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.
(1) x represents the number of apples bought, y represents the number of bananas.
(2) each term represents the total costs of a given fruit, so 0.50x is the total cost of apples and 0.30y is total cost of bananas.
(3) The coefficients are unit prices: coefficient 0.50 is the price of 1 apple, 0.30 is the price of 1 banana.
The answer to the problem are -3 and -8 because the two equation are being solved for 0
You are given the equation 36 = 9x² + 4y². You are asked to find the slopes of the asymptotes of the hyperbola. A hyperbola has the following general equation x²/a² + y²/b² = 1. the goal here is to find the slopes of the hyperbolic equation. So divide both sides by 36
36 = 9x² + 4y²
(1/36)[36 = 9x² + 4y²]
1 = x²/4 + y²/9
a² = 4
a = 2
and
b² = 9
b = 3
To find the slope, divide a/b and you will get 2/3.