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3 years ago

Given the diagram below, if P is the incenter of AJRL,

Mathematics

1 answer:

sp2606 [1]3 years ago

6 0

Answer:

13. PM=31 14. KN=34 15. OL=36.6 KP=46

Step-by-step explanation:

13. PM≅PN≅PO 14.KM≅KN

15. $x^{2}+31^{2}=48^{2}$

$x^{2} +961=2304\\$

subtract 961 from both sides

$\sqrt{x^2} =\sqrt{1343}\\x=36.6$

16. $31^{2} +34^{2}=x^{2}$

$961+1156=x^{2}$

add 961 and 1156 together

$\sqrt{2117^2} }=\sqrt{x^{2} }$ $x=46.0$

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What is the equation of the parabola with vertex (6,7) and focus (7,7)?

Delicious77 [7]

Answer:

Step-by-step explanation:

If you plot these points on a coordinate plane, you see that they are on the same horizontal line, y = 7, with the focus 1 unit to the right of the vertex. This means that the parabola is a sideways opening parabola, to the right, to be more specific. That means that it has the basic vertex form

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where p is the distance in units from the vertex to the focus, h is the first coordinate in the vertex, and k is the second coordinate in the vertex. For us, p = 1, h = 6, and k = 7. Now we will just fill the vertex form of the equation in with our values:

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3 years ago

Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other

kondaur [170]

Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

Explanation :

Since we have shown in the figure below :

a=70 mi.

b=52 mi.

c=x mi.

$\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}$

So, we use the cosine rule , which states that

$c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03$

So, c = x= 106.03 mi.

Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

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