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zysi [14]
3 years ago
12

Two bonds are available on the market as follows:

Mathematics
2 answers:
erastova [34]3 years ago
7 0

Answer:

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

P represents the principal or initial amount invested.

R represents the interest rate.

T represents duration of the investment in years

From the information given,

P = $750

R = 5%

T = y years

I = the total return of Bond 1 - principal

I = 1000 - 750 = $250

Therefore,

250 = (750 × 5 × y)/100

250 = 37.5y

y = 250/37.5

y = 6.7 years

Vedmedyk [2.9K]3 years ago
4 0

Answer:

The correct answer is 7 years.

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Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.
Allushta [10]
Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
f_x=5yz=0\implies y=0\text{ or }z=0
f_y=5xz=0\implies x=0\text{ or }z=0
f_z=5xy=0\implies x=0\text{ or }y=0


Taken together, we find that (0, 0, 0) appears to be the only critical point on f within the ball. At this point, we have f(0,0,0)=0.

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)

with partial derivatives (set to 0)

L_x=5yz+2\lambda x=0
L_y=5xz+2\lambda y=0
L_z=5xy+2\lambda z=0
L_\lambda=x^2+y^2+z^2-1=0

We then observe that

xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2

So, ignoring the critical point we've already found at (0, 0, 0),


5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}
5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}
5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of \left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right), at which points we get a value of either of \pm\dfrac5{\sqrt3}, with the maximum being the positive value and the minimum being the negative one.
5 0
3 years ago
Write each decimal as a fraction or mixed number in simplest form. 2.75=?
Mamont248 [21]
2.75 as a mixed number would be:

2 \frac{3}{4}
4 0
3 years ago
Read 2 more answers
Which expression does the fraction 3/8 equal to A. 3 times 8 B. 3 divided by eight C. 8 divided by 3 D. 3 - 8
jek_recluse [69]

Answer:

B. 3 divided by eight

Step-by-step explanation:

3/8  means 3 divided by 8

A fraction bar is division

5 0
3 years ago
A line that includes the point (0,0) has a slope of -9. What is its equation in slope-intercept
ikadub [295]
Y=-9x because y=mx+b is the formula so plug in the slope, m(-9) and the x-intercept, x(0)
3 0
3 years ago
An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest cir
Serhud [2]

Answer:

The artist used 8.6\ in more of silver wire

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

we know that

The Perimeter of the square is equal to

P=4a

where

a is the length side of the square

P=40\ in

so

40=4a

a=10\ in

so

Each side of the square has a length of 10 in

step 2

Find the circumference of the circle

The diameter of the circle is equal to the length of the side of  the square

The circumference is equal to

C=\pi D

we have

D=10\ in

substitute

C=(3.14)(10)=31.4\ in

step 3

Find the difference

40\ in-31.4\ in=8.6\ in

4 0
4 years ago
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