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3 years ago

Dragon had a lot of bands 12 of them tour then he had 39 left how many did he have at the start

Mathematics

1 answer:

GuDViN [60]3 years ago

8 0

Answer:

Step-by-step explanation:

12+39=51

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Find the general solution of dz/dt=5ze^(sint)cost+2e^(sint)cost

gizmo_the_mogwai [7]

Answer:

The general solution of given differential equation is $\frac{1}{5}ln|5z+2|=e^{\sin t}+C$ .

Step-by-step explanation:

The given differential equation is

$\frac{dz}{dt}=5ze^{\sin t}\cos t+2e^{\sin t}\cos t$

Taking out common factors.

$\frac{dz}{dt}=(5z+2)e^{\sin t}\cos t$

Using variable separable method, we get

$\frac{dz}{5z+2}=e^{\sin t}\cos t dt$

Integrate both sides.

$\int\frac{dz}{5z+2}=\int e^{\sin t}\cos t dt$

$I_1=I_2$ .... (1)

First solve LHS,

$I_1=\int\frac{dz}{5z+2}$

Substitute $5z+2=u$

$5\frac{dz}{du}=1$

$dz=\frac{1}{5}du$

$I_1=\frac{1}{5}\int\frac{du}{u}$

$I_1=\frac{1}{5}ln|u|+C_1$

$I_1=\frac{1}{5}ln|5z+2|+C_1$

Now, solve RHS,

$I_2=\int e^{\sin t}\cos t dt$

Substitute $\sin t=v$ ,

$\cos t\frac{dt}{dv}=1$

$\cos tdt=dv$

$I_2=\int e^{v}dv$

$I_2=e^{v}+C_2$

$I_2=e^{\sin t}+C_2$

Subtitle the values of I₁ and I₂ in equation (1).

$\frac{1}{5}ln|5z+2|+C_1=e^{\sin t}+C_2$

$\frac{1}{5}ln|5z+2|=e^{\sin t}+C_2-C_1$

$\frac{1}{5}ln|5z+2|=e^{\sin t}+C$

Therefore the general solution of given differential equation is $\frac{1}{5}ln|5z+2|=e^{\sin t}+C$ .

4 0

2 years ago

The Lopez family left Dallas and went to Houston. Then they went from Houston to Austin. Then they took the shortest route back

ruslelena [56]

Answer:

I would assume they drove a car.

If so, then Dallas to Houston: 239.3 miles.

Then, Houston to Austin: 165.3 miles

Shortest route back to Texas: 913.5.

I used g o o g l e m a p s to find my answer.

Now add the numbers up:

239.3+165.3+913.5= 1318.1

They traveled 1318.1 miles in all.

4 0

2 years ago

If P(x) = 8x and R(x) = 9x -8, find P(x) • R(x).

Airida [17]

Answer:

Given

P( x) = 8x

R ( x) = 9x - 8

Step-by-step explanation:

P(x) . R ( x) 

= 8x ( 9x - 8 )

= 72x^2 - 64x

8 0

2 years ago

Let f(x)=4x2−5 . A new quadratic function g(x) is the function f(x) stretched vertically by a factor of 2. What is the equation

soldi70 [24.7K]

To vertically strech a function, f(x) by a factor of c, that is cf(x)

so strech vertically by 2 means times whole thing by 2
so
2 times (4x^2-5) =8x^2-10

g(x)=8x^2-10

5 0

2 years ago

I need help for number 3

Sladkaya [172]

Answer: 3/2

Step-by-step explanation: 24 ÷ 2² + 8 (3/2) = 3/2

4 0

2 years ago

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