As both are moving in the same direction ,both<span> will travel the </span>same distance<span> till catch up time --</span><span>d</span>
Answer:
0.761
Step-by-step explanation:
first you do 3 divided by 2.2 and get .733 which you round to .7
next you do 3 divided by 2.28 and get .76
last you do 3 divided by 2.283 and get .761
Apply the distance formula and find an expression for the distance between the points;
![A(2,4) and B(-6,x)](https://tex.z-dn.net/?f=%20A%282%2C4%29%20and%20B%28-6%2Cx%29%20)
Recall that the distance formula is given by,
![d=\sqrt((x_2 - x_1 )^2 +(y_2 - y_1)^2](https://tex.z-dn.net/?f=d%3D%5Csqrt%28%28x_2%20-%20x_1%20%29%5E2%20%2B%28y_2%20-%20y_1%29%5E2)
![10=\sqrt((-6-2)^2 + (x-4)^2))](https://tex.z-dn.net/?f=%2010%3D%5Csqrt%28%28-6-2%29%5E2%20%2B%20%28x-4%29%5E2%29%29%20)
This implies that
![10=\sqrt((-8)^2 + (x-4)^2))](https://tex.z-dn.net/?f=%2010%3D%5Csqrt%28%28-8%29%5E2%20%2B%20%28x-4%29%5E2%29%29)
![10=\sqrt(64 + (x-4)^2))](https://tex.z-dn.net/?f=%2010%3D%5Csqrt%2864%20%2B%20%28x-4%29%5E2%29%29)
Squaring both sides
![100=64 + (x-4)^2](https://tex.z-dn.net/?f=%20100%3D64%20%2B%20%28x-4%29%5E2)
![100-64=(x-4)^2](https://tex.z-dn.net/?f=%20100-64%3D%28x-4%29%5E2)
![36=(x-4)^2](https://tex.z-dn.net/?f=%2036%3D%28x-4%29%5E2)
Taking square root of both sides gives
![\sqrt(36)=(x-4)](https://tex.z-dn.net/?f=%20%5Csqrt%2836%29%3D%28x-4%29)
![6=(x-4)](https://tex.z-dn.net/?f=%206%3D%28x-4%29)
![6+4=x](https://tex.z-dn.net/?f=%206%2B4%3Dx)
![x=10](https://tex.z-dn.net/?f=%20x%3D10)
Answer:
obtuse
Step-by-step explanation:
A "form factor" can be computed whose sign will tell you the classification of the triangle. For short sides a, b and long side c, the form factor is ...
f = a² +b² -c²
And the interpretation is ...
- f > 0 . . . acute
- f = 0 . . . right
- f < 0 . . . obtuse
__
<h3>form factor</h3>
For the given side lengths, the form factor is ...
f = 11² +15² -20² = 121 +225 -400
f = -54
<h3>interpretation</h3>
The value is less than zero, signifying an obtuse triangle.
_____
<em>Additional comment</em>
The value f/(2ab) = -54/(2·11·15) = -9/55 is the cosine of the largest angle. Here, the largest angle is arccos(-9/55) ≈ 99.4°. This is greater than 90°, hence an obtuse angle.
This cosine relation comes from the Law of Cosines. The interpretation of the "form factor" can be developed by considering the Pythagorean theorem (f=0 ⇒ right triangle) and the relationship between sides and angles. If the longest side is longer than necessary for a right triangle, the largest angle will be greater than 90°.
1 In general, given
a
x
2
+
b
x
+
c
ax
2
+bx+c, the factored form is:
a
(
x
−
−
b
+
b
2
−
4
a
c
2
a
)
(
x
−
−
b
−
b
2
−
4
a
c
2
a
)
a(x−
2a
−b+
b
2
−4ac
)(x−
2a
−b−
b
2
−4ac
)
2 In this case,
a
=
3
a=3,
b
=
−
54
b=−54 and
c
=
343
c=343.
3
(
y
−
54
+
(
−
54
)
2
−
4
×
3
×
343
2
×
3
)
(
y
−
54
−
(
−
54
)
2
−
4
×
3
×
343
2
×
3
)
3(y−
2×3
54+
(−54)
2
−4×3×343
)(y−
2×3
54−
(−54)
2
−4×3×343
)
3 Simplify.
3
(
y
−
54
+
20
3
ı
6
)
(
y
−
54
−
20
3
ı
6
)
3(y−
6
54+20
3
)(y−
6
54−20
3
)
4 Factor out the common term
2
2.
3
(
y
−
2
(
27
+
10
3
ı
)
6
)
(
y
−
54
−
20
3
ı
6
)
3(y−
6
2(27+10
3
)
)(y−
6
54−20
3
)
5 Simplify
2
(
27
+
10
3
ı
)
6
6
2(27+10
3
)
to
27
+
10
3
ı
3
3
27+10
3
.
3
(
y
−
27
+
10
3
ı
3
)
(
y
−
54
−
20
3
ı
6
)
3(y−
3
27+10
3
)(y−
6
54−20
3
)
6 Factor out the common term
2
2.
3
(
y
−
27
+
10
3
ı
3
)
(
y
−
2
(
27
−
10
3
ı
)
6
)
3(y−
3
27+10
3
)(y−
6
2(27−10
3
)
)
7 Simplify
2
(
27
−
10
3
ı
)
6
6
2(27−10
3
)
to
27
−
10
3
ı
3
3
27−10
3
.
3
(
y
−
27
+
10
3
ı
3
)
(
y
−
27
−
10
3
ı
3
)
3(y−
3
27+10
3
)(y−
3
27−10
3
I hope this help you