MATHEMATICS COLLEGE

Find the product of (5.2 · 10^-6) and (8 · 10^3).A) 416 · 106-4
B) 4.16 · 10^-2
C) 41.6 · 10^-3
D) 0.416 · 10^-1

Answers

Answer 1
Answer:

Answer: B) 4.16\cdot10^(-2)

Step-by-step explanation:

The given product : (5.2\cdot10^(-6))\cdot (8\cdot10^3)

First open parenthesis :

5.2\cdot10^(-6)\cdot 8\cdot10^3

Write decimal values together and power of 10s together.

5.2\cdot 8\cdot10^(-6)\cdot10^3

Using Law of exponent :a^m\cdot a^n= a^(m+n)

The above expression becomes.

41.6\cdot10^(-6+3)=41.6*10^(-3)

In scientific notation, the decimal must be placed after one digit (from left).

41.6*10^(-3)=4.16*10*10^(-3)\n\n=4.16\cdot10^(-3+1)\n\n=4.16\cdot10^(-2)

Hence, the correct answer is B) 4.16\cdot10^(-2) .
Answer 2
Answer:

 

\displaystyle\n(5.2\cdot10^(-6))*(8\cdot10^3)=\n\n=\underbrace{5.2*8}_(41.6)*\underbrace{10^(-6)*10^(3)}_(10^(-6+3))=\n\n=41.6*10^(-6+3)=\boxed{\bf41.6*10^(-3)}\n\n\texttt{Correct answer:}~~\boxed{\bf C)}

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True or False
100% of any number must greater than or
equal to 100

Answers

False
For example 100% of 2 is 2

Did i do this correctly?​

Answers

Answer:

R" has coordinates (-4,6)

Explanation:

The pre-image is the original, while the image is the altered form. The image is notated by a '. When you alter the image ('), you get ".

T is dilated (multiplied) by 5, so it goes from T = (1,-2) to T' = (5, -10)

R = (-2, 3) → (multiply by 5) → R' = (-10, 15) → (multiply by 2/5 or 0.4) → R" = (-4, 6)

Minimizing Construction Costs The management of the UNICO department store has decided to enclose a 945 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $4/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)

Answers

Answer:

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Step-by-step explanation:

Let 'B' be the length of each side constructed of pine boards, and 'S' be the length of the side with the steel fencing, the area (A) and cost (C) functions are:

945 = B*S\nB=(945)/(S) \nC= 4*S+7*2B\nC=4S+(13,230)/(S)

The value of S for which the derivate of the cost function is zero, minimizes cost:

C'=0=4+(-13,230)/(S^2)\n S=√(3,307.5) \nS=57.5 ft

The value of B is:

B=(945)/(57.5)\nB=16.4 \ ft

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Final answer:

To minimize the construction costs for the enclosure, the dimensions should be calculated using the calculus optimization technique. By incorporating the cost and area requirements into calculated equations and solving, you will find x = 2 times y. This is how you minimize the cost.

Explanation:

This problem involves the application of calculus and optimization techniques. Given that the area of the enclosure needs to be 945 ft2, and that it is adjacent to an external wall of the department store, we can infer that its shape is rectangular.

Let the width of the enclosure parallel to the department store be x (feet), and its length perpendicular to the store be y (feet). According to the area requirement, we have the equation x*y = 945 ft2.

The cost of the enclosure is the sum of the cost of the pine board fences and the steel fence. Since 2 sides are made of pine boards, and 1 side made of steel, the cost can be expressed as C = 2xy p + y s, where 'p' is the cost of pine board per foot ($7), and 's' is the cost of steel per foot ($4).

Since we are looking for the minimum cost, we derive this equation and set it equal to zero to find the dimensions x and y. After substituting and simplifying, we find that the minimum cost is obtained when x = 2 y. By substituting this into the area equation, we can solve for the dimensions of the enclosure.

Learn more about Calculus Optimization here:

brainly.com/question/30795449

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Given the expression 2x(y + z)2, which is TRUE? A) The factor 2x depends on (y + z)2. B) The factor (y + z)2 depends on 2x. C) The factors 2x and (y + z)2 are dependent of each other. D) The factors 2x and (y + z)2 are independent of each other.

Answers

If we assume that x, y, and z are independent variables, then the appropriate choice is ...
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For this line 3x−4y−12=0, which statement is true? 1- The x-intercept is 4, and the y-intercept is 3. 2-The x-intercept is 4, and the y-intercept is -3 3-The x-intercept is 3, and the y-intercept is -4. 4-The x-intercept is 3, and the y-intercept is 4.

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9514 1404 393

Answer:

  2. The x-intercept is 4, and the y-intercept is -3

Step-by-step explanation:

The given equation is in general form. I find it easier to see the intercepts when the equation is written in standard form:

  3x -4y = 12

Setting y=0 and solving for x, we have the x-intercept:

  3x = 12   ⇒   x = 12/3 = 4

Setting x=0 and solving for y, we have the y-intercept:

  -4y = 12   ⇒   y = 12/-4 = -3

The x-intercept is 4; the y-intercept is -3.

What is 75miles/hr in feet/second?(1mile = 5280feet)

Answers

Answer:

110 feet/sec

Step-by-step explanation:

75 miles x 5280 feet

= 396000

396000/60 min

=6600

6600/60 secs

=110 feet/second
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