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3 years ago

What is the unit's digit of 3127 to the power of 173

1 answer:

8 0

3127^173 ≡ 7^173 mod 10

Now - let's look at the powers of 7 mod 10:

7^1 = 7 mod 10
7^2 = 49 ≡ 9 mod 10
7^3 ≡ 3 mod 10
7^4 ≡ 1 mod 10

And this cycle repeats. So

7^173 ≡ 7^1 ≡ 7 mod 10

The last digit is 7.

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In the figure, angle B measures 44°, angle A measures 62°, and angle E measures 50°.

Gre4nikov [31]

We don't need the figure
angle b = 44 degrees
angle a = 62 degrees
angle e = 50 degrees
angle f = unknown
we know that
angle a + b + e + f = 180 degrees
50 + 44 + 62 + f =180 degrees
f= 180-50-44-62
but here there is only one blank so we have to add 44 and 62 to make one number that is 106
therefore, f = 180-50-106
if you further want to solve it angle f is 24

3 0

3 years ago

A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let x be the width and y the length of the rectangular field.

Let C the total cost of the rectangular field.

The side made of heavy duty material of length of x costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are x, y, y. Thus

$C=4x+4y+4y+16x\\C=20x+8y$

We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0

3 years ago

What are two differences between factors and multiples

Feliz [49]

Answer:

Factor is a number that can be multiplied with a particular number to obtain another number. Conversely, multiples are the product, which is reached after multiplying the number by an integer. The number of factors of a particular number is limited, but the number of multiples of a given number is endless.

Step-by-step explanation:

4 0

3 years ago

How to find algebraic expressions using a table of values

Makovka662 [10]

I think that the answers is b

6 0

3 years ago

Is -1, 6, -36, 216 geometric or not?

monitta

Yes that sequence is geometric although it’s negative

3 0

3 years ago