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3 years ago

What is the units digit of 2 to the 50th power

1 answer:

6 0

Notice that

$2^1=2$
$2^2=4$
$2^3=8$
$2^4=16$
$2^5=32$

so that for each power of 2, there is a pattern of period 4. This means that for integers $k\ge0$ , each of $2^{4k}$ , $2^{4k+1}$ , $2^{4k+2}$ , and $2^{4k+3}$ have the same units digit.

We can write $50=4(12)+2$ , and since $3=4(0)+2$ , it follows that $2^{50}$ and $2^3$ share the same units digits. So the units digit of $2^{54}$ is 8.

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Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137

Nata [24]

Answer:

Camera 2nd has to cover the maximum angle, i.e. $78.70^\circ$ .

Step-by-step explanation:

Please have a look at the triangular park represented as a triangle $\triangle ABC$ with sides

a = 110 ft

b = 158 ft

c = 137 ft

1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.

We can use law of cosines here, to find out the angles $\angle A, \angle B, \angle C$

As per Law of cosine:

$cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}$

Putting the values of a,b and c to find out angles $\angle A, \angle B, \angle C$ .

$cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ$

$cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ$

$cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ$

Camera 2nd has to cover the maximum angle, i.e. $78.70^\circ$ .

6 0

4 years ago

Helppp i need help on this question on my hw

yaroslaw [1]

Answer:

B)m^2/3n^5/3

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

In a class full of men and women, 5/9 of the class are women. What is the ratio of men to women in its simplest form?

andrew-mc [135]

Answer:

4/5

Step-by-step explanation:

5x are women

9x are full class

9x - 5x = 4x

4x are men

$\frac{4x}{5x} = \frac{4}{5}$ is the ratio of men to women in its simplest form

Hope this helps ^-^

3 0

3 years ago

What is the midpoint between points (1, 4) and (9, 16)?

Ostrovityanka [42]

To find the midpoint you find the average x and the average y values. The average of 1 and 9 is 5, and the average of 4 and 16 is 10. The midpoint would be (5,10).

5 0

3 years ago

1)Evaluate 2A - 3B for A = 7 and B = -2.

Gnom [1K]

Hey Brion,

1) Evaluate 2A - 3B for A = 7 and B = -2.
To solve this start by filling in the variables.
2(7) - 3(-2)

Now multiply, remember that a positive times a negative is a negative.
14 - (-6)

Finally, subtract. Remember, Keep, Change, Change (KCC). Keep the first number, change symbol (for subtraction use addition), and change the negative number to a positive number.
14 + 6 = 20

2) If x = -3, then x 2-7x + 10 equals
Start by filling in the variables.
-3(2) - 7(-3) + 10

Now follow PEMDAS (Parentheses, Exponents, Multiplication & Division, Addition & Subtraction) to solve. Remember K.C.C (no. 1 above)
-3(2) - 7(-3) + 10
(-6) - (-21) + 10
(-6) + (21) + 10
15 + 10
25*****See NOTE!***
_____________________________________________________________
Note: For #2 you may be missing a symbol between the first "x" and "2" because the answer I got above (25) is not one of your choices. Let me know what symbol is missing in the equation: x 2-7x + 10, and I will help you solve it.

5 0

3 years ago