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LuckyWell [14K]
3 years ago
7

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. T

he tree meets the ground at a right angle. At approximately what angle does the wire meet the ground?
33.6
39.8
50.2
56.4

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
8 0

Answer:

(D)56.4

Step-by-step explanation:

According to the question, Let AB=10, AC=12 and m∠B=90°.

Thus, from ΔABC, using trigonometry, we have

\frac{AB}{AC}=sinx

\frac{10}{12}=sinx

\frac{5}{6}=sinx

sinx=0.83

x=sin^{-1}(0.83)

x=56.4

Therefore, at x=56.4 the wire meet the ground.

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Find the domain of the function y = 3 tan(23x)
solmaris [256]

Answer:

\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right)  \; \right| k \in \mathbb{Z}  \right\rbrace.

In other words, the x in f(x) = 3\, \tan(23\, x) could be any real number as long as x \ne \displaystyle \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) for all integer k (including negative integers.)

Step-by-step explanation:

The tangent function y = \tan(x) has a real value for real inputs x as long as the input x \ne \displaystyle k\, \pi + \frac{\pi}{2} for all integer k.

Hence, the domain of the original tangent function is \mathbb{R} \backslash \displaystyle \left\lbrace \left. \left(k\, \pi + \frac{\pi}{2}\right)  \; \right| k \in \mathbb{Z}  \right\rbrace.

On the other hand, in the function f(x) = 3\, \tan(23\, x), the input to the tangent function is replaced with (23\, x).

The transformed tangent function \tan(23\, x) would have a real value as long as its input (23\, x) ensures that 23\, x\ne \displaystyle k\, \pi + \frac{\pi}{2} for all integer k.

In other words, \tan(23\, x) would have a real value as long as x\ne \displaystyle \frac{1}{23} \, \left(k\, \pi + \frac{\pi}{2}\right).

Accordingly, the domain of f(x) = 3\, \tan(23\, x) would be \mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right)  \; \right| k \in \mathbb{Z}  \right\rbrace.

4 0
2 years ago
Write in y=mx+b form
DENIUS [597]

Step-by-step explanation:

b =-4 (y-intercept)

x =0

m = 0 (the line doesn't have a slope)

y = mx + c

y = 0(0) + (-4)

y = - 4

7 0
3 years ago
Can you please help me THAKS! IN A HURRY IT'S midnight and I am trying to finish my work from home My parents allow me to ask
rusak2 [61]

Answer: 6.82

Step-by-step explanation:

So we know the Law of Sines which is that Sin A/a = Sin B/b = Sin C/c. The Sin on top of the fraction is the angle, and the letter on the bottom is the side opposite from that angle.

Our first step is going to be finding the last angle. We have 2 angles already, but one that's missing. We know that all triangles' angles add up to 180, so we can add 68+40=108. Then do 180-108 to get 72. Now we know the third and final angle.

Ok so back to Law of Sines. Now we can plug into that equation. We only need Sin A/a = Sin B/b (It doesn't matter what order you put them in). And remember the lowercase letter at the bottom represents the OPPOSITE side from one of the angles. Since the problem wants the side opposite Sin 68, let's set up a proportion.

\frac{Sin72}{7} =\frac{Sin 68}{x}

Set up we have what we know. We know one side, and opposite that is the angle we already solved for. Now we can cross multiply and end up with:

x (Sin 72)= 7(Sin 68)

Since we want to isolate x, we can divide each side by Sin 72.

x= 7(Sin 68)/Sin 72

So now let's put it into the calculator:

7(Sin 68)=6.2853

Now let's divide 6.2853/Sin 72

And you should be left with 6.82 if you round it!

7 0
3 years ago
Steve drove at a constant rate to the beach for a vacation. In the equation below, t is the time in hours it took Steve to drive
Sindrei [870]

9514 1404 393

Answer:

  A.  64 miles per hour

Step-by-step explanation:

In a linear equation, the "unit rate" is generally the coefficient of the variable. The units of the unit rate depend on the definition of the relationship.

Here, the time t is in hours, so the "unit rate" will be <something> per hour. The answer choices suggest that the <something> is "miles". That is, the units of the equation are ...

  (miles/hour) × (hours) = miles

With numbers/variables, that is ...

  (64 miles/hour) × (t hours) = 384 miles

The unit rate is 64 miles per hour.

6 0
3 years ago
Please help!!! All these need to be simplified
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