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3 years ago

It can be shown that every integer can be uniquelyrepresented in the form of

Mathematics

1 answer:

Alexeev081 [22]3 years ago

8 0

a. $5_{10}=1(-1)(-1)_{\mathrm{bal}3}$ because

5 = 9 - 3 - 1 = 3^2 - 3^1 - 3^0

b. $13_{10}=111_{\mathrm{bal}3}$ because

13 = 9 + 3 + 1 = 3^2 + 3^1 + 3^0

c. $37_{10}=1101_{\mathrm{bal}3}$ because

37 = 27 + 9 + 1 = 3^3 + 3^2 + 3^0

d. $79_{10}=100(-1)1_{\mathrm{bal}3}$ because

79 = 81 - 3 + 1 = 3^4 - 3^1 + 3^0

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Can someone help me with number 3 please??!!

ipn [44]

There are 2 way to solve this.

one using Pythagoras theorem and 2nd using trigonometry

so lets solve it by both

using Pythagoras theorem we know

base^2 + perpendicular^2 = hypotanes^2

6^2 + x^2 = 12^2

36 + x^2 = 144

x^2 = 144- 36 = 108

x = √(108) = √( 2×2×3×3×3)

= (2×3) √ (3) = 6 √3

so answer is option 2

bow lets use trigonometry

we know
sin theta = perpendicular / hypotanes
sin 60 = x /12
x = 12 × sin 60
we kNow sin 60 = √3/ 2
so
x = 12×√3 /2 = 6√3

7 0

3 years ago

The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and

lawyer [7]

Functions can be used to model real life situations.

The hose is 3.2 feet above the ground, at a horizontal distance of 4 fee

The function is given as:

$f(x) =-0.3x^2 + 2x$

At a horizontal distance of 4 feet, the value of x is 4

i.e. $x = 4$

Substitute 4 for x in f(x).

So, we have:

$f(4) =-0.3(4)^2 + 2(4)$

Evaluate the exponent

$f(4) =-0.3(16) + 2(4)$

Open both brackets

$f(4) =-4.8 + 8$

Add -4.8 and 8

$f(4) =3.2$

Hence, the hose is 3.2 feet above the ground

Read more about functions at:

brainly.com/question/10837575

7 0

2 years ago

The length of time required for the periodic maintenance of an automobile or another machine usually has a mound-shaped probabil

maks197457 [2]

Solution :

Mean time for an automobile to run a 5000 mile check and service = 1.4 hours

Standard deviation = 0.7 hours

Maximum average service time = 1.6 hours for one automobile

The z - score for 1.6 hours = $\frac{1.6-1.4}{0.7 / \sqrt{50}}$

= 2.02

Now checking a normal curve table the percentage of z score over 2.02 is 0.0217

Therefore the overtime that will have to be worked on only 0.217 or 2.017% of all days.

8 0

3 years ago

98 POINTS! PLEASE HELP! I been stuck on this assignment for over 2 weeks. My teacher gave me a simple explanation when I asked f

Colt1911 [192]

See the attached picture.

Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.

The resulting box has a volume

$V(x)=x(8-x)(12-x)=x^3-20x^2+96x$

because the volume of a box is the product of its width $(12-x)$ , length $(8-x)$ , and height $(x)$ .

find the zeroes

You know right away from the factored form of $V(x)$ that the zeroes are $x=0,8,12$ . (zero product property)

sketch the graph of the function

Easy to plot by hand. You know the zeroes, and you can check the sign of $V(x)$ for any values of $x$ between these zeros to get an idea of what the graph of $V(x)$ looks like. See the second attached picture.

Here's what I mean by "check the sign" in case you don't follow. We know $V(x)=0$ when $x=0$ and $x=8$ . So we pick some value of $x$ between them, say $x=1$ , and find that

$V(1)=1(8-1)(12-1)=7\cdot11=77$

which is positive, so $V(x)$ will be positive for any other $x$ between 0 and 8. Similarly we would find that $V(x)$ for $x$ between 8 and 12, and so on.

What is the size of the cutout he needs to make so that he can fit the most marbles in the box?

It's impossible to answer this without knowing the volume of each marble...

If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be?

Thomas wants $V(x)=12$ , so you solve

$x^3-20x^2+96x=12$

While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions

$x\approx0.1284$