Figure (4)

x = 129° [Vertical angles]

Figure (5)

x° = 90° [Given]

z° + 34° = 90°

z° = 90° - 34°

z° = 56°

Since, x° + y° + z° = 180° [Linear angles]

90° + y° + 56° = 180°

y° + 146° = 180°

y° = 180° - 146°

y° = 34°

7 0
2 years ago
A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it tak
IgorC [24]

Answer

According to newton law of cooling

\dfrac{d T}{dt} = k (T - T_a)

and

T = Ce^{kt} + T_a

now At Ta = 100

T₀ = 10 °C

T₁ = 12° C

T(0) = Ce^{0} + T_a

10 = C + 100

C = -90

now,

12 = -90e^k + 100

e^k = \dfrac{88}{90}

k = ln{\dfrac{88}{90}}

at time equal to t

T(t) = 70

T(t) = -90 (\dfrac{88}{90})^t + 100

70 = -90(\dfrac{88}{90})^t + 100

(\dfrac{88}{90})^t = \dfrac{1}{3}

t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{3})

t = 48.88 s

hence, after 48.88 s the temperature of the body will be 70°C

b) time taken to reach 98°C

T(t) = -90 (\dfrac{88}{90})^t + 100

98 = -90(\dfrac{88}{90})^t + 100

(\dfrac{88}{90})^t = \dfrac{1}{45}

t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{45})

t = 390 s

hence, after 390 s the temperature of the body will be 98°C

5 0
2 years ago
Graph the linear equation x=-1
kipiarov [429]

Answer:

See below

Step-by-step explanation:

It's just a vertical line drawn at x=-1. See the graph for a visual.

6 0
3 years ago
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