What are the vertices of the hyperbola whose equation is (x+3)^2/4

max2010maxim [7]

Your answer should be 314

4 x 16=64

10 x 25 (25 is the height)=250

64 + 250=314

5 0

3 years ago

The general solution to the second-order differential equation y′′+10y=0 is in the form y(x)=c1cosβx+c2sinβx. Find the value of

allsm [11]

Answer:β=√10 or 3.16 (rounded to 2 decimal places)

Step-by-step explanation:

To find the value of β :

we will differentiate the y(x) equation twice to get a second order differential equation.
We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β

y(x)=c1cosβx+c2sinβx

we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.

Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate βx in each case and multiply with the differential of c1cosx and c2sinx respectively.

lastly the differential of sinx= cosx and for cosx = -sinx.

Knowing all these we can proceed to solving the problem.

y=c1cosβx+c2sinβx

y'= β×c1×-sinβx+β×c2×cosβx

y'=-c1βsinβx+c2βcosβx

y''=β×-c1β×cosβx + (β×c2β×-sinβx)

y''= -c1β²cosβx -c2β²sinβx

factorize -β²

y''= -β²(c1cosβx +c2sinβx)

y(x)=c1cosβx+c2sinβx

therefore y'' = -β²y

y''+β²y=0

now we compare this with the second order D.E provided in the question

y''+10y=0

this means that β²y=10y

β²=10

B=√10 or 3.16(2 d.p)

5 0

3 years ago

At a certain restaurant 8 Delmonico steaks cost 218$. Three tacos and 12 Delmonico steaks cost 267$. Write a system of equations

Leto [7]

There is 600 Dollars

4 0

3 years ago

Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

ANSWER

${r}^{2} = 4 \cos2\theta$

EXPLANATION

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

7 0

3 years ago

You are biking to the park. After six minutes 40% of the distance still need to be traveled. How long does it take to bike to th

nikklg [1K]

Answer:

$y = (100-10x)\%$

It takes 10 minutes to the park.

Step-by-step explanation:

Given that:

Time taken = 6 minutes

Distance left to be traveled = 40%

To find:

The equation to represent the distance $y$ , that still needs to be traveled after $x$ minutes.

Solution:

As per given statement, distance traveled in 6 minutes = 60%

We can say that:

Distance traveled each minute = $\frac{60\%}{6}$ = 10%

After 1 minute, distance traveled = 10%

Distance left = 100 - 10 = 90%

After 2 minutes, distance traveled = 20%

Distance left = 100 - 20 = 80%

After $x$ minutes, distance traveled = 10 $x$ %

Distance left, $y$ = (100 - 10 $x$ )%

Therefore, the equation is:

$y = (100-10x)\%$

Time taken by the bike to reach to the park can be found by putting $y$ = 0 (i.e. distance left to be traveled = 0)

$0 = 100 -10x\\\Rightarrow 10x = 100\\\Rightarrow x = \bold{10\ minutes}$

8 0

2 years ago

What are the vertices of the hyperbola whose equation is (x+3)^2/4 - (y-5)^2/16 =1