Ah okay so in differential equations you usually want the top variable isolated. To do this, multiply by dt and 2u and you get

Now just integrate both sides. The integral of 2u with respect to u is u². The integral of (2t + sec²(t) with respect to t is t² + ∫sec²(t)dt. The last part is just tan(x) because d/dt(tan(t)) is sec²(t) so just integrating gets us back. Now we have

Where c and k are arbitrary constants. Subtracting c from k and you get

Where b is another constant. To find b, just plug in u(0) = -1 where u is -1 and t is 0. This becomes

tan(0) is 0 so b = 1. Take the plus or minus square root on both sides and you finally get

But Brainly didn't let me do but juat remember there is a plus or minus square root on the left.
If $200 is the maximum a coach can spend on new shorts, and needs at least 15 shorts, then you could divide or use an inequality. first take the maximum number (200) and the minimum amount (15s) and use the minimum and maximum signs of knowledge to form an inequality. you should end up with 15s<200.
Answer:
D (You got it right.)
Step-by-step explanation:
Whenever the sign is facing them we will always shade the top. Then we have to find the slope which in this case would be 3(the number that is being multiplied by x. Lastly is the sign does not have a line under it or an equal sign. it won't be a straight line it will have little gaps.
Symbolically, write this:
C
7 5. Know how to evaluate that?
C stands for "combination."
Volume of the cone:
V = 3.14 x 3^2 x 9/3 = 84.78
Volume of half sphere on top of cone:
V = (4/3 x 3.14 x 3^3 )/2 = 56.52
Total volume = 56.52 + 84.78 = 141.3 cm^3