H varies jointly as R and the square of C. If C = 10 and H = 207.1 when R = 8, find H when C = 4 and R = 6. (Round off your answer to the nearest tenth.) 1725.8 O 24.9 248.5 O 275.6​

The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).

The given system of equations can be solved using the substitution method. We can begin by solving the first equation,\(a^2 + b^2\), for either a or b. Let's solve for a:

\(a^2 + b^2 = 0\)

\(a^2 + b^2 = 0\)

\(a^2 = -b^2\)

\(a = \pm\sqrt(-b^2)\)

We can substitute this expression for a into the second equation, \(3a^2 - 2ab - b^2 = 0\), and simplify:

\(3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0\)

\(3b^2 - 2b^2 - b^2 = 0\)

0 = 0

Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation \(a^2 + b^2 = 0\) will also satisfy the equation \(3a^2 - 2ab - b^2 = 0\)

However, the equation \(a^2 + b^2 = 0\) only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).

Learn more about substitution here:

brainly.com/question/22340165

#SPJ1

Answer:

20 grams

Step-by-step explanation:

3+2=5 grams for 1 week

5x4=20

Answer:

x=7

Step-by-step explanation:

The graphs are different because they are transformed from the parent functions f(x) differently

From the question, we have the following parameters that can be used in our computation:

Parent function, f(x) = x

Also, we have: g(x) = (x - 2) + 1, g(x) = 3x - 6, g(x) = 2(x + 3) + 10 and  g(x) = (6x - 1)

The equations listed below represent transformations of the parent graph of f(x) = x:

g(x) = (x - 2) + 1

The graph of g(x) is obtained by shifting the parent graph of f(x) = x to the right by 2 units and up by 1 unit.

g(x) = 3x - 6

The graph of g(x) is obtained by vertically stretching the parent graph of f(x) = x by a factor of 3 and then shifting it downward by 6 units.

g(x) = 2(x + 3) + 10

The graph of g(x) is obtained by shifting the parent graph of f(x) = x to the left by 3 units, vertically stretching it by a factor of 2, and then shifting it upward by 10 units.

g(x) = (6x - 1)

The graph of g(x) is obtained by stretching the parent graph of f(x) = x horizontally by a factor of 1/6 and then shifting it downward by 1 unit.

Read more about transformation at

https://brainly.com/question/15654078

#SPJ1

Complete question

Use the graphing tool to see what happens to the functions when you change more than one parameter at a time. In what ways is this new graph different than the parent graph of f(x)

Write down your observations for each of these transformed functions, then try a few of your own.

g(x) = (x - 2) + 1

g(x) = 3x4 - 6

g(x) = 2(x + 3) + 10

g(x) = (6x - 1)

The income I from the train in terms of the ticket price p is given by the expression:

I = -0.08x² + 30x + 800p

Let's start by defining some variables:

x: the number of 4 cents increases in the fare

p: the original ticket price in dollars

q: the new ticket price after x increases of 4 cents

From the problem, we know that for each 4 cents increase in the fare, 2 fewer people will ride the train. This can be expressed mathematically as:

number of passengers = 800 - 2x

We also know that the fare is increased by 4 cents for each 4 cents increase in the ticket price. Therefore, the new ticket price q can be expressed as:

q = p + 0.04x

Finally, we need to express the income I from the train in terms of the ticket price p. This can be done by multiplying the number of passengers by the ticket price:

I = p * (800 - 2x)

Substituting q into the equation for I, we get:

I = (p + 0.04x) * (800 - 2x)

Expanding the brackets, we get:

I = 800p - 2px + 32x - 0.08x²

Simplifying this expression, we get:

I = -0.08x² + 30x + 800p

Therefore, the income I from the train in terms of the ticket price p is given by the equation:

I = -0.08x² + 30x + 800p

Learn more about income on:

https://brainly.com/question/15834358

#SPJ1

Answer:

Step-by-step explanation:

(-∝;2)

Answer: (-infinity, 2]

Step-by-step explanation:

The graph of the piecewise function is the one in option D-

First, we know that:

f(x) = 4  when x ≤ 3

So, we want to have a horizontal line in the left side of the graph, such that it ends in a closed circle at x = 3 (we need to have a closed circle because the symbol ≤ is used).

From the given graphs, the only one with that form is D.

Learn more about piecewise functions at:

https://brainly.com/question/3628123

#SPJ1

Answer:

\(x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} \)

Answer:

The second integer is greater than the first.

Step-by-step explanation:

Since the first integer is the leftmost out of the two, this means that the second one must be greater than the first since it is to the right of it.

