What is : b squared+14b+ 24 over b squared+5b+6 divided by 1 over b+3

The radius of a circle is doubled. Which of the following describes the effect of this change on the area? PLZZZ HELP!!! THE RED

goblinko [34]

Answer:

The area is multiplied by 4

Step-by-step explanation:

The area of a circle is directly proportional to its square radius so if the radius is increased by x, the area will be increased by x ^ 2

4 0

3 years ago

Read 2 more answers

The acceleration of an object (in m/s^2) is given by the function a(t) = 9 sin(t). The initial velocity of the object is v(0) =

pentagon [3]

a) Acceleration is the derivative of velocity. By the fundamental theorem of calculus,

$v(t)=v(0)+\displaystyle\int_0^ta(u)\,\mathrm du$

so that

$v(t)=\left(-11\frac{\rm m}{\rm s}\right)+\int_0^t9\sin u\,\mathrm du$

$\boxed{v(t)=-\left(2+9\cos t)\right)\frac{\rm m}{\rm s}}$

b) We get the displacement by integrating the velocity function like above. Assume the object starts at the origin, so that its initial position is $s(0)=0\,\mathrm m$ . Then its displacement over the time interval [0, 3] is

$s(0)+\displaystyle\int_0^3v(t)\,\mathrm dt=-\int_0^3(2+9\cos t)\,\mathrm dt=\boxed{-6-9\sin3}$

c) The total distance traveled is the integral of the absolute value of the velocity function:

$s(0)+\displaystyle\int_0^3|v(t)|\,\mathrm dt$

$v(t)$ for $0\le t$ and $v(t)\ge0$ for $\cos^{-1}\left(-\frac29\right)\le t\le3$ , so we split the integral into two as

$\displaystyle\int_0^{\cos^{-1}\left(-\frac29\right)}-v(t)\,\mathrm dt+\int_{\cos^{-1}\left(-\frac29\right)}^3v(t)\,\mathrm dt$

$=\displaystyle\int_0^{\cos^{-1}\left(-\frac29\right)}(2+9\cos t)\,\mathrm dt-\int_{\cos^{-1}\left(-\frac29\right)}^3(2+9\cos t)\,\mathrm dt$

$\displaystyle=\boxed{2\sqrt{77}-6+4\cos^{-1}\left(-\frac29\right)-9\sin3}$

4 0

3 years ago

A woman has eight keys on a key ring, one of which fits the door she wants to unlock. Sherandomly selects a key and tries it. If

natulia [17]

Answer:

The expected number of keys she will try before she opens the door is 4.5.

Step-by-step explanation:

A woman has eight keys on a key ring, one of which fits the door she wants to unlock.

Each of them is equally as likely to be the one to work, which means that this situation is represented by an uniform distribution with lower bound $a = 1$ and upper bound $b = 8$ .