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icang [17]
3 years ago
13

What is this fraction?

Mathematics
1 answer:
e-lub [12.9K]3 years ago
5 0

\sqrt{361}=19\ \text{because}\ 19^2=361

\dfrac{361}{\sqrt{361}}=\dfrac{361}{19}=19

19 is

A: real

B: whole

C: integer

D: rational

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The height of a wooden pole, h, is equal to 15 feet. Ataut wire is stretched from a point on the ground to the top of the pole.
Taya2010 [7]

The question is incomplete. Here is the complete question:

The height of a wooden pole, h, is equal to 15 feet. A taut wire is stretched from a point on the ground to the top of the pole. The  distance from the base of the pole to this point on the ground, b. is equal to 8 feet. What is the length of the wire?

Answer:

Length of wire = 17 feet

Step-by-step explanation:

Given:

The height of the wooden pole is, h=15\ ft

The distance from the base of the pole to this point on the ground is, b=8\ ft

Let the length of the wire be 'l'.

Now, consider the triangle formed by the pole, the base, and the wire. The length of the wire is the slant length and hence the hypotenuse of the triangle.

Using Pythagorean theorem, we can find the hypotenuse.

(Hypotenuse)^2=(height)^2+(base)^2\\l^2=h^2+b^2

Plug in the given values and solve for 'l'. This gives,

l^2=15^2+8^2\\\\l^2=225+64\\\\l^2=289\\\\l=\sqrt{289}\\\\l=\pm17

As length can never be negative, we ignore the negative result.

Therefore, the length of the wire is 17 feet.

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3 years ago
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Step-by-step explanation:

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Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number x such that taking it mod 4, 5, and 7 leaves the desired remainders:

x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6

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x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4

so we multiply the first term by 3.

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x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5

so we multiply the second term by 2.

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x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7

so we multiply the last term by 7.

Now,

x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147

By the CRT, the system of congruences has a general solution

n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}

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AnnyKZ [126]

Answer:

A

Step-by-step explanation:

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cupoosta [38]

Answer:

See attached picture

Step-by-step explanation:

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• Multiplying the function by a number greater than 1 stretches it away from the x-axis.

The equation for g has been subtracted inside the parenthesis by 2 which will shift the graph 2 units to the right.

The equation for g has also been subtracted outside the parenthesis by 3 which will shift the  graph 3 units down.

The graph is shown in black while f(x) is show in purple in the attached picture.

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