Mohammad would like to graph the line that represents the total number of baseball cards he will have collected, T, after m mont

hs, given that he buys 5 cards each month and he started with no cards. He would like the graph to show the number of cards after 6 and 12 months. Select from the drop-down menus to correctly complete each statement. To best show this information, the scale for the T-axis of his graph should go from 0 to at least , and the m-axis of his graph should go from 0 to at least .

Mathematics

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How many natural numbers are there between 8² and 9²

Svet_ta [12734]

Soccer game theory posits that the earliest participants in the game will play.

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3 months ago

(a) For what values of k does the function y = cos(kt) satisfy the differential equation 81y'' = −4y? (Enter your answers as a c

tester [12383]

Answer:

$k = \frac{2}{9}, k=\frac{-2}{9}$

Step-by-step explanation:

The initial scenario is a specific case of the subsequent one, so we will address the second case first.

Consider $y = A\sin(kt) + B\cos(kt)$ . Through the utilization of derivatives and trigonometric function properties, it is determined that

$y' = A\cdot k \cos(kt)- B \cdot k \sin(kt) = k (A\cos(kt)-B\sin(kt))$

$y'' = k(-A\cdot k \sin(kt)-B\cdot k \cos(kt)) = -k^2(y)$

The equation is represented as $81y''=-4y$ . It's important to note that since $y'' = -k^2y$ it leads to the equation

$-k^2 81y=-4y$ ,

which signifies that $k^2 = \frac{4}{81}$ . Consequently, $k=\pm\frac{2}{9}$

It's notable that in this instance, the value of k is independent of A and B. Thus, it applies universally to any values of A and B. The first scenario is included since it corresponds to A=0 and B=1.

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3 months ago

The University of Central Florida's cheerleading team has eighteen males and twenty-one females. If h represents the height of a

Leona [12618]

Answer:

The range of cheerleaders' heights lies within the interval [58, 74)

It includes all real numbers from 58 inches and above, but below 74 inches.

Step-by-step explanation:

we have

$260 \leq 4h+28$