Uppose r⃗ (t)=cos(πt)i+sin(πt)j+5tk represents the position of a particle on a helix, where z is the height of the particle. (a) what is t when the particle has height 15? t= 3 \displaystyle{3}3 (b) what is the velocity of the particle when its height is 15? v⃗ = < -pisin(3pi),picos(3pi),5> \displaystyle< -\pi{\sin{{\left({3}\pi\right)}}},\ pi{\cos{{\left({3}\pi\right)}}},{5} > < −πsin(3π),πcos(3π),5> (c) when the particle has height 15, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). find a vector parametric equation for the position of the particle (in terms of the original parameter t) as it moves along this tangent line.

i am currently in the exact same situation rn. algebra2/adv algebra is killing

step-by-step explanation:

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

the answer would be 150 books

step-by-step explanation:

if you divide 300 by 2 you will get 150