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3 years ago

Translate to an equation and solve: The sum of two-fifths and f is one-half. Provide f=

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

3 0

Answer:

9/10

1/2+2/5

Since these fractions have different denominators, we need to find the least common multiple of the denominators.The least common multiple of 2 and 5 is 10, so we need to multiply to make each of the denominators = 10

1/2 ∗ 5/5 = 5/10

5/2∗ 2/2= 4/10

Since these fractions have the same denominator, we can just add the numerators

5/10+ 4/10 = 9/10

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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

4 0

3 years ago

If x^2 + 1/x^2 = 7 , find the value of x^3 + 1/x^3 and x^4 + 1/x^4

Maksim231197 [3]

Answer:

pls show me the question

7 0

2 years ago

elect the correct answer. graph A graph B graph C graph D A credit card company uses these rules to calculate the minimum amount

laila [671]

The graph that correctly shows the minimum amount due for a credit amount (x) is graph B.

<h3>How to determine the graph with the minimum amount due?</h3>

First of all, we would assign a variable to the different amount of money as follows:

Let x be the credit amount.

Let y be the minimum amount due.

Translating the word problem into an algebraic expression, we have;

For a bill of less than $100, the entire amount is due:

0 ≤ x < $100, therefore, y = x

For a bill of at least $100 but less than $500, the minimum due is $100: $100 ≤ x < $500, therefore, y = 100

For a bill of at least $500 but less than $1,000, the minimum due is $300:

$500 ≤ x < $1000, therefore, y = $300

For a bill of $1,000 or more, the minimum due is $500:

Since the credit limit is equal to $2000, we have $1000 ≤ x < $2000 and y = $500

In conclusion, the graph that correctly shows the minimum amount due for a credit amount (x) is graph B.

Read more on graphs here: brainly.com/question/16883029

#SPJ1

5 0

2 years ago

John has a goal to ride his bike at least 200 miles this summer. John has ridden 12 miles thus far. There are 40 days left in th

Alex Ar [27]

Answer:

4.7 miles per day

Step-by-step explanation:

400-12=188

188÷40

=4.7 miles

7 0

3 years ago

A radio telescope has a parabolic surface, as shown below.

krek1111 [17]

OK, so the graph is a parabola, with points x=0,y=0; x=6,y=-9; and x=12,y=0

Because the roots of the equation are 0 and 12, we know the formula is therefore of the form

y = ax(x - 12), for some a

So put in x = 6

-9 = 6a(-6)

9 = 36a

a = 1/4

So the parabola has a curve y = x(x-12) / 4, which can also be written y = 0.25x² - 3x

The gradient of this is dy/dx = 0.5x - 3

The key property of a parabolic dish is that it focuses radio waves travelling parallel to the y axis to a single point. So we should arrive at the same focal point no matter what point we chose to look at. So we can pick any point we like - e.g. the point x = 4, y = -8

Gradient of the parabolic mirror at x = 4 is -1

So the gradient of the normal to the mirror at x = 4 is therefore 1.

Radio waves initially travelling vertically downwards are reflected about the normal - which has a gradient of 1, so they're reflected so that they are travelling horizontally. So they arrive parallel to the y axis, and leave parallel to the x axis.

So the focal point is at y = -8, i.e. 1 metre above the back of the dish.

5 0

2 years ago