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2 years ago

5

During a chemical reaction the temperature in a beaker decreased every minute by the same number of degrees the temperature was

16°C at 11:08 AM by 11:52 AM the temperature had dropped to -17°C by how many degrees did it change each minute

1 answer:

Zarrin [17]2 years ago

6 0

Answer:

.75 degrees Celsius

Step-by-step explanation:

1152-1108=44 16+17=33 33divided by 44=0.75

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7. ***HINT: MEAN = AVERAGE *

Korolek [52]

The mean is 4.9 miles per day

3 0

3 years ago

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

5 0

1 year ago

3 The volume of a cube is 8 ft}. What is the length of each<br> edge of the cube?

Sliva [168]

Answer: 2

Formula for cube is x^3 = 8
2^3 = 8

3 0

3 years ago

Read 2 more answers

Enter the missing numbers in the boxes to complete the table of equivalent ratios

son4ous [18]

Answer:

Time(min)

2

6

8

15

Distance(km)

6

18

24

45

Step-by-step explanation:

the time is 1/3rd of the distance. it's a 1:3 ratio

4 0

3 years ago

Please help! Will mark Brainiest!

DochEvi [55]

Answer:

27.93 square yard

Step-by-step explanation:

For semicircle:

Radius (r) = 7 yards

For Triangle:

b = 2r = 2*7 = 14 yd

h = 7 yard

Area of shaded region = Area of semicircle - Area of triangle

$= \frac{1}{2} \times \pi {r}^{2} - \frac{1}{2} \times b \times h \\ \\ = \frac{1}{2} \times 3.14 \times {7}^{2} - \frac{1}{2} \times 14\times 7 \\ \\ = \frac{1}{2} \times 3.14 \times 49 - \frac{1}{2} \times 98\\ \\ = 3.14 \times 24.5 - 49 \\ \\ = 76.93 - 49 \\ \\ = 27.93 \: {yd}^{2} \\$

7 0

2 years ago