Write the equation of the conic section shown below. (Its a triangle)
√10
19 answers
Sorry, it is not possible to write the equation of a triangle as a conic section. Conic sections are curves that result from intersecting a cone with a plane, and triangles are not curves. Can you provide more information about the context or shape you are referring to?
The triangle below is equilateral. Find the length of the side x in simplest radical form with a rational denominator.
√10
√10
If the triangle is equilateral, then all sides have the same length. Let's call that length "s".
Using the Pythagorean theorem on one of the right triangles formed by cutting the equilateral triangle in half, we have:
(s/2)^2 + x^2 = s^2
Simplifying this equation:
s^2/4 + x^2 = s^2
x^2 = s^2 - s^2/4 = 3s^2/4
x = sqrt(3s^2/4) = (sqrt(3)/2) s
We know that the length of one side is √10. Setting √10 = (sqrt(3)/2) s and solving for s, we get:
s = (2/sqrt(3)) √10 = (2/3) sqrt(30)
Now we can plug this value of s into the equation we found earlier for x:
x = (sqrt(3)/2) s = (sqrt(3)/2) (2/3) sqrt(30) = sqrt(10/3) = (sqrt(30)/3)
Using the Pythagorean theorem on one of the right triangles formed by cutting the equilateral triangle in half, we have:
(s/2)^2 + x^2 = s^2
Simplifying this equation:
s^2/4 + x^2 = s^2
x^2 = s^2 - s^2/4 = 3s^2/4
x = sqrt(3s^2/4) = (sqrt(3)/2) s
We know that the length of one side is √10. Setting √10 = (sqrt(3)/2) s and solving for s, we get:
s = (2/sqrt(3)) √10 = (2/3) sqrt(30)
Now we can plug this value of s into the equation we found earlier for x:
x = (sqrt(3)/2) s = (sqrt(3)/2) (2/3) sqrt(30) = sqrt(10/3) = (sqrt(30)/3)
Find the length of side x in simplest radical form with a rational denominator.
7
7
More information is needed to solve this problem. Please provide a diagram or additional context.
Find the length of side x in simplest radical form with a rational denominator.
√7
√7
More information is needed to solve this problem. Please provide a diagram or additional context.
Find the length of side x in simplest radical form with a rational denominator.
one side = 7
one side = 7
More information is needed to solve this problem. Please provide a diagram or additional context.
its a triangle. Has three sides one is 7 and one is x
It is not possible to determine the length of side x without additional information about the triangle, such as angles or the length of the third side.
the third side is a right angle
If the triangle is a right triangle and one side is 7, and the hypotenuse is x, then we can apply the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse. In this case, a = 7 and c = x, so we have:
7^2 + b^2 = x^2
Simplifying:
49 + b^2 = x^2
Subtracting 49 from both sides:
b^2 = x^2 - 49
Taking the square root of both sides:
b = sqrt(x^2 - 49)
Therefore, the length of the third side (the other leg) is sqrt(x^2 - 49).
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse. In this case, a = 7 and c = x, so we have:
7^2 + b^2 = x^2
Simplifying:
49 + b^2 = x^2
Subtracting 49 from both sides:
b^2 = x^2 - 49
Taking the square root of both sides:
b = sqrt(x^2 - 49)
Therefore, the length of the third side (the other leg) is sqrt(x^2 - 49).
hmmm WRONG
I apologize for my error. If one side of the triangle is 7 and the triangle is a right triangle with the hypotenuse x, we can use the Pythagorean theorem to find x:
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse. In this case, a = 7 and c = x, so we have:
7^2 + b^2 = x^2
Simplifying:
49 + b^2 = x^2
To find b in terms of x, we can subtract 49 from both sides:
b^2 = x^2 - 49
Taking the square root of both sides, we get:
b = sqrt(x^2 - 49)
Therefore, the length of the other leg is sqrt(x^2 - 49).
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse. In this case, a = 7 and c = x, so we have:
7^2 + b^2 = x^2
Simplifying:
49 + b^2 = x^2
To find b in terms of x, we can subtract 49 from both sides:
b^2 = x^2 - 49
Taking the square root of both sides, we get:
b = sqrt(x^2 - 49)
Therefore, the length of the other leg is sqrt(x^2 - 49).
what is 1 + 1
1 + 1 = 2
no 1 + 1 = 11
I apologize for my previous response. In some numeration systems, such as the unary numeral system, 1 + 1 may be represented as 11, where the digits do not refer to different orders of magnitude. However, in the decimal system commonly used today, 1 + 1 = 2.
1 answer