Write the equation of a sine or cosine function to describe the graph.

What is the radius, in centimeters, of a circle that has a circumference of 161 centimeters?

elena-14-01-66 [18.8K]

Answer:

25.63694268 = r

Step-by-step explanation:

The circumference is

C = 2*pi*r

161 = 2*(3.14) *r

161 = 6.28 r

Divide each side by 6.28

161/6.28 = r

25.63694268 = r

3 0

2 years ago

Miss Stoner purchase a new computer for $1,150 at the Apple store if sales tax is 7.5% what is the total of her purchase

Thepotemich [5.8K]

Answer:

$1236.25

Step-by-step explanation:

We can convert the percentage to 0.075 to make it easier. Then, multiply 1150 by 1.075 to get 1236.25. We add the one because we need to include the initial $1150.

4 0

2 years ago

What is the value of x in the equation 3x-5=1/2x+2x

creativ13 [48]

Answer:

10

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3x−5=

1

2

x+2x

3x+−5=

1

2

x+2x

3x−5=(

1

2

x+2x)(Combine Like Terms)

3x−5=

5

2

x

3x−5=

5

2

x

Step 2: Subtract 5/2x from both sides.

3x−5−

5

2

x=

5

2

x−

5

2

x

1

2

x−5=0

Step 3: Add 5 to both sides.

1

2

x−5+5=0+5

1

2

x=5

Step 4: Multiply both sides by 2.

2*(

1

2

x)=(2)*(5)

x=10

4 0

3 years ago

Find the general solution of x'1 = 3x1 - x2 + et, x'2 = x1.

Ann [662]

Note that if ${x_2}'=x_1$ , then ${x_2}''={x_1}'$ , and so we can collapse the system of ODEs into a linear ODE:

${x_2}''=3{x_2}'-x_2+e^t$
${x_2}''-3{x_2}'+x_2=e^t$

which is a pretty standard linear ODE with constant coefficients. We have characteristic equation

$r^2-3r+1=\left(r-\dfrac{3+\sqrt5}2\right)\left(r+\dfrac{3+\sqrt5}2\right)=0$

so that the characteristic solution is

${x_2}_C=C_1e^{(3+\sqrt5)/2\,t}+C_2e^{-(3+\sqrt5)/2\,t}$

Now let's suppose the particular solution is ${x_2}_p=ae^t$ . Then

${x_2}_p={{x_2}_p}'={{x_2}_p}''=ae^t$

and so

$ae^t-3ae^t+ae^t=-ae^t=e^t\implies a=-1$

Thus the general solution for $x_2$ is

$x_2=C_1e^{(3+\sqrt5)/2\,t}+C_2e^{-(3+\sqrt5)/2\,t}-e^t$

and you can find the solution $x_1$ by simply differentiating $x_2$ .

7 0

3 years ago

A bag contains 5 blue marbles, 2black marbles ,and 3 red marbles. A marine is randomly drawn from the bag The probability of not

notka56 [123]

Answer:

80%; 30%

Step-by-step explanation:

There is 5 blue marbles, 2 black marbles, and 3 red marbles. In other words, there is a total of 10 marbles.

There are only 2 black marbles and 8 marbles that are not black. Therefore, the probability of <em>not</em> drawing a black marble is 8/10 or 4/5 or 80%.

There are only 3 red marbles out of the 10 total marbles. Therefore, the probability of drawing a red marble is 3/10 or 30%.

6 0

2 years ago