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Dahasolnce [82]
2 years ago
7

An athlete signs a contract that guarantees a ​$ 9​-million salary 6 yr from now. Assuming that money can be invested at 6.7​% w

ith interest compounded​ continuously, what is the present value of that​ year's salary?
Mathematics
1 answer:
frozen [14]2 years ago
6 0

Answer:

$6,020,826.711

Step-by-step explanation:

The computation of the present value of that year salary is shown below:

As we know that

Present value in case of continuous compounding, the formula is

= \frac{Guaranteed\ amount}{e^{0.067 \times 6}}

where,

The Guaranteed amount is $9,000,000

The Time period is 6 years

And, the interest rate is 6.7%

Now placing these values

So, the present value is

= \frac{\$9,000,000}{e^{0.067 \times 6}}

= $6,020,826.711

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Which value is needed in the expression below to create a perfect square trinomial?
Klio2033 [76]

Answer:

The value which is needed to be added to transform the quadratic expression x^{2}+8x as a perfect square trinomial is 16.

Step-by-step explanation:

A quadratic expression is an expression in which the highest power of the variable is 2 or it can be said that the degree of the expression is 2.  

The identity for (a+b)^{2} is given as follows:  

(a+b)^{2}=a^{2}+b^{2}+2\times(a)\times(b)

<u>Step 1:  </u>

Break down the given polynomial x^{2}+2\times(x)\times(4).

<u>Step 2:  </u>

Now compare the polynomial with the above indentity.  

On comparing it is observed that the value of a is x and the value of b is 4.  

<u>Step 3:  </u>

In order to make the polynomial x^{2}+8x+ a perfect square, add 16 to the broked down polynomial because on comparing the above polynomials the value of b is 4 and the square of 4 is 16.  

x^{2}+2\times(x)\times4+16  

<u>Step 4:</u>  

Now as per the identity (a+b)^{2}=a^{2}+2\times(a)\times(b)+b^{2} the polynomial x^{2}+2\times(x)\times4+16 is written as follows:  

(x+4)^{2}.  

Therefore, the perfect square for the given polynomial is (x+4)^{2} which is created by adding 16 to the given expression.  

Learn more:  

  1. A problem to obtain the y-intercept of a quadratic function brainly.com/question/1332667  
  2. A problem to obtain the binomial and trinomial brainly.com/question/1394854  

Answer details  

Grade: Middle school  

Subject: Mathematics  

Chapter: Quadratic expression  

Keywords: Quadratic, quadratic expression, polynomial, quadratic polynomial, perfect square, trinomial, degree, highest power, transform, identities, break down, perfect square, middle term split, x^2+8x,methamatics, algebra.

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2 years ago
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The Roe family of four showers once a day with an average of 10 minutes per shower. The shower has a flow rate of 5 gallons per
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4 people x 10 minutes each = 40 minutes per day.

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