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Yuri [45]
3 years ago
10

Delaware was the first state to enter the Union and Hawaii was the 50th. If we order the positions of entry for the rest of the

states, we find that State A entered the Union right after State B, and the product of their order-of-entry numbers is 132. Use the given information to complete each statement. State A was the th state to enter the Union. State B was the th state to enter the Union.
Mathematics
1 answer:
Anna71 [15]3 years ago
5 0

Answer:

State A was the <u>12th</u> state to enter the Union. State B was the <u>11th</u> state to enter the Union.

Step-by-step explanation:

Let's call x to the order-of-entry of State B, therefore the order-of-entry of State A is x+1. Given that he product of their order-of-entry numbers is 132:

x*(x+1) = 132

x² + x - 132 = 0

Using quadratic formula:

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

x = \frac{-1 \pm \sqrt{1^2 -4(1)(-132)}}{2(1)}

x = \frac{-1 \pm 23}{2}

x_1 = \frac{-1 + 23}{2}

x_1 = 11

x_2 = \frac{-1 - 23}{2}

x_2 = -12

The negative solution has no sense in the context of our problem, then the solution is x = 11.

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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:

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k \approx \pm 0.028

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

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2 years ago
URGENT!!!! PLEASE HELP SHOW WORK!!!!!!!!!!!!!!!!!!!!! PLEASE!!!!!!! I HAVE BEEN WAITING SO LONG!!!!!!!!!
garik1379 [7]
You would do 69sq×3.1416. that gives you 14,957.1576 round it to the nearest hundreth, 14,957.16

7 0
3 years ago
HOw do you do this its very confusing
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Answer:

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