Answer:
The coordinates for point E are (0, 1.5)
Hope this helps!!
Answer:
-2x^2+12x
Step-by-step explanation:
Part A.
Ashwin had a 4-cm cube.
volume of cube = side^3
volume = (4 cm)^3 = 64 cm^3
Ashwin has 64 small cubes.
We need to find the volumes of all prisms in Part A. Only prisms with at most 64 cm^3 volume can be the answer.
A. v = 2 * 4 * 7 = 28
B. v = 4 * 5 * 6 = 120
C. v = 5 * 5 * 4 = 100
D. v = 4 * 7 * 5 = 140
E. v = 3 * 5 * 4 = 60
Part A. answer: A, E
Part B.
Dora had a 5-cm cube.
volume of cube = side^3
volume = (5 cm)^3 = 125 cm^3
Dora has 125 small cubes.
We need to find the volumes of all prisms in Part B. Only prisms with at most 125 cm^3 volume can be the answer.
A. v = 3 * 3 * 8 = 72
B. v = 3 * 4 * 5 = 60
C. v = 6 * 6 * 4 = 144
D. v = 5 * 8 * 4 = 160
E. v = 3 * 5 * 4 = 60
Part B. answer: A, B, E
Answer:
-5, -8, -11
Step-by-step explanation:
it every -3
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Let

(that is the range of the inverse sine function).
So,
![\mathsf{sin\,\theta=sin\!\left[sin^{-1}(x)\right]}\\\\ \mathsf{sin\,\theta=x\qquad\quad(i)}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%3Dsin%5C%21%5Cleft%5Bsin%5E%7B-1%7D%28x%29%5Cright%5D%7D%5C%5C%5C%5C%20%5Cmathsf%7Bsin%5C%2C%5Ctheta%3Dx%5Cqquad%5Cquad%28i%29%7D)
Square both sides:

Since

then

is positive. So take the positive square root and you get

Then,
![\mathsf{tan\,\theta=\dfrac{sin\,\theta}{cos\,\theta}}\\\\\\ \mathsf{tan\,\theta=\dfrac{x}{\sqrt{1-x^2}}}\\\\\\\\ \therefore~~\mathsf{tan\!\left[sin^{-1}(x)\right]=\dfrac{x}{\sqrt{1-x^2}}\qquad\qquad -1\ \textless \ x\ \textless \ 1.}](https://tex.z-dn.net/?f=%5Cmathsf%7Btan%5C%2C%5Ctheta%3D%5Cdfrac%7Bsin%5C%2C%5Ctheta%7D%7Bcos%5C%2C%5Ctheta%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7Btan%5C%2C%5Ctheta%3D%5Cdfrac%7Bx%7D%7B%5Csqrt%7B1-x%5E2%7D%7D%7D%5C%5C%5C%5C%5C%5C%5C%5C%20%5Ctherefore~~%5Cmathsf%7Btan%5C%21%5Cleft%5Bsin%5E%7B-1%7D%28x%29%5Cright%5D%3D%5Cdfrac%7Bx%7D%7B%5Csqrt%7B1-x%5E2%7D%7D%5Cqquad%5Cqquad%20-1%5C%20%5Ctextless%20%5C%20x%5C%20%5Ctextless%20%5C%201.%7D)
I hope this helps. =)
Tags: <em>inverse trigonometric function sin tan arcsin trigonometry</em>