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EleoNora [17]
3 years ago
5

I need to equation for the radius of a 400m running track I know the answer is 36.5 and I know the formula is =2

//tex.z-dn.net/?f=%20%5Cpi%20" id="TexFormula1" title=" \pi " alt=" \pi " align="absmiddle" class="latex-formula">r
Mathematics
1 answer:
miskamm [114]3 years ago
6 0
This formula only applies if the track is circular.  If it is, then we write the equation:

2*r*pi=400

Dividing by 2pi, we see that:

r=200/pi

This is approximately 63.66.
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For the given bond, whose interest rate is provided, find the semiannual interest payment and the
Vika [28.1K]

Answer:

The semiannual interest payment is $485.5

The total interest earned over the life of the bond is $10,681

Step-by-step explanation:

The formula of the simple interest is I = Prt, where

  • P is the money invested
  • r is the interest rate in decimal
  • t is the time in years

∵ The bond is $20,000

∴ P = 20,000

∵ First Income Fund 11-year bond at 4.855%

∴ t = 11

∴ r = 4.855%

- Change it to decimal by divide it by 100

∴ r = 4.855 ÷ 100 = 0.04855

∵ The semiannual interest payment = P × r × half a year

∴ The semiannual interest payment = 20,000 × 0.04855 × \frac{1}{2} (1)

∴ The semiannual interest payment = 485.5

The semiannual interest payment is $485.5

∵ I = Prt

- Substitute the values of P, r and t in the formula

∴ I = 20,000(0.04855)(11)

∴ I = 10,681

The total interest earned over the life of the bond is $10,681

6 0
3 years ago
Solve the equations by factoring:<br><br>x^2−3x−40=0<br><br>4x^2−81=0
Alja [10]

Answer:

see explanation

Step-by-step explanation:

Given

x² - 3x - 40 = 0

Consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term (- 3)

The factors are - 8 and + 5, since

- 8 × 5 = - 40 and - 8 + 5 = - 3, thus

(x - 8)(x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x + 5 = 0 ⇒ x = 5

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Given

4x² - 81 = 0 ← this is a difference of squares and factors in general as

a² - b² = (a + b)(a - b), thus

4x² - 81

=(2x)² - 9²

= (2x + 9)(2x - 9) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 9 = 0 ⇒ 2x = - 9 ⇒ x = - \frac{9}{2}

2x - 9 = 0 ⇒ 2x = 9 ⇒ x = \frac{9}{2}

8 0
3 years ago
Read 2 more answers
A picture frame (see figure) has a total perimeter of 3 feet. The width of the frame is 0.64 times its length. Find the dimensio
Naya [18.7K]

Answer:

\approx 0.59\text{ ft by }0.91\text{ ft}

Step-by-step explanation:

Let \ell represent the length of the rectangle. The width can be represented as 0.64\ell.

The perimeter of a rectangle with lengths l and w is given by p=2l+2w.

Thus, we have:

2\ell+2(0.64\ell)=3,\\2\ell +1.28\ell=3,\\3.28\ell=3,\\\ell=0.91463414634\approx 0.91

The width is then 0.64(0.91463414634)=0.58536585365\approx 0.59.

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Answer:

\large\boxed{y=\dfrac{1}{4}x+3}

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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From the graph we have the points (4, 4) and (0, 3) → b = 3.

We have the equation:

y=mx+3

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

Put the coordinates of the points:

m=\dfrac{3-4}{0-4}=\dfrac{-1}{-4}=\dfrac{1}{4}

Finally we have:

y=\dfrac{1}{4}x+3

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Answer:

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Step-by-step explanation:

45+30=75

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2 years ago
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