Place value through billion chart

Find positive numbers a and b so that the change of variables s=ax,t=by transforms the integral ∫∫rdxdy into ∫∫t∣∣∣∂(x,y)∂(s,t)∣

densk [106]

S = ax
It is required to find the value of a which make:
0 ≤ s ≤ 1 when 0 ≤ x ≤ 15
∴ s = 0 when x = 0 ⇒⇒⇒ a = 0 (unacceptable)
or s = 1 when x = 15 ⇒⇒⇒ a = s/x = 1/15

Similarly, t = by 
It is required to find the value of b which make:
0 ≤ t ≤ 1 when 0 ≤ y ≤ 60
∴ t = 0 when y = 0 ⇒⇒⇒ b = 0 (unacceptable)
or t = 1 when y = 60 ⇒⇒⇒ b = t/y = 1/60

$a = \frac{1}{15} \ \ \ and \ \ \ b= \frac{1}{60}$

∴ x = 15s and y = 60t

$J ( \frac{x,y}{s,t}) = \left[\begin{array}{ccc} \frac{dx}{ds} & & \frac{dx}{dt} \\ & & \\ \frac{dy}{ds} & & \frac{dy}{dt} \end{array}\right] = \left[\begin{array}{ccc}15& &0\\ & & \\0& &60\end{array}\right] = 900$

Note: it is not matrix it is determinant

8 0

2 years ago

How much is 8% of 800 tons?

bonufazy [111]

1. We assume, that the number 800 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 800 is 100%, so we can write it down as 800=100%.
4. We know, that x is 8% of the output value, so we can write it down as x=8%.
5. Now we have two simple equations:
1) 800=100%
2) x=8%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
800/x=100%/8%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 8% of 800

800/x=100/8
(800/x)*x=(100/8)*x - we multiply both sides of the equation by x
800=12.5*x - we divide both sides of the equation by (12.5) to get x
800/12.5=x
64=x
x=64

now we have:
8% of 800 tons =64 Tons
I hope this helped!!

5 0

2 years ago

Please help ASAP !!!!!

sasho [114]

Since the denominators (bottom of the fraction) are the same, we can subtract the numerators (the top parts) easily.

14/19 - 5/19 = 9/19

ANSWER: 9/19

3 0

3 years ago

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Choose the table that represents g(x) = −2⋅f(x) when f(x) = x + 4

fomenos

Answer:

x g(x)

1 −10

2 −12

3 −14

Step-by-step explanation:

Substitute the values and do the arithmetic.

Table values for x are 1, 2, 3. We only need to find g(1) to determine which table is the correct choice.

f(1) = 1 +4 = 5 . . . . . . . . . put 1 where x is and do the arithmetic

g(1) = -2·f(1) = -2·5 = -10 . . . . . matches the 3rd choice

6 0

2 years ago

Write an explicit formula for an the nth term of the sequence 7,3, 1,....

mestny [16]

Answer:

20

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers