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3 years ago

I HAVE 5 MINS ANSWER THIS FOR (15 POINTS)

Mathematics

2 answers:

slamgirl [31]3 years ago

3 0

Answer:

Step-by-step explanation:

vladimir1956 [14]3 years ago

3 0

Answer:

Domain: 0,2,3

Range: -1,-3,-2

Step-by-step explanation:

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Jessica has an account with a credit union. Her account earns 2.2% simple interest yearly. Exactly a year and a half ago, she op

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4 years ago

Need help asap i will help u if u help me

sammy [17]

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4 years ago

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Use the elimination method to solve the system of equations. Choose the correct ordered pair.

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5 0

3 years ago

A piece of wire 28 ft long is cut into two pieces. One piece is used to form a square, and the remaining piece is used to form a

marusya05 [52]

Answer:

Wire should be cut in two parts with the length = 15.69 ft and 12.31 ft

Step-by-step explanation:

Length of the wire = 28 ft has been cut in two pieces.

One piece is used to form a square and remaining piece to form a circle.

Let the length of the wire which forms the square is 'l' ft.

Area of the square = (side)²

Perimeter of the square = 4(side) = l

Length of one side = $\frac{l}{4}$

So, the area of the square = $\frac{l^{2}}{16}$ ft²

Now length of the remaining part = perimeter of the circle = (28 - l) ft

2πr = (28 - l)

r = $\frac{28-l}{2\pi }$

Area of the circle formed = πr²

= $\frac{\pi(28-l)^{2} }{4(\pi )^{2} }$

= $\frac{(28-l)^{2}}{4\pi }$

Combined area of the square and circle

= $\frac{l^{2}}{16}$ + $\frac{(28-l)^{2}}{4\pi }$

Now to maximize the area we will find the derivative of the area with respect to l.

$\frac{dA}{dl}=\frac{d}{dl}[\frac{l^{2}}{16}+\frac{(28-l)^{2}}{4\pi}]$

= $\frac{d}{dl}[\frac{l^{2}}{16}+\frac{(28)^{2}+l^{2}-56l }{4\pi }]$

= $\frac{2l}{16}+\frac{(2l-56)}{4\pi }$

Now equate the derivative to zero.

$\frac{2l}{16}+\frac{(2l-56)}{4\pi }$ = 0

$(2l-56)=-\frac{2l}{16}\times 4\pi$

$(2l-56)=-\frac{\pi l}{2}$

$2l+\frac{\pi l}{2}=56$

$\frac{(4l+l\pi )}{2}=56$

l(4 + π) = 112

l(4 + 3.14) = 112

l = $\frac{112}{7.14}$

l = 15.69 ft

Length of the other part = 28 - 15.69 = 12.31 ft

Therefore, wire should be cut in two parts with the length = 15.69 ft and 12.31 ft

8 0

3 years ago

A town has a population of 20000 and grows at 4% every year. How long will it be until the population will reach 39400?

olga55 [171]

Answer:

The population will be 39400 in approximately 17 years

Step-by-step explanation:

The increase in population after t years is given by the formula

$P_t = P_0(1+r)^t$

Here

P_0 is the initial population

r is the growth rate and t is time in years

So far we know,

P_0 = 20000

r = 4%

P_t = 39400

Putting the values in the formula

$39400 = 20000(1+0.04)^t\\39400 =20000(1.04)^t\\\frac{39400}{20000} = (1.04)^t\\1.97 = (1.04)^t$

Taking natural log on both sides

$ln |(1.04)^t| = ln |1.97|\\t\ ln\ |1.04| = ln\ |1.97|\\t = \frac{ln\ 1.97}{ln\ 1.04}\\t = 17.287\\t \approx 17$

Hence,

The population will be 39400 in approximately 17 years

8 0

3 years ago