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exis [7]
3 years ago
5

If the radius of a circle measures 2 inches, what is the measure of its diameter?

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
4 0
The diameter is twice the radius.
So, the answer is b (4 inches)
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Find the solution of the differential equation that satisfies the given initial condition. (du)/(dt) = (2t + sec^2 t)/(2u), u(0)
Delicious77 [7]
Ah okay so in differential equations you usually want the top variable isolated. To do this, multiply by dt and 2u and you get
2udu = 2t + { \sec(t) }^{2} dt
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
{u}^{2}   + c =  {t}^{2}  +  \tan(t)  + k
Where c and k are arbitrary constants. Subtracting c from k and you get
{u}^{2}  =  {t}^{2}  +  \tan(t)  + b
Where b is another constant. To find b, just plug in u(0) = -1 where u is -1 and t is 0. This becomes
1 =  \tan(0)  + b
tan(0) is 0 so b = 1. Take the plus or minus square root on both sides and you finally get
u =  \: { {t}^{2} }  +  \tan(t)  + 1
But Brainly didn't let me do but juat remember there is a plus or minus square root on the left.
3 0
3 years ago
Suppose y varies directly with x and y=12 when x=-3 what is the value of y when x=6?
coldgirl [10]

Answer:

A. -24

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a directly or proportional variation if it can be expressed in the form k=\frac{y}{x} or y=kx

In this problem we have

For x=-3, y=12

Find the value of the constant of proportionality k

k=\frac{y}{x}

substitute the given values

k=\frac{12}{-3}=-4

so

The linear equation is equal to

y=-4x

what is the value of y when x=6?

substitute the value of x in the linear equation and solve for y

y=-4(6)=-24

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Gekata [30.6K]

Step-by-step explanation:

5 gallons 3 quarts +4 gallons 2 quarts

5.3

+

4.2

=9.5 gallons

5 0
3 years ago
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