Answer:(a)x^2+2y^2=2
(b)In the attached diagram
Step-by-step explanation:Step 1: Multiply both equations by t
xt=t(cost -sint)\\ty\sqrt{2} =t(cost +sint)
Step 1: Multiply both equations by t
xt=t(cost -sint)\\ty\sqrt{2} =t(cost +sint)
Step 2:We square both equations
(xt)^2=t^2(cost -sint)^2\\(ty)^2(\sqrt{2})^2 =t^2(cost +sint)^2
Step 3: Adding the two equations
(xt)^2+(ty)^2(\sqrt{2})^2=t^2(cost -sint)^2+t^2(cost +sint)^2\\t^2(x^2+2y^2)=t^2((cost -sint)^2+(cost +sint)^2)\\x^2+2y^2=(cost -sint)^2+(cost +sint)^2\\(cost -sint)^2+(cost +sint)^2=2\\x^2+2y^2=2 hopes this helps
Answer:
S = 8
Step-by-step explanation:
An infinite geometric series is defined as limit of partial sum of geometric sequences. Therefore, to find the infinite sum, we have to find the partial sum first then input limit approaches infinity.
However, fortunately, the infinite geometric series has already set up for you. It’s got the formula for itself which is:
We can also write in summation notation rather S-term as:
Keep in mind that these only work for when |r| < 1 or else it will diverge.
Also, how fortunately, the given summation fits the formula pattern so we do not have to do anything but simply apply the formula in.
Therefore, the sum will converge to 8.
Please let me know if you have any questions!
Answer:
64
Step-by-step explanation:
Find the area of both triangles inside the bigger triangle and add them together.
Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:
a² + b² = c²
8² + b² = 10²
64 + b² = 100
36 = b²
6 = b
Calculate the area of the smaller triangle:
1/2(<em>b</em>x<em>h</em>)
1/2(6 x 8)
1/2(48)
24
Calculate the area of the bigger triangle:
<em>We know that the longer leg is 10 units because we were able to subtract the length of the smaller triangle's leg from 16.</em>
1/2(<em>b</em>x<em>h</em>)
1/2(10 x 8)
1/2(80)
40
Add both areas to find the area of the largest triangle:
40 + 24 = 64
