If |u| = 10, |v| = 8, and the angle formed between them is 60°, then u

Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, co

sineoko [7]

2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Step-by-step explanation:

The given is,

Initial investment - $5000

Future amount - $6000

Interest rate - 7.5% (compounded quarterly)

Step:1

Formula to calculate the Future amount with compound interest,

$F = P(1+\frac{r}{n} )^{nt}$ ...................................(1)

Where, F - Future amount

P - Initial amount

r - Rate of interest

n - No. of compounding in a year

t - Time period

From given,

F = $6000

P = $5000

r = 7.5%

n = 4 (compounded quarterly)

Equation (1) becomes,

$6000=5000(1+\frac{0.075}{4} )^{(t)(4)}$

$\frac{6000}{5000} =(1+0.01875)^{4t}$

$1.2 = (1.01875)^{4t}$

Take log on both sides,

$log 1.2 = 4(t) log 1.01875$

Substitute log values,

0.07918 = 4(t) (0.0080676)

= (t) (0.0322705)

$t = \frac{0.07918}{0.0322705}$

= 2.45

t ≅ 2.5 years

Result:

2.5 years required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

3 0

2 years ago

A flat circular plate has the shape of the region x squared plus y squared less than or equals 1x2+y2≤1. the plate, including t

vredina [299]

You're looking for the extreme values of $x^2+3y^2+13x$ subject to the constraint $x^2+y^2\le1$ .

The target function has partial derivatives (set equal to 0)

$\dfrac{\partial(x^2+3y^2+13x)}{\partial x}=2x+13=0\implies x=-\dfrac{13}2$

$\dfrac{\partial(x^2+3y^2+13x)}{\partial y}=6y=0\implies y=0$

so there is only one critical point at $\left(-\dfrac{13}2,0\right)$ . But this point does not fall in the region $x^2+y^2\le1$ . There are no extreme values in the region of interest, so we check the boundary.

Parameterize the boundary of $x^2+y^2\le1$ by

$x=\cos u$

$y=\sin u$

with $0\le u$ . Then $t(x,y)$ can be considered a function of $u$ alone:

$t(x,y)=t(\cos u,\sin u)=T(u)$

$T(u)=\cos^2u+3\sin^2u+13\cos u$

$T(u)=3+13\cos u-2\cos^2u$

$T(u)$ has critical points where $T'(u)=0$ :

$T'(u)=-13\sin u+4\sin u\cos u=\sin u(4\cos u-13)=0$

$(1)\quad\sin u=0\implies u=0,u=\pi$

$(2)\quad4\cos u-13=0\implies\cos u=\dfrac{13}4$

but $|\cos u|\le1$ for all $u$ , so this case yields nothing important.

At these critical points, we have temperatures of

$T(0)=14$

$T(\pi)=-12$

so the plate is hottest at (1, 0) with a temperature of 14 (degrees?) and coldest at (-1, 0) with a temp of -12.

4 0

2 years ago

David worked in the library on Friday and Saturday he worked a total of 7 3/4 hours during these two days if he worked 4 1/4 Hou

aleksandr82 [10.1K]

Answer:

3 1/2 hours.

Step-by-step explanation:

We subtract>

Number of hours worked on a Saturday

= 7 3/4 - 4 1/4

= (7 - 4) + (3/4 - 1/4)

= 3 + 1/2

= 3 1/2 hours.

6 0

2 years ago

Function F(x)=x+1 and g(x)=5x+1 find the f(4)=g(x+1)

Lapatulllka [165]

The function of f(4) = g(x+1) gives the value of x that is -1/5.

<h3>What is the function addition?</h3>

It is the addition of two functions similar to the addition of any two polynomial functions.

Given;

F(x)=x+1

g(x)=5x+1

We need to find f(4)=g(x+1)

First substitute x = 4 in f(x)

F(x)=x+1

F(4) = 4 + 1

F(4) = 5

Now substitute x = x + 1 in g(x)

g(x)=5x+1

g(x + 1) = 5(x + 1) + 1

g(x + 1) = 5x + 5 + 1

g(x + 1) = 5x + 6

Then ,

F(4) = g(x + 1)

5 = 5x + 6

5x = 5 - 6

5x = -1

x = -1/5.

The function of f(4) = g(x+1) gives the value of x that is -1/5.

Learn more about function;

brainly.com/question/14438192

#SPJ1

7 0

2 years ago

What is the exact volume of the cylinder

vladimir1956 [14]

Answer:

Volume = πr2h

= π×52×9

= 225π

= 706.85 inches3

Step-by-step explanation:

8 0

2 years ago

If |u| = 10, |v| = 8, and the angle formed between them is 60°, then u · v = ?