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taurus [48]
2 years ago
13

For what power of q is its value 1?​

Mathematics
1 answer:
DedPeter [7]2 years ago
4 0

Answer:

  0, for q ≠ 0 and q ≠ 1

Step-by-step explanation:

Assuming q ≠ 0, you want to find the value of x such that ...

  q^x = 1

This is solved using logarithms.

__

  x·log(q) = log(1) = 0

The zero product rule tells us this will have two solutions:

  x = 0

  log(q) = 0   ⇒   q = 1

If q is not 0 or 1, then its value is 1 when raised to the 0 power. If q is 1, then its value will be 1 when raised to <em>any</em> power.

_____

<em>Additional comment</em>

The applicable rule of logarithms is ...

  log(a^b) = b·log(a)

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There are 33 of them altogether and pay £311 in total. How many kids are in the family? Adults pay £15 and kids pay £7
Marrrta [24]

Answer:

Step-by-step explanation

  1. Let x be the number of adults and y the number of kids

We can then write this two equations :

          x+y= 33

          15x+7y= 311

  • let's solve the two eaquations

to do that we should combine them both in a way that help us get rid of one of the variables.

             Let's multiply the first equation by -7 to get rid of y by adding it to thr second equation

             -7x-7y= -231

        now add both equations .

              15x+7y-7x-7y=311-231

    we get :  8x = 80

as you notice y is gone and we get a classic easy equation to solve

                x= 80/8

                   = 10

so the number of adults is 10

let's go back to the first equation ( x+y= 33) and replace x with 10

                10+y= 33

                  y= 33-10

                     =23

let's check using the second equation :

            (10*15)+(23*7) = 311

that is true

so :

  •  the number of adults is 10
  • the number of kids is 23
4 0
3 years ago
The automobile assembly plant you manage has a Cobb-Douglas production function given by p = 10x^0.2 y^0.8
Zepler [3.9K]

Answer:

The variation needed for the daily buget to follow the increase in production for the first year is 12.38 $/year.

This value of Δy is not constant for a constant increase in production.

Step-by-step explanation:

We know that the production function is p = 10x^{0.2} y^{0.8}, and in the current situation p=1200 and x=130.

With this information we can calculate the actual budget level:

p_0 = 10x^{0.2} y^{0.8}\\\\1200=10*130^{0.2} y^{0.8}\\\\1200=26.47*y^{0.8}\\\\y=(1200/26.47)^{1/0.8}=45.33^{1.25}=117.62

The next year, with an increase in demand of 100 more automobiles, the production will be p_1=1300.

If we calculate y for this new situation, we have:

y_1=(\frac{p_1}{10x^{0.2}} )^{1.25}=(\frac{1300}{26.47} )^{1.25}=49.10^{1.25}=130

The budget for the following year is 130.

The variation needed for the daily buget to follow the increase in production for the first year is 12.38 $/year.

\Delta y=y_1-y_0=130.00-117.62=12.38

This value of Δy is not constant for a constant increase in production.

3 0
3 years ago
a car travels along the highway to yuma at steady speed. when it begins, it is 400 miles from yuma. After 7 hours, it is 59 mile
klemol [59]

Answer:

y= -50x + 400

Step-by-step explanation:

-50 miles from the place which means they are going further and further away so it is negative. And its 400 because y=mx+b the b is 400 because thats where they started.  Also it said it was correct on A-p-e-x.

4 0
3 years ago
How do you write 4.40 × 10^3 in standard form?
Sindrei [870]

Answer:

4400 is the answer

Step-by-step explanation: You move the decimal point to the right 3 spaces. If it was 10^-3 you would move the decimal point to the left 3 spaces.

8 0
3 years ago
Mario start collecting stamps in January and buys 12 stamps each month.Karen starts collecting stamps in July and buys 18 starts
Goryan [66]

Answer:

12 months

Step-by-step explanation:

Given that:

Mario:

12 stamps per month

Since January

Karen :

18 stamps per month

Starts on july

Number of stamps collected by Mario till the end of June :

12 * 6 = 72 stamps

For Mario :

72 + 12x

For karen:

18x

Where x is the number of months after karen starts :

Equate both equations

72 + 12x = 18x

72 = 18x - 12x

72 = 6x

x = 72/6

x = 12

After 12 months

Number of months after karen starts, will they have same amount of stamp

7 0
3 years ago
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