Twenty-six students will attend the field trip to the career center. The cost to attend the career center is $x. Fifteen of thes
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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.
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.
In calculus, we use derivatives to find the instantaneous rate of change at any point on a graph. To find the average rate of change, we just find the slope of the secant line that intercepts two points on the graph.
We find slope with the following equation:
In this case, we are looking for the slope from x = -1 to x = 1. We have both x values, so next we need the y values.
F(-1) = (-1)^2 - (-1) - 1 = 1
F(1) = (1)^2 - (1) - 1 = -1
Now plug in the x and y values to find the slope:
The answer is -1.
We find slope with the following equation:
In this case, we are looking for the slope from x = -1 to x = 1. We have both x values, so next we need the y values.
F(-1) = (-1)^2 - (-1) - 1 = 1
F(1) = (1)^2 - (1) - 1 = -1
Now plug in the x and y values to find the slope:
The answer is -1.