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3 years ago

$16.000 is deposited into a savings account with an annual interest rate of 2% compounded continuously. How much will be in the

Mathematics

1 answer:

rjkz [21]3 years ago

8 0

Answer:

A) $17,332.59

Step-by-step explanation:

$16,000(e^(0.02[or 2%] * 4)) = $16,000(e^0.08)

e^0.08 = 1.08328706767 * $16,000 ≈ $17,332.59

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What is the measurement of 3/4 in simplest form

stepan [7]

Answer:

It is in simplest form

Step-by-step explanation:

6 0

3 years ago

A potential energy function is given by U = A x3 + B x2 − C x + D . For positive parameters A, B, C, D this potential has two eq

Ivenika [448]

Answer:

7.8655

Step-by-step explanation:

Given the functionl

$U=Ax^3+Bx^2-cx+D$

Where,

$A=1.45J/m^3\\B=2.85J/m^2\\c= 1.7J/m\\D=0.6J$

We have, replacing,

$U=1.45x^3+2.85x^2-1.7x+0.6$

We need to derivate and verify for stable equilibrum that,

$\frac{d^2 U}{dx^2}>0$

Then,

$U'(x) = 4.32x^2+5.7x-1.7$

Roots in,

$x_1=-1.57008\\x_2=0.250636$

We obtain U"(x), then we have

$\frac{d^2U}{dx}=8.64x+5.7$

For $x=-1.57, U"(x)=-7.86549$ Unestable

For $x=0.250636 U"(x)=7.8655>0$ Stable

7 0

3 years ago

I'm having a hard time with this question so someone help please

bulgar [2K]

Answer:

7.7 km

Step-by-step explanation:

This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.

<h3>Law of Sines</h3>

The Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...

t/sin(T) = p/sin(P) = j/sin(J)

We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.

<h3>Setup</h3>

We know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:

7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j

<h3>Solution</h3>

This can be solved in two steps. First, we find angle P, then we use that to find length j.

sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847

P = arcsin(0.642847) ≈ 40.0045°

Now, we can find j:

j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km

The distance from the tower to the plane is about 7.7 km.

<em>Additional comment</em>

We have used T, P, and J to refer to the vertices at the tower, plane, and jet.

The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.

3 0

2 years ago

chubhunter [2.5K]

MNOP is similar to QRST with ratio of 5:4<span>. That means the MP:QT ratio would also be 5:4

The length of QT would be
</span>MP/QT = 5/4<span>
85mm/QT=5/4
85mm*4= 5*QT
5QT= 340
QT=68mm</span>

8 0

3 years ago

6-10 divide, another onee thank you!!

eduard

Answers:

10.) $\displaystyle \pm{5}$

9.) $\displaystyle 1\frac{1}{2}$

8.) $\displaystyle \pm{1\frac{1}{2}}$

7.) $\displaystyle \pm{1\frac{1}{2}}$

6.) $\displaystyle \pm{\frac{1}{2}}$

Step-by-step explanations:

10.) $\displaystyle \frac{\sqrt{200}}{\sqrt{8}} \hookrightarrow \sqrt{25} \hookrightarrow \frac{\pm{10\sqrt{2}}}{\pm{2\sqrt{2}}} \\ \\ \boxed{\pm{5}}$

9.) $\displaystyle \frac{\sqrt[3]{135}}{\sqrt[3]{40}} \hookrightarrow \sqrt[3]{3\frac{3}{8}} \hookrightarrow \frac{3\sqrt[3]{5}}{2\sqrt[3]{5}} \\ \\ \boxed{1\frac{1}{2}}$

8.) $\displaystyle \frac{\sqrt[4]{162}}{\sqrt[4]{32}} \hookrightarrow \sqrt[4]{5\frac{1}{16}} \hookrightarrow \frac{\pm{3\sqrt[4]{2}}}{\pm{2\sqrt[4]{2}}} \\ \\ \boxed{\pm{1\frac{1}{2}}}$

7.) $\displaystyle \frac{\sqrt{63}}{\sqrt{28}} \hookrightarrow \sqrt{2\frac{1}{4}} \hookrightarrow \frac{\pm{3\sqrt{7}}}{\pm{2\sqrt{7}}} \\ \\ \boxed{\pm{1\frac{1}{2}}}$

6.) $\displaystyle \frac{\sqrt{12}}{\sqrt{48}} \hookrightarrow \sqrt{\frac{1}{4}} \hookrightarrow \frac{\pm{2\sqrt{3}}}{\pm{4\sqrt{3}}} \\ \\ \boxed{\pm{\frac{1}{2}}}$

I am joyous to assist you at any time.

5 0

2 years ago