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1 year ago

Given the table values, Determine the base for the expoent function

Mathematics

1 answer:

-BARSIC- [3]1 year ago

3 0

To determine the value of the exponential function:

$y=a^x$

we use the first values from the table and plug them in the expression for the function:

$\begin{gathered} \frac{1}{81}=a^{-\frac{1}{2}} \\ \frac{1}{a^2}=\frac{1}{81} \\ a^2=81 \\ a=\sqrt[]{81} \\ a=9 \end{gathered}$

Therefore the base of the exponent function is 9

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You asked amusement park visitors the question "How many times did you ride a roller coaster today?" as they left the park. The

VladimirAG [237]

Answer:4

Step-by-step explanation:

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3 years ago

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A flying cannonball’s height is described by formula y=−16t^2+300t. Find the highest point of its trajectory. In how many second

Yakvenalex [24]

<span>Highest point = 1406.25 Number of seconds = 9.375 We've been given the quadratic equation y = -16t^2 + 300t which describes a parabola. Since a parabola is a symmetric curve, the highest value will have a t value midway between its roots. So using the quadratic formula with A = -16, B = 300, C = 0. We get the roots of t = 0, and t = 18.75. The midpoint will be (0 + 18.75)/2 = 9.375 So let's calculate the height at t = 9.375. y = -16t^2 + 300t y = -16(9.375)^2 + 300(9.375) y = -16(87.890625) + 300(9.375) y = -1406.25 + 2812.5 y = 1406.25 So the highest point will be 1406.25 after 9.375 seconds. Let's verify that. I'll use the value of (9.375 + e) for the time and substitute that into the height equation and see what I get.' y = -16t^2 + 300t y = -16(9.375 + e)^2 + 300(9.375 + e) y = -16(87.890625 + 18.75e + e^2) + 300(9.375 + e) y = -1406.25 - 300e - 16e^2 + 2812.5 + 300e y = 1406.25 - 16e^2 Notice that the only term with e is -16e^2. Any non-zero value for e will cause that term to be negative and reduce the total value of the equation. Therefore any time value other than 9.375 will result in a lower height of the cannon ball. So 9.375 is the correct time and 1406.25 is the correct height.</span>

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3 years ago

At the movie theatre, child admission is $5.30 and adult admission is $9.70. On Wednesday, 156 tickets were sold for a total sal

serious [3.7K]

Answer:

The number of adult tickets are 57.

Step-by-step explanation:

Given,

Total number of tickets = 156

Total money = $1077.60

Solution,

Let the number of adult be x and of child be y .

So, Total number of tickets = Number of adults + Number of child

$\therefore x+y = 156\ \ \ \ \ \ equation\ 1$

Now, according to question;

Total money = $Number\ of\ adults\times admission\ fee + Number\ of\ child\times admission\ fee$

$\therefore x\times 9.70+y\times 5.30 = 1077.60\ \ \ \ \ \ equation\ 2$

On multiplying by 10 on both side, we get;

$97x+53y=10776\ \ \ \ \ \ equation\ 3$

Now multiplying equation 1 by 53 then subtract it from equation 3, we get;

$(x+y)\times53 = 156\times53\\53x+53y=8268\\(97x+53y=10776)-(53x+53y=8268)\\44x=2508\\x=\frac{2508}{44} =57$

Since x is the number of adults,

Number of adults=57

Number of child = y = 156-57=99

Thus the number of adult tickets are 57.

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3 years ago

John wants to join a gym so that he can work out during the evenings. There are two gyms in his town that he is considering. Ext

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Answer:

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To get the answer you need to multiply 1,000 by 7.15 then move your decimal to make it accurate and you should end up with 7150

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4 years ago