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3 years ago

HELP HELP HELP

Mathematics

2 answers:

mojhsa [17]3 years ago

8 0

Answer:

2998 ; 17%

Step-by-step explanation:

Given the function:

t(c)=-3970.9(ln c)

c = % of carbon remaining ; t = time

1.) c = 47% = 47/100 = 0.47

t(0.47) = - 3970.9(In 0.47)

t = - 3970.9 * −0.755022

t = 2998.119

t = 2998

B.)

t = 7000

t(c)=-3970.9(ln c)

7000 = - 3970.9(In c)

7000 / - 3970.9 = In c

−1.762824 = In c

c = exp(−1.762824)

c = 0.1715596

c = 0.1715596 * 100%

c = 17.156% ; c = 17%

Lapatulllka [165]3 years ago

5 0

Answer: For plato family

The function t relates the age of a plant fossil, in years, to the percentage, c, of carbon-14 remaining in the fossil relative to when it was alive.

Use function t to complete the statements.

A fossil with 47% of its carbon-14 remaining is approximately

years old.

A fossil that is 7,000 years old will have approximately

17% of its carbon-14 remaining.

Step-by-step explanation:

The first box is 2,998

The second box is 17%

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The perimeter of a rectangle is 30.8 km and it’s diagonal length is 11 km. Find it’s length and width

blsea [12.9K]

Answer:

Length of the rectangle is 15.0325 km and width is 0.3765 km.

Explanation:

Given:

Perimeter of a rectangle = 30.8 km

Length of diagonal of rectangle = 11 km

To find:

The length and width of rectangle=?

Solution:

Lets assume length of the rectangle = x km

And assume width of the rectangle = y km

Lets first create equation using given perimeter

perimeter of rectangle = 2 ( length + width )

=> 30.8 km = 2 ( x + y )

=> $x + y = \frac{30.8}{2}$

=> y = 15.4 – x ------(1)

As diagonal and two sides of rectangle forms right angle triangle whose hypoteneus is diagonal ,

=> $length^2 + width^2 = diagonal^2$

=> $x^2 + y^2 = 11^2$

=> $x^2 + y^2 = 121$

On substituting value of y from (1) in above equation we get

=> $x^2 + (15.4-x)^2 = 121$

=> $x^2 + (15.4)^2 + x^2 – 2 x 15.4 \times x = 121$

=> $2x^2-30.8x + 237.16 -121 = 0$

=> $2x^2-30.8x + 116.16 = 0$

Solving above quadratic equation using quadratic formula

General form of quadratic equation is

$ax^2 +bx +c = 0$

And quadratic formula for getting roots of quadratic equation is

$x= \frac{ -b\pm\sqrt{(b^2-4ac)}}{2a}$

As equation is $2x^2-30.8x + 116.16 = 0$ , in our case

a = 2 , b = -30.8 and c = 116.16

Calculating roots of the equation we get

$x=\frac{ -(-30.8)\pm\sqrt{(-30.8)^2-4(2)( 11)} } {(2\times2)}$

$x=\frac{30.8\pm\sqrt{(948.64-88)}}{4}$

$x=\frac{30.8\pm\sqrt{860.64}}{4}$

$x=\frac{(30.8\pm29.33)}4$

$x=\frac{(30.8+29.33)}{4}$

$x=\frac{(30.8-29.33)}{4}$

=> x = 15.0325 or x = 0.3675

As generally length is longer one ,

So x = 1.0325

From equation (1) y = 15.4 – x = 0.3765

Hence length of the rectangle is 15.0325 km and width is 0.3765 km.

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Answer:

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Step-by-step explanation:

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1) It's best to draw out a picture of a rectangle and label each corner with the coordinates given: Let's say (-5, 2) is point A, (-5, -2 1/3) is point B, (2 1/2, 2) is point C, and (2 1/2, -2 1/3) is point D.

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