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3 years ago

Define complex fraction. Give two examples of a complex fraction

Mathematics

1 answer:

Charra [1.4K]3 years ago

6 0

A complex fraction are two fractional expressions, one over the other.
Example 1: 7/8 over 3/4
Example 2: 1/4 over 5/6

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Numerical expression 5+9

ycow [4]

5+9=14 in numerical expression

4 0

3 years ago

The length of one side of a square pond is 15 feet. The pond is surrounded by a 3 foot wide walkway. What is the total area of t

rewona [7]

Answer:

Area = 324 ft²

Step-by-step explanation:

Given

Length = 15ft

Walkway = 3ft

Required

Determine the area of the pond + the walkway

To calculate the required area, we need to get the total length of a side .

This is calculated by adding the length of a side of the pond and the side of the walkway

Total Length = Pond Length + Walkway

Total Length = 15ft + 3ft

Total Length = 18ft

Now, the required area can be calculated as thus:

Area = Total Length * Total Length

Area = 18ft * 18ft

Area = 324 ft²

8 0

3 years ago

The equation 8 − 4x = 0 has <br> real solution

omeli [17]

The equation above has no real solution because it has no real number 0 is not a number that can take place of a real solution.
Hope This helped;D

5 0

3 years ago

Read 2 more answers

The equation r(t) = sin(4t)i + cos(4t)j, 0t≥0 describes the motion of a particle moving along the unit circle. Answer the follo

lorasvet [3.4K]

Answer:

a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).

Step-by-step explanation:

a) Let is find first the velocity vector by differentiation:

$\vec v = \frac{dr_{x}}{dt} i + \frac {dr_{y}}{dt} j$

$\vec v = 4\cdot \cos 4t\, i - 4 \cdot \sin 4t \,j$

$\vec v = 4 \cdot (\cos 4t \, i - \sin 4t\,j)$

Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:

$\|\vec u \| = 1$

Then,

$\| \vec u \| = \sqrt{\cos^{2} 4t + \sin^{2}4t }$

$\| \vec u \| = \sqrt{1}$

$\|\vec u \| = 1$

Hence, the particle has a constant speed of 4.

b) The acceleration vector is obtained by deriving the velocity vector.

$\vec a = \frac{dv_{x}}{dt} i + \frac {dv_{y}}{dt} j$

$\vec a = 16\cdot (-\sin 4t \,i -\cos 4t \,j)$

Velocity and acceleration are orthogonal to each other only if $\vec v \bullet \vec a = 0$ . Then,

$\vec v \bullet \vec a = 64 \cdot (\cos 4t)\cdot (-\sin 4t) + 64 \cdot (-\sin 4t) \cdot (-\cos 4t)$

$\vec v \bullet \vec a = -64\cdot \sin 4t\cdot \cos 4t + 64 \cdot \sin 4t \cdot \cos 4t$

$\vec v \bullet \vec a = 0$

Which demonstrates the orthogonality between velocity and acceleration vectors.

c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is: $t \geq 0$

And cosine decrease and sine increase inasmuch as t becomes bigger.

d) Let evaluate the vector in $t = 0$ .

$r(0) = \sin (4\cdot 0) \,i + \cos (4\cdot 0)\,j$

$r(0) = 0\,i + 1 \,j$

False, the particle begin at the point (0,1).

7 0

3 years ago

How much would $300 invested at 4 percent interest compounded monthly be worth after 8 years round your answer to the nearest ce

ratelena [41]

We will use the equation $A(t)=P(1+ \frac{r}{n})^{(n)(t)}$ , where P is the initial amount invested, r is the interest rate in decimal form, n is the number of times in a year the money is compounded, and t is the number of years the money will be invested. Our P = 300, r = .04, n = 12 (there are 12 months in a year), and t = 8. Filling in accordingly, $A(t)=300(1+ \frac{.04}{12})^{(12)(8)}$ . Simplifying what we can gives us $A(t)=300(1+.00333333)^{96}$ . Doing that addition inside the parenthesis and then raising that number to the 96th power gives us A(t) = 300(1.376395075) so A(t) = $412.92, choice B above.

8 0

3 years ago