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Tatiana [17]
3 years ago
11

Need help quick, please?

Mathematics
1 answer:
My name is Ann [436]3 years ago
8 0
Remember that the general formula for a circle is <span> 
(x – h)</span>² + (y – k)² = r²<span>, where (h,k) is the coordinate of the center. 
We already know that (h,k) = (5,-4), since we know the center's coordinates. We need to find r, the radius, using the distance between the center and the point (-3,2). 
To do this, we can either use the distance formula, or plug in the points in our circle equation and solve for r.
Let's do the second one, plugging in and solving for r.
We can use the point (-3,2) for (x,y):
</span>(x – h)² + (y – k)² = r²
(-3 - 5)² + (2 - -4)² = r²
(-8)² +(6)² = r²
64 + 36 = r²
100 = r²
r = 10
We know that r=10, and that r² = 100
Using h, k, and r, we can now solve for the equation of the circle in standard form.
The equation of the circle is:
(x – 5)² + (y + 4)² = 100
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a utility worker is 5.5 feet tall and is casting a shadow 4 feet long at the same time a nearby utility pole casts a shadow 20 f
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So this is essentially a proportion problem. They want you to be able to recognize a relationship between the two. The easiest way to go about this is to draw a picture (I have included one). What you want to do is notice that you are given both shadow lengths. This is essentially going to be your first step to creating the proportion.


Understanding that we know the shadow lengths, we can turn these into a fraction such as so:


4ft/20ft.


Now that we know that, we need to look at are unknown. Our unknown is the height of the utility pole. We can solve this by substituting for X since we know the utility worker is 5.5 ft tall.


Your fraction for that would look like:


5.5ft/X


Make sure to always make your top to top match, such as since I put the utility worker's shadow on top, I need to put his height on top.

Now we can solve.

4ft/20ft =5.5ft/X


We need to cross multiply to get an equation we can work with. If we cross multiply, Your equation will look like:


4x = 110ft


This is a simple one step equation. Divide both sides by 4 to get your answer.

x= 27.5ft.

This means your Utility pole's height is 27.5ft.

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A pill contains 1,257 mg of an active ingredient. How many grams is that?
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Hope thus helped!

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