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Andrew [12]
3 years ago
13

Suppose r varies directly as the square of​ m, and inversely as s. If r equals 11 when m equals 6 and s equals 4​, find r when m

equals 12 and s equals 4.
Mathematics
1 answer:
77julia77 [94]3 years ago
7 0

Answer: r=44

Step-by-step explanation:

The combine variation equation will have the folllowing form:

y=\frac{kx}{z}

Where "k" is the constantn of variation.

You know that "r" varies directly as the square of​ "m", and inversely as "s". Then the equation is:

r=\frac{m^2k}{s}

Knowing that r=11 when m=6 and s=4, you can substitute values into the equation and solve for "k" in order to find its value:

11=\frac{6^2(k)}{4}\\\\\frac{11*4}{6^2}=k\\\\k=\frac{11}{9}

Now, to find the value of "r" when m=12 and s=4, you need tot substitute these values and the the constant of variation into  r=\frac{m^2k}{s} and then evaluate:

 r=\frac{(12^2)(\fra{11}{9}}{4}\\\\r=44

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Pls,pls,pls,help me I will give lots of pound 100+ points
Bond [772]

Answer:

  1. 3log(10) -2log(5) ≈ 1.60206
  2. no; rules of logs apply to any base. ln(x) ≈ 2.302585×log(x)
  3. no; the given "property" is nonsense

Step-by-step explanation:

<h3>1.</h3>

The given expression expression can be simplified to ...

  3log(10) -2log(5) = log(10^3) -log(5^2) = log(1000) -log(25)

  = log(1000/25) = log(40) . . . . ≠ log(5)

  ≈ 1.60206

Or, it can be evaluated directly:

  = 3(1) -2(0.69897) = 3 -1.39794

  = 1.60206

__

<h3>2.</h3>

The properties of logarithms apply to logarithms of any base. Natural logs and common logs are related by the change of base formula ...

  ln(x) = log(x)/log(e) ≈ 2.302585·log(x)

__

<h3>3.</h3>

The given "property" is nonsense. There is no simplification for the product of logs of the same base. There is no expansion for the log of a sum. The formula for the log of a power does apply:

  \log(a)\log(b)=\log(a^{\log(b)})=\log(b^{\log(a)})

Numerical evaluation of Mr. Kim's expression would prove him wrong.

  log(3)log(4) = (0.47712)(0.60206) = 0.28726

  log(7) = 0.84510

  0.28726 ≠ 0.84510

  log(3)log(4) ≠ log(7)

4 0
2 years ago
The statement tan theta -12/5, csc theta -13/5, and the terminal point determined by theta is in quadrant 2."​
Harlamova29_29 [7]

Answer:

Answer C:

Cannot be true because csc(\theta)  is greater than zero in quadrant 2.

Step-by-step explanation:

When the csc of an angle is negative, since the cosecant function is defined as:

csc(\theta)=\frac{1}{sin(\theta)}

that means that the sin of the angle must be negative, and such cannot happen in the second quadrant. The sine function is positive in the first and second quadrant.

Therefore, the correct answer is:

Cannot be true because  csc(\theta)  is greater than zero in quadrant 2.

6 0
3 years ago
Find the total cost of a $43 dinner if you leave 18% gratuity (tip).   
AleksandrR [38]
50.74
B/c 43*.18=7.74 
7.74+43=50.74

hope this helps
8 0
3 years ago
Pls help give u a free brainlist
Brilliant_brown [7]

Answer:

correct answer is J

Step-by-step explanation:

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3 years ago
I don’t really understand?
aksik [14]

Go over the x axis up 5  and over the y axis left 1

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