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4 years ago

In trapezoid ABCD, the measure of

Mathematics

1 answer:

Airida [17]4 years ago

4 0

Answer:

Step-by-step explanation:

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Find the roots of h(t) = (139kt)^2 − 69t + 80

Sonbull [250]

Answer:

The positive value of $k$ will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let $h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ , roots are those values of $t$ so that $h(t) = 0$ . That is:

$19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0$ (1)

Roots are determined analytically by the Quadratic Formula:

$t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}$

$t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$

The smaller root is $t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ , and the larger root is $t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ .

$h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ has one real root when $\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0$ . Then, we solve the discriminant for $k$ :

$\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}$

$k \approx \pm 0.028$

The positive value of $k$ will result in exactly one real root is approximately 0.028.

7 0

3 years ago

When Devon cashed a $450 check at the bank, the teller gave him 18 bills, all $20 bills and $50 bills. Which system of equations

Neporo4naja [7]

B is the answer to the equation

7 0

3 years ago

What is the quotient of 8887/4

Savatey [412]

Answer:

2221.75

Step-by-step explanation:

8887 ÷ 4 = 2221.75

4 0

3 years ago

Read 2 more answers

Ethan plotted points E, F, G, H, and I on a number line, as shown below. Which two points that Ethan plotted represent numbers t

nirvana33 [79]

Answer:

F and H

Step-by-step explanation:

From the image attached, the location of the points are E = -9, F = -6, G = -2, H = 6, I = 8. The law of additive inverse states that for a number a, its additive inverse is a number that when added to a equals to zero. This number is usually opposite in sign to a and of the same magnitude i.e -a. The law is given as:

a + (-a) = 0

From the points, F is the additive inverse of H, hence:

F + H = 0

6 + (-6) = 6 - 6 = 0

Hence the two points are F ad H

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3 years ago

Explain how you can use base-ten blocks or as a decimal models to find 3.15 divided by 3. Include pictures to support your expla

AlladinOne [14]

You have to turn the number or ratio and simplified the number and put it in to the chart like the norm number

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4 years ago