2x-4=49
2x=54
x is equal to 27
This ratio is in a form of dogs:cats.
The ratio given means there are 3 dogs for every 2 cats.
You can rewrite it as 3 dogs:2 cats.
If there are 30 cats, you would write the ratio as x dogs:30 cats.
Since the same must be done to both sides, you must find how many times 2 was multiplied to get 30 then multiply dogs by that number.
30 / 2 = 15
3 • 15 = 45
So if a shelter has 30 cats, then it has 45 dogs.
This can be written in a ratio as 45:30, or 45 dogs:30 cats.
Answer:
x = 9
Step-by-step explanation:
The angles in red are equivalent and the triangle is isosceles.
This means the sides with lengths 12 and x + 3 are equivalent.
x + 3 = 12
x + 3 - 3 = 12 - 3
x = 9
:)
By converting into parametric equations,
<span>{<span><span>x<span>(θ)</span>=r<span>(θ)</span><span>cosθ</span>=<span>cos2</span>θ<span>cosθ</span></span><span>y<span>(θ)</span>=r<span>(θ)</span><span>sinθ</span>=<span>cos2</span>θ<span>sinθ</span></span></span></span>
By Product Rule,
<span>x'<span>(θ)</span>=−<span>sin2</span>θ<span>cosθ</span>−<span>cos2</span>θ<span>sinθ</span></span>
<span>x'<span>(<span>π2</span>)</span>=−<span>sin<span>(π)</span></span><span>cos<span>(<span>π2</span>)</span></span>−<span>cos<span>(π)</span></span><span>sin<span>(<span>π2</span>)</span></span>=1</span>
<span>y'<span>(θ)</span>=−<span>sin2</span>θ<span>sinθ</span>+<span>cos2</span>θ<span>cosθ</span></span>
<span>y'<span>(<span>π2</span>)</span>=−<span>sin<span>(π)</span></span><span>sin<span>(<span>π2</span>)</span></span>+<span>cos<span>(π)</span></span><span>cos<span>(<span>π2</span>)</span></span>=0</span>
So, the slope m of the curve can be found by
<span>m=<span><span>dy</span><span>dx</span></span><span>∣<span>θ=<span>π2</span></span></span>=<span><span>y'<span>(<span>π2</span>)</span></span><span>x'<span>(<span>π2</span>)</span></span></span>=<span>01</span>=0</span>
I hope that this was helpful.
Answer:
The height of the statue is <u>21.4 feet.</u>
Step-by-step explanation:
Given:
Distance of the person from the statue = 50 ft
Angle of elevation of the top of statue = 16°
Angle of depression of the bottom of statue = 8°
The diagram is drawn below.
In triangle ABC:
BC = 50 ft, ∠ABC = 16°
Using trigonometric formula;
Now, let us determine the height of man, 'x'.
Consider triangle BDE.
ED = 50 ft, ∠BDE = 8°
Using trigonometric formula;
Now, from the diagram, it is clear that, height of statue is given as: