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Eva8 [605]
1 year ago
7

a utility pole is 8m high. a cable is stretched from the top of the pile to a point in the ground that is 7 m from the bottom of

the pole. how long is the cable? round to 2 decimal places
Mathematics
1 answer:
Olin [163]1 year ago
5 0

We can draw this as:

We can use the Pythagorean theorem to find the length of the cable, as it is the hypotenuse of a right triangle:

\begin{gathered} c^2=7^2+8^2 \\ c^2=49+64 \\ c^2=113 \\ c=\sqrt[]{113} \\ c\approx10.63 \end{gathered}

Answer: the cable length is 10.63 m.

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How do you convert the general equation form of a circle to standard form? Answer correctly to get 20 points. Please provide an
ivanzaharov [21]

Answer:

Step-by-step explanation:

The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius. To convert an equation to standard form, you can always complete the square separately in x and y.

5 0
2 years ago
Evaluate the integral ∫2−1|x−1|dx
defon

I think you might be referring to the definite integral,

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx

Recall the definition of absolute value:

|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x

Then |x-1|=x-1 if x\ge1, and |x-1|=1-x is x. So spliting up the integral at <em>x</em> = 1, we have

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \int_{-1}^1(1-x)\,\mathrm dx + \int_1^2(x-1)\,\mathrm dx

The rest is simple:

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \left(x-\dfrac{x^2}2\right)\bigg|_{-1}^1 + \left(\dfrac{x^2}2-x\right)\bigg|_1^2 \\\\ = \left(\left(1-\frac12\right)-\left(-1-\frac12\right)\right) + \left(\left(2-2\right)-\left(\frac12-1\right)\right) \\\\ = \boxed{\frac52}

5 0
3 years ago
If b=4 and c=2, what is 2b-3c?
Paraphin [41]
First, fill in the variables with the numbers given so that
2b-3c
will then become
2(4)-3(2)
next, you refer to the order of operations to simplify the problem down, the multiplication being the first doable operations in this problem.
8-6
and next operation being subtraction.
2
is the final answer
6 0
3 years ago
Read 2 more answers
I need help please???):
Ket [755]

Answer:

The first option is correct.

Step-by-step explanation:

how do we multiply x - 9 by something? we put it in brackets

(x - 9) × (-3) = 51

that can be written like this

(x - 9)(-3) - 51

5 0
3 years ago
Find the perimeter of the figure. Round your answer to the nearest tenth.
zloy xaker [14]
Counting the straight sides gives you 23 units and using the distance formula on the bottom side gives you about 11.18 units. 23+11.18=34.18 and round that to the nearest tenth to get the answer of 34.2 units.
8 0
3 years ago
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