Answer:

c

Step-by-step explanation:

Answer:

13.88 (if you round up)

Step-by-step explanation:

2.99+5.99+3.99 = 12.97

12.97 * 7% = .9079

12.97 + .9079 = 13.8779

Answer:

y=-8x+4

Step-by-step explanation:

Isolate the Y variable by balencing the equation! Khan acadamy has great videos on how to do this!

Answer:

Y=4-8x

OR if you want it more specific (slope intercept form)

y= -8x+4

Same thing

Step-by-step explanation:

SO when asked for y you just have to isolate the y

SO we can do that by subtracting 2x on both sides

1/4y=1-2x

Now to get y isloated we can just divide 1/4 on each sides

y=4-8x

THere you go or if you want it in slope intercept form just reverse the signs when switching the positions becuase y=mx+b

y= -8+4

Step-by-step explanation:

Distance = positive value

a + a = 2a

Answer:

I think its 0

Step-by-step explanation:

becuase if you add the same number but on is negative and the other is positve it is always a 0.

Example:

10 + (-10) = 0

Answer: You should try to multiply and divide try then question me back. But the answers are neither of them.

Step-by-step explanation:

Answer:

5 * 5 * 6 = 25 * 6 = 150 in^2

Answer:

the second one -9/4 divided (-2/3)

Step-by-step explanation:

Answer:

a) P(t) = 6.57e ^{0.0287t}P(t)=6.57e

0.0287t

b) P(6) = 7,805\ millionP(6)=7,805 million

c) t = 14.64\ yearst=14.64 years

d) t = 24.15\ yearst=24.15 years

Step-by-step explanation:

a) The function of exponential growth for a population has the following formula:

P(t) = p_0e ^{rt}P(t)=p

0

e

rt

In this equation:

p_0p

0

is the initial population

r is the growth rate

t is the time in years

In this problem we know that

r = 2.87\% = 0.0287r=2.87%=0.0287

p_0= 6.57p

0

=6.57 million in the year 2012.

So the equation is:

P(t) = 6.57e ^{0.0287t}P(t)=6.57e

0.0287t

Where t = 0t=0 represents the year 2012

b) If t = 0t=0 in 2012, then in 2018 t = 6t=6

The population in 2018 is:

\begin{gathered}P(t = 6) = 6.57e ^{0.0287(6)}\\\\P(6) = 7,805\ million\end{gathered}

P(t=6)=6.57e

0.0287(6)

P(6)=7,805 million

c) To know when the population is equal to 10 million we must equal P(t) to 10 and solve for t.

\begin{gathered}P(t) = 10 = 6.57e ^{0.0287t}\\\\\frac{10}{6.57} = e ^{0.0287t}\\\\ln(\frac{10}{6.57}) = 0.0287t\\\\t = \frac{ln(\frac{10}{6.57})}{0.0287}\end{gathered}

P(t)=10=6.57e

0.0287t

6.57

10

=e

0.0287t

ln(

6.57

10

)=0.0287t

t=

0.0287

ln(

6.57

10

)

t = 14.64\ yearst=14.64 years

d) The function is doubled when P(t) = 2p_0P(t)=2p

0

P(t) = 2(6.57) = 13.14 = 6.57e ^{0.0287t}P(t)=2(6.57)=13.14=6.57e

0.0287t

We solve for t.

\begin{gathered}\frac{13.14}{6.57} = e ^{0.0287t}\\\\ln(\frac{13.14}{6.57}) = 0.0287t\\\\t = ln{13.14}{6.57})}{0.0287})\

end

{gathered}

6.57

13.14

=e

0.0287t

ln(

6.57

13.14

)=0.0287t

t=

0.0287

ln(

6.57

13.14

)

)

t = 24.15\ yearst=24.15 years

The percentage of increase in sales from last month to this month is 9%.

Given,

Sales for last month = £180 000.

Sales for this month = £196 200.

To calculate the percentage increase, we must first find the difference in sales between the two months:-

Difference between the two months = £180,000 -  £196,200 = £16,200

Percentage of this difference = (16,200 ÷ 180,000) * 100 = 9

Thus, the percentage of increase is 9% from the last month to this month.

To learn more about percentages:

https://brainly.com/question/24877689

Answer:

\(y - 4 = - 3(x - 2)\)

Step-by-step explanation:

f(x)    takes the sqrt of x      f(x ) = \(\sqrt{x}\)

g(x) does the rest of the computation  g(x ) = x^2 - 5x

Hello :D

To do this we need to do:

$2.40/12 = $0.20

Answer = $0.20

Answer: 0.20

Step-by-step explanation:

Above is correct! and same question as you

Answer:

5 dollars

Step-by-step explanation:

last year he got 5 they were 7 dollars because 7x5 is 35 so do the same thing to do other it also equals 35

Answer: Swinging an arc from the first endpoint of the copied segment that comes directly after measuring the distance of the original segment

Answer:

\(x = \frac{1}{2} \)

\(x = - \frac{3}{2} \)

Answer:

Step-by-step explanation:

The expression for the bone mass of a human femur in terms of outer radius R, inner radius r, length L, and density p is given as:

M = π r² L [p − (p − 1) * k²]

where k = r/R is the ratio of inner radius to outer radius.

