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2 years ago

14

Daphne borrows $2500 from a financial institution that charges 6% annual interest, compounded monthly, for 2 years. The amount t

hat Daphne will need to pay back at the end of the term is

1 answer:

Gnom [1K]2 years ago

7 0

1350$ is the right answer to your problem trust me I know this

You might be interested in

Dy/dx = 2xy^2 and y(-1) = 2 find y(2)

Anarel [89]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2887301

—————

Solve the initial value problem:

dy
——— = 2xy², y = 2, when x = – 1.
dx

Separate the variables in the equation above:

$\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\
\mathsf{y^{-2}\,dy=2x\,dx}$

Integrate both sides:

$\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\
\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\
\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{y}=x^2+C_1}$

$\mathsf{\dfrac{1}{y}=-(x^2+C_1)}$

Take the reciprocal of both sides, and then you have

$\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}$

In order to find the value of C₁ , just plug in the equation above those known values for x and y, then solve it for C₁:

y = 2, when x = – 1. So,

$\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\
\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\
\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}$

$\mathsf{C_1=-\,\dfrac{3}{2}}$

Substitute that for C₁ into (i), and you have

$\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\
\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\
\mathsf{y=-\,\dfrac{2}{2x^2-3}}$

So y(– 2) is

$\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

Tags: <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

7 0

3 years ago

90 POINTS!!!!! Given: KLIJ inscr. in k(O),m∠K = 64°, measure of arc LI = 69°, measure of arc IJ = 59°, measure of arc KJ =97°

Kay [80]

In any cyclic quadrilateral, angles opposite one another are supplementary, meaning

$m\angle K+m\angle I=m\angle L+m\angle J=180^\circ$

and given that $\boxed{m\angle K=64^\circ}$ , we have $\boxed{m\angle I=116^\circ}$ .

By the inscribed angle theorem,

$m\angle JLK=\dfrac12m\widehat{KJ}$

$m\angle ILJ=\dfrac12m\widehat{IJ}$

and since

$m\angle L=m\angle JLK+m\angle ILJ$

we have

$m\angle L=\dfrac{97^\circ+59^\circ}2\implies\boxed{m\angle L=78^\circ}$

and it follows that

$m\angle J=180^\circ-m\angle L\implies\boxed{m\angle J=102^\circ}$

5 0

3 years ago

HELP ASAP. <br><br> I’m so confused can someone tell me what to do on this? I’ll mark brainliest

DENIUS [597]

9514 1404 393

Answer:

52°: angles 4, 13, 18
128°: angles 1, 3, 14, 17
44°: angles 5, 12, 15
136°: angles 2, 6, 11, 16
84°: angles 7, 10
96°: angles 8, 9

Step-by-step explanation:

Where a transversal (t or u) crosses parallel lines (m and n), there are four angles formed at each intersection. Corresponding and vertical angles are congruent.

Angles in a linear pair are always supplementary. Of course, the angles interior to a triangle always total 180°. These facts let you find the relationships of all the angles in the figure.

Angle 13 corresponds to the given angle 52°, so has the same measure. Angles 4 and 18 are vertical angles with respect to those, so also have the same measure. Angles 1 and 3, 14 and 17 are supplementary to the ones just named, so all have measure 128°.

In the same way, angles on the other side of the figure can be found from the one marked 44°. Angles 5, 12, and 15 also have that measure; and angles 2, 6, 11, and 16 are supplementary, 136°. Angles 7 and 10 finish the triangle interior so that its sum is 180°. That means they are 180° -52° -44° = 84°. Of course, angles 8 and 9 are the supplement of that value, 96°.

In summary:

52°: angles 4, 13, 18
128°: angles 1, 3, 14, 17
44°: angles 5, 12, 15
136°: angles 2, 6, 11, 16
84°: angles 7, 10
96°: angles 8, 9

6 0

2 years ago

Her senior year of college, Giselle decides to live off campus. In order to cover rent, she wants to get a job as a waitress.

SCORPION-xisa [38]

She would have to work at least 12 hours.

At Chili’s, she would be paid 11.75x + 33 per week, with x being the number of hours she worked.

At the Cheesecake Factory, Giselle would be paid 14.50x per week, with x being how many hours she worked.

We want to know how many hours Gisele would have to work for her pay at the Cheesecake Factory to be more than her pay at Chili’s

The inequality 11.75x + 33 < 14.50x is what has to be set up to solve the problem. At how many hours will the pay on the left be less than the pay on the right?

11.75x + 33 < 14.50x
33 < 2.75x
12 < x

So Giselle has to work greater 12 hours a week for her to make more money at the Cheesecake Factory.

5 0

3 years ago

DISNEY SONG QUIZ FIRST ONE TO GET IT RIGHT GETS BRAINLIEST!!

AysviL [449]

Answer:

D singing

Step-by-step explanation:

Hopefully this is right!

7 0

3 years ago