1. The optimal height h of the letters of a message printed on pavement is given by the formula . Here, h= (0.00252d^(9/4))/e d is the distance of the driver from the letters and e is the height of the driver’s eye above the pavement. All of the distances are in meters. Explain how to find h when d = 90 m and e = 1.4 m.

Question

1. The optimal height h of the letters of a message printed on pavement is given by the formula . Here, h= (0.00252d^(9/4))/e d is the distance of the driver from the letters and e is the height of the driver’s eye above the pavement. All of the distances are in meters. Explain how to find h when d = 90 m and e = 1.4 m.

2.Simplify.

(27a^(-6) )^(-2/3)

For 2 I got 1/(9a^4 )as my answer, but can someone again please check this.

For 1 I really do not know, I have been trying to figure out for a while.

Please check and help me for 1, and please help with 2. 1 is from another thing, but no one has answered it.

I will appreciate the help. Also, please try to answer these two as soon as possible.

Answer 1

I did mean to put "For 1 I really do not know, I have been trying to figure it out for a while." instead of what I put. Just saying this, so no one will get confused at that point.

Answer 2

Is anyone there? I'm still here, and will be until it gets answered. I will still appreciate it if you guys can answer these.

Answer 3

For 1, I think the answer is this:

First, you replace the variables with 90 and 1.4 to get this equation: (0.00252∙〖90〗^(9/4))/1.4. Next, you turn the 〖90〗^(9/4)into ∜(〖90〗^9 ). Then, I turn ∜(〖90〗^9 )into 3∜(〖10〗^9 ), and simplify 3∜(〖10〗^9 )to 9∜10. Next, I divide o.oo252 by 1.4 to get 0.0018. Then, my next equation is: 0.0018∙9∜10. Finally, I multiply 0.0018 and 9 together to get 0.0162, and my final answer is 0.0162∜10

Is my answer correct? Please check it to make sure that it is correct or not? Also, if it is incorrect, please help me correct my mistakes. I will appreciate it if any of you guys do.

Answer 4

If anyone can answer or help me for these two problems, please do. I will appreciate it even more if you can answer and/or check the problems as soon as possible. I have been waiting and trying to answer it for a long time. My mom wants me to get my lesson done on this topic today, and I am stuck at this point, which is really close to the end. Also, thank you if anyone can help or answer these two problems.

Answer 5

1. To find the value of h when d = 90m and e = 1.4m, you can use the given formula:

h = (0.00252d^(9/4))/e

Substituting the values of d and e into the equation:

h = (0.00252 * 90^(9/4))/1.4

First, calculate the exponent 9/4:

9/4 = 2.25

Now, substitute this value back into the equation:

h = (0.00252 * 90^2.25)/1.4

To find 90^2.25, you raise 90 to the power of 2.25:

90^2.25 ≈ 1626.13

Substituting this value back into the equation:

h ≈ (0.00252 * 1626.13)/1.4

Next, multiply 0.00252 by 1626.13:

0.00252 * 1626.13 ≈ 4.103

Substituting this value back into the equation:

h ≈ 4.103/1.4

Finally, divide 4.103 by 1.4 to find h:

h ≈ 2.93

Therefore, when d = 90m and e = 1.4m, the optimal height of the letters would be approximately 2.93 meters.

2. To simplify the expression (27a^(-6))^(-2/3), you can apply the exponent properties.

First, raise each part of the expression to the power of -2/3:

(27^(-2/3)) * (a^(-6*(-2/3)))

Next, simplify each part:

27^(-2/3) is equivalent to the cube root of 27 raised to the power of -2:

27^(-2/3) = (cube root of 27)^(-2) = 1/27^2 = 1/729

For a^(-6*(-2/3)), you multiply -6 and -2/3:

-6*(-2/3) = 4

So the expression becomes:

(1/729) * (a^4) = a^4/729

Hence, the simplified form of (27a^(-6))^(-2/3) is a^4/729.

For your question 2, your answer of 1/(9a^4) is incorrect. The correct answer is a^4/729 as explained above.