To find the rate of change of bone mass with respect to time, we need to differentiate this expression with respect to time t, assuming that p and k are functions of t. Using the product rule and the chain rule of differentiation, we get:

dM/dt = π L [(2r dr/dt) p - r² dp/dt - (p - 1) (2r dr/dt) k dk/dt]

Note that the first term in the square brackets involves the derivative of r with respect to time, which we are given as -0.5 mm/year. Also, when r = 40 mm, L = 300 mm, and p = 2, we can substitute these values in the expression to get:

M = π (40 mm)² (300 mm) [2 − (2 − 1) * (40/300)²] = 3.267 x 10^6 g

We can also calculate the value of k at this point as k = r/R = 40/R.

Now, to find the rate of change of bone mass with respect to time, we substitute the given values and simplify:

dM/dt = π (300 mm) [(2)(40 mm)(-0.5 mm/year)(2) - (40 mm)² dp/dt - (2-1)(2)(40 mm)(-0.5 mm/year)(40/R)(-1/R)]

dM/dt = -6032.35 dp/dt

Therefore, the rate of change of bone mass with respect to time is equal to -6032.35 times the rate of change of density with respect to time. If the density increases with time, then the bone mass will decrease at a rate of 6032.35 times the rate of increase in density, and vice versa.

The tank holds approximately 994,040 liters.

The volume of a right circular cylinder is given by the formula:

V = πr^2h

Where

The cylinder's diameter is specified as 13 m, hence the radius may be computed using the formula: r = d/2 = 13/2 = 6.5 m

The cylinder is described as having a 6 m length.

These values are substituted into the volume calculation to produce the following result:

V = π(6.5)^2(6)

V ≈ 994.04 cubic meters

Since 1 cubic meter equals 1000 liters, we can convert the volume to liters by multiplying by 1000.

V = 994.04 cubic meters x 1000 liters/cubic meter

V = 994,040 liters

Therefore, the tank holds approximately 994,040 liters.

Learn more about volume of cylinder here : brainly.com/question/27535498

#SPJ1

Answer: 0

Step-by-step explanation:

Let's solve your equation step-by-step.

5+2(n+1)=2n

Step 1: Simplify both sides of the equation.

5+2(n+1)=2n

5+(2)(n)+(2)(1)=2n(Distribute)

5+2n+2=2n

(2n)+(5+2)=2n(Combine Like Terms)

2n+7=2n

2n+7=2n

Step 2: Subtract 2n from both sides.

2n+7−2n=2n−2n

7=0

Step 3: Subtract 7 from both sides.

7−7=0−7

0=−7

1) For our first job, PROBLEM A, it has a mean of 515 points and a standard deviation of 114 points. We're given the goal of calculating what % belongs between 401 and 629. As we can see, if we remove 515, then subtract 114 from 515, we obtain our first value of 401, then if we add our standard deviation tournament, we get our second number of 629. So, using the empirical rule, we know that in this scenario, 68 of our data points will fall inside this range.

2) Part B requires us to identify the scores that are less than 401 and larger than 629. So, in part A, we have the inclusive section of this, and now we have the exclusive section. Simply remove 60 percent from 100 percent, and we get 32 percent outside of this range.

The program is an illustration of loops and conditional statements and the part of the complete program is

n = int(input())

for i in range(1,n+1):

  if not(i%3 == 0 or i%5==0):

The program written in Python where comments are used to explain each line is as follows:

#This gets input for n

n = int(input())

#This iterates through n

for i in range(1,n+1):

  #If the current number is not a multiple of 3 and 5

  if not(i%3 == 0 or i%5==0):

      #This prints the number

      print(i,end="")

  else:

      #This prints "Fizz", if the current number is a multiple of 3

      if i%3 == 0:

          print("Fizz",end="")

      #This prints "Buzz", if the current number is a multiple of 5

      if i%5==0:

          print("Buzz",end="")

  #This prints a new line

  print()

Read more about loops and conditional statements at:

brainly.com/question/26098908

#SPJ1

Answer:

D. The limit does NOT exist

Explanation:

We are given that:

Hence, the correct answer is: option D. The limit does NOT exist