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r-ruslan [8.4K]
3 years ago
5

Please Please Please Please Help Me.... Show your work if you can. It'll be very helpful.

Mathematics
1 answer:
pantera1 [17]3 years ago
6 0

Answer:

The table can be filled as shown below.

Step-by-step explanation:

The first function is

f(x)=4x+8

Put different values of x and find values of f(x).

For x=-2

f(-2)=4(-2)+8=0

For x=-1

f(-1)=4(-1)+8=4

Similarly for x=0,1,2 the value of f(x) are 8,12,16 respectively.

The second function is

f(x)=\frac{2}{3}x+8

For x= -6

f(-6)=\frac{2}{3}(-6)+8=4

For x= -3

f(-3)=\frac{2}{3}(-3)+8=6

Similarly for x=0,3,6 the value of f(x) are 8,10,12 respectively.

The third function is

f(x)=5^{x-2}+7

For x= 2

f(2)=5^{2-2}+7=8

For x= 3

f(3)=5^{3-2}+7=12

Similarly for x=4,5,6 the value of f(x) are 32,132,632 respectively.

The fourth function is

f(x)=(\frac{1}{4})^x-5

For x=-4

f(-4)=(\frac{1}{4})^{-4}-5=4^4-5=251

For x=-3

f(-3)=(\frac{1}{4})^{-3}-5=4^3-5=59

Similarly for x=-2,-1,0 the value of f(x) are 11,-1,-4 respectively.

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The length of the hypotenuse of a right triangle is 24. If the length of one leg is 8, what is approximate length of the other l
Verdich [7]

Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.

Now, Pythagoras' Theorem is defined as follows:

c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:

c^2 = a^2 + b^2

24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)

b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)

b = √(24^2 - 8^2) (Take the square root of both sides)

b = √512 (Evaluate 24^2 - 8^2)

b = 16√2 (Simplify √512)

= 22.627 (to three decimal places)

I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.

4 0
3 years ago
Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3
Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

\frac{dV}{dt} = -kA

Using Euler's method

\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i}    \\

Where initial droplet volume is:

V(0) = \frac{4pi}{3} * r(0)^3 =  \frac{4pi}{3} * 2.5^3 = 65.45 mm^3

Hence, the iterative solution will be as next:

  • i = 1, ti = 0, Vi = 65.45

V'_{i}  = -k *4pi*(\frac{3*65.45}{4pi})^(2/3)  = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88

  • i = 2, ti = 0.5, Vi = 63.88

V'_{i}  = -k *4pi*(\frac{3*63.88}{4pi})^(2/3)  = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33

  • i = 3, ti = 1, Vi = 62.33

V'_{i}  = -k *4pi*(\frac{3*62.33}{4pi})^(2/3)  = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\

The average change of droplet radius with time is:

Δr/Δt = \frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0
3 years ago
11154 ÷ 52. Express the remainder as a fraction in the lowest terms
Andrew [12]
11154/52= 214 1/2 is the answer to this question
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3 years ago
A container that holds sugar is shaped like a cylinder. The radius of the container is 3 inches,
kicyunya [14]

Answer:

B

Step-by-step explanation:

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3 years ago
Simplest form for 16/56
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The answer is 2/7 because you're finding the greatest common factor of both numbers. The gcf is 8, so divide both by 8 and you'll get 2/7
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