This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2
A and B are the legs and C is the hypotenuse.
We can plug C in the equation:
a^2 + b^2 = 128
What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?
8^2 + 8^2 = 128
64 + 64 = 128
128=128
Yes the value 8 works so the length of two legs of the triangle is 8.
<u>Solution-</u>
The two parabolas are,
By solving the above two equations we calculate where the two parabolas meet,
Given the symmetry, the area bounded by the two parabolas is twice the area bounded by either parabola with the x-axis.
![\therefore Area=2\int_{-c}^{c}y.dx= 2\int_{-c}^{c}(16x^2-c^2).dx\\=2[\frac{16}{3}x^3-c^2x]_{-c}^{ \ c}=2[(\frac{16}{3}c^3-c^3)-(-\frac{16}{3}c^3+c^3)]=2[\frac{32}{3}c^3-2c^3]=2(\frac{26c^3}{3})\\=\frac{52c^3}{3}](https://tex.z-dn.net/?f=%5Ctherefore%20Area%3D2%5Cint_%7B-c%7D%5E%7Bc%7Dy.dx%3D%202%5Cint_%7B-c%7D%5E%7Bc%7D%2816x%5E2-c%5E2%29.dx%5C%5C%3D2%5B%5Cfrac%7B16%7D%7B3%7Dx%5E3-c%5E2x%5D_%7B-c%7D%5E%7B%20%5C%20c%7D%3D2%5B%28%5Cfrac%7B16%7D%7B3%7Dc%5E3-c%5E3%29-%28-%5Cfrac%7B16%7D%7B3%7Dc%5E3%2Bc%5E3%29%5D%3D2%5B%5Cfrac%7B32%7D%7B3%7Dc%5E3-2c%5E3%5D%3D2%28%5Cfrac%7B26c%5E3%7D%7B3%7D%29%5C%5C%3D%5Cfrac%7B52c%5E3%7D%7B3%7D)
![So \frac{52c^3}{3}=\frac{250}{3}\Rightarrow c=\sqrt[3]{\frac{250}{52}}=1.68](https://tex.z-dn.net/?f=So%20%5Cfrac%7B52c%5E3%7D%7B3%7D%3D%5Cfrac%7B250%7D%7B3%7D%5CRightarrow%20c%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B250%7D%7B52%7D%7D%3D1.68)
Answer:
the answer is probably 7/6
hope I am correct and if not I'm sorry
Answer:
there's not options :/ nobody can answer this
Answer:
2x2 matrix
Step-by-step explanation:
Given
Dimension of matrices A = 2x2 matrix
Dimension of matrices B = 2x1 matrix
The dimension of matrix AB can be gotten by cancelling the row of matrices 1 and column of matrices 2.
After cancelling both row and column, the remaining dimension will be 2x2 matrix. Hence the dimension of AB is 2x2 matrix
