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Alja
22 days ago
14

Russell collected 30 stones at his grand parents' house. He decided to give his little sister 1 / 5 of the stones. How many ston

es did he give his sister?
Mathematics
1 answer:
tester [8.8K]22 days ago
5 0
He gives his sister 6 stones.
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Mary put in a total of 16 1/2 hours mowing lawns during 5 days the past week. How long was her average work day?
Leona [9303]

Answer:

To find the average, divide 16 1/2 by 5.

Converting 16 1/2 to decimal form gives 16.5, and when divided by 5, the outcome is 3.3, which can also be represented as 3 and 3/10 in fractional form.

Thus, her average workday lasted 3.3 hours.

7 0
3 days 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 [8870]

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.

5 0
26 days ago
Jerry is a judge he hears 5 cases every 2 3/8 per hours Jerry hears case at a constant rate How many cases does he hear per hour
tester [8870]
Approximately 2, I believe... I calculated it to be around 2.10. 
5 0
1 month ago
Read 2 more answers
Given the equation −4Square root of x minus 3 = 12, solve for x and identify if it is an extraneous solution.
Inessa [9038]

Answer:

The provided radical equation has no solution.

x = 225/16 is not a valid solution.

Step-by-step explanation:

The given equation is  

Add 3 to both sides of the equation

Squaring both sides

Divide both sides by 16

Check by substituting the value of x back into the original equation to confirm the extraneous solution.

 

Since -18 is not equal to 12, thus the value of x fails to satisfy the equation.

Consequently, x = 225/16 is an extraneous solution.

Step-by-step explanation:

4 0
19 days ago
Read 2 more answers
What is the domain of the square root function graphed below ?
AnnZ [9126]

The graph indicates that x never goes below 0. This means the point (-1,0) is not included in the graph. Therefore, D is the only valid option.

8 0
29 days ago
Read 2 more answers
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