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queenjanet46
26.12.2019 •
Mathematics
Need on these 2 questions and my last 2 uploads !
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Ответ:
19.![\frac{3\pi}{2}](/tpl/images/0434/1419/234a0.png)
20. The work is the answer
Step-by-step explanation:
19. We begin with the equation (for my ease, I will swap theta with x)
First, we can use the Pythagorean Identity to substitute in
for ![cos^{2} (x)](/tpl/images/0434/1419/4c96a.png)
This gives us
Next, we can subtract 1 from each side
Now, we can divide each side by![sin(x)](/tpl/images/0434/1419/dbf14.png)
Now we move the negative to the other side
Now we can do the inverse of sin to find our value
With this inverse, we are looking for an angle that has the sin (or the y value) of -1. As this is an inverse sin function, it has the domain restriction of
From this information, we find that![x=-\frac{\pi}{2}](/tpl/images/0434/1419/8997c.png)
But this answer does not fit the initial interval that we were given. Luckily,
is the same location as
, so that is our answer.
20. We begin with the expression
and we have to prove that it is equal to ![-sin(x)](/tpl/images/0434/1419/70603.png)
First, we need to use the Difference of 2 Angles Trig Identity. This says:
When we apply this to our expression, we get
Next, we can simplify our the two finite aspects
When we plug in these two values, we get
This simplifies to
which is what we were trying to verify.
Ответ:
Given:
The smallest cube has a edge length of 6 inches.
The ratios of similarity to the smallest cube are 1.25, 43 , 1.5, 74 , and 2 respectively.
To find:
The edge lengths of the other cubes.
Solution:
If two figures are similar, then the ratios of similarity is equal to the ratio of their corresponding sides.
Let the edge of other cube be x.
It means, the edges of other cubes are 6 times of the ratio of similarity to the smallest cube.
Now,
Therefore, the edges of other cubes are 7.5, 8, 9, 10.5 and 12 respectively.