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andrew11 [14]
2 years ago
13

The pair of points is on the graph of an inverse variation. Find the missing value. (9,5) and (x,6)

Mathematics
2 answers:
olchik [2.2K]2 years ago
7 0
(9,5)
Y=k/x
5=k/9 solve for k
K=5*9=45 now use it to solve for the second pair
(X,6)
Y=k/x
6=45/x solve for x
X=45/6==7.5.....answer
Dominik [7]2 years ago
4 0

Answer:

The missing value x is, \frac{15}{2} or 7\frac{1}{2}

Step-by-step explanation:

The Inverse variation problems can be solved by using the equation, i.e,

y \propto \frac{1}{x}.

use constant variation k to write the above equation as:

y=\frac{k}{x}                         ......[1]

Now, use the given information to calculate the value of k;

we need to find the value of k ; when x=9  and y=5

5=\frac{k}{9} or

k =9\times 5

Simplify:

k =45.

Rewrite the equation [1] by substituting the value of k =45,

⇒ y = \frac{45}{x}                     ......[2]

Substitute the value y=6 in equation[2] to find x:

6 =\frac{45}{x} or

x = \frac{45}{6} or x=\frac{15}{2}=7\frac{1}{2}

Therefore, the missing value x is, \frac{15}{2}=7\frac{1}{2}



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A certain college graduate borrows 7864 dollars to buy a car. The lender charges interest at an annual rate of 13%. Assuming tha
White raven [17]

Answer:

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = =$1573.17

Step-by-step explanation:

Consider A represent the balance at time t.

A(0)=$ 7864.

r=13 % =0.13

Rate payment = $k

The balance rate increases by interest (product of interest rate and current balance) and payment rate.

\frac{dB}{dt} = rB-k

\Rightarrow \frac{dB}{dt} - rB=-k.......(1)

To solve the equation ,we have to find out the integrating factor.

Here p(t)= the coefficient of B =-r

The integrating factor =e^{\int p(t) dt

                                     =e^{\int (-r)dt

                                     =e^{-rt}

Multiplying the integrating factor the both sides of equation (1)

e^{-rt}\frac{dB}{dt} -e^{-rt}rB=-ke^{-rt}

\Rightarrow  e^{-rt}dB - e^{-rt}rBdt=-ke^{-rt}dt

Integrating both sides

\Rightarrow \int e^{-rt}dB -\int e^{-rt}rBdt=\int-ke^{-rt}dt

\Rightarrow e^{-rt}B=\frac{-ke^{-rt}}{-r} +C        [ where C arbitrary constant]

\Rightarrow B(t)=\frac{k}{r} +Ce^{rt}

Initial condition B=7864 when t =0

\therefore 7864= \frac{k}{r} - Ce^0

\Rightarrow  C= \frac{k}{r} -7864

Then the general solution is

B(t)=\frac{k}{r}-( \frac{k}{r}-7864)e^{rt}

To determine the payment rate, we have to put the value of B(3), r and t in the general solution.

Here B(3)=0, r=0.13 and t=3

B(3)=0=\frac{k}{0.13}-( \frac{k}{0.13}-7864)e^{0.13\times 3}

\Rightarrow- 0.48\frac{k}{0.13} +11614.98=0

⇒k≈3145.72

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = ${(3145.72×3)-7864}

                                                 =$1573.17

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