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3 years ago

Hi.Please its urgent See image for question Answer no 16 and 17

Mathematics

1 answer:

bagirrra123 [75]3 years ago

6 0

9514 1404 393

Eexplanation:

16. Suppose the roots are α and kα. Then we can write the equation as ...

a(x -α)(x -kα) = 0

ax² -ax(α +kα) +akα² = 0

Comparing to the original equation, we can equate coefficients to get ...

b = -aα(1+k)
c = akα²

Solving the first for α gives ...

α = -b/(a(1+k)

Substituting into the second, we have ...

c = ak(-b/(a(1+k)))²

Multiplying by a(1+k)², we get ...

(1+k)²ac = kb²

Using k=2 gives ...

9ac = 2b² . . . . . as required

17. Using the previous result with k=1 (equal roots), we have ...

(1+k)²ac = kb²

4ac = b² . . . . . for k=1

______

<em>Additional comment</em>

We observed that the problems were similar, but had different factors relating the roots. So, we elected to solve the general case, then fill in the specific values for the two problems.

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It is thought that not as many Americans buy presents to celebrate Valentine's Day anymore. A random sample of 40 Americans yiel

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98% confidence interval of the true proportion of all Americans who celebrate Valentine's Day

(0.3672 , 0.7328)

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<u><em>Explanation:</em></u>-

Given Random sample size n =40

Sample proportion

$p = \frac{x}{n} = \frac{22}{40} = 0.55$

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$(p-Z_{\alpha } \sqrt{\frac{pq}{n} } , p + Z_{\alpha } \sqrt{\frac{pq}{n} } )$

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3 years ago

Read 2 more answers

You can afford a $950 per month mortgage payment. You've found a 30 year loan at 7% interest. a) How big of a loan can you affor

Lubov Fominskaja [6]

Based on the amount to be paid per month, the size of the loan you can afford is $142,792.19.

The total amount you pay to the loan company is $342,000.

The interest on the money is $199,207.81.

The size of the loan is the present value associated with that loan payment that you can afford:

950 = (7/12% x Present value) / ( 1 - (1 + 7/12%)⁻⁽³⁰ ˣ ¹²⁾

950 = (7/12% x Present value) / 0.8767

Present value = $142,792.19

The total amount of money paid is:

= Number of periods x Payment per period

= 30 years x 12 months per year x 950

= $342,000

The interest is:

= 342,000 - 142,792.19

= $199,207.81.

Find out more on interest payments on loans at brainly.com/question/13005100

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