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kolezko [41]
3 years ago
15

Suppose the growth rate of GDP in the United States is 4.2 percent. If 2.9 percent and 1.3 percent of GDP growth are? due, respe

ctively, to capital and labor? growth, the amount resulting from technological progress is
Mathematics
1 answer:
Neporo4naja [7]3 years ago
6 0

Answer:

zero percent

Step-by-step explanation:

Given data in the problem:

The growth rate of GDP in the United States = 4.2 percent

The growth of GDP due to the capital = 2.9 percent

The growth of GDP due to the labor = 1.3 percent

now, the contribution of the capital and labor in the growth of GDP = 2.9 percent + 1.3 percent = 4.2 percent

Now, the contribution from labor and the capital sums up the total growth rate of the GDP of the united States.

Hence, the growth rate from the technical progress is <u>zero percent </u>

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At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as
MAXImum [283]

<u>Answer-</u>

At x= \frac{1}{2304e^4-16e^2} the curve has maximum curvature.

<u>Solution-</u>

The formula for curvature =

K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}

Here,

y=4e^{x}

Then,

{y}' = 4e^{x} \ and \ {y}''=4e^{x}

Putting the values,

K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

 {k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}

Now, equating this to 0

(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0

\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})

\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})

\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}

\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}

\Rightarrow 2304e^{2x}-16e^{2x}-1=0

Solving this eq,

we get x= \frac{1}{2304e^4-16e^2}

∴ At  x= \frac{1}{2304e^4-16e^2} the curvature is maximum.




6 0
3 years ago
Given a right triangle find the measure of all the angles of one angle is a right angle in the measure of the second angle is si
vfiekz [6]

Answer:

12°, 78°, 90°

Step-by-step explanation:

let the third angle be x then the second angle is 7x - 6

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

x + 7x - 6 + 90 = 180, that is

8x + 84 = 180 ( subtract 84 from both sides )

8x = 96 ( divide both sides by 8 )

x = 12

Thus second angle = 12° and third = 7(12) - 6 = 84 - 6 = 78°

The 3 angles are 12°, 78° and 90°

5 0
3 years ago
Read 2 more answers
A set of data has 12 pieces of data. Which of the following statements is NOT TRUE?
BARSIC [14]
To help you understand this, it is helpful to create a sample set of data:

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A. The first 3 lines are 3 pieces of data in the first quartile.

B. here are 6 pieces of data between the 1st and 3rd quartiles.

D. There are 3 pieces of data in the upper quartile.
                                 

5 0
3 years ago
What are the solutions of the quadratic equation? 2 x 2 – 16 x + 32 = 0
Evgen [1.6K]

Answer:

4 - 16 x + 32 = 0

- 16 x = - 4 - 32

- 16 x = - 36

X = 2.25

3 0
4 years ago
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Ronnie bought 6 ice cream cones for himself and his friends. Seventeen cents tax was added to the price of each cone. The total
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Price of a cone after tax = 14.58/6 = 2.43
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In short, Your Answer would be $2.26

Hope this helps!
3 0
3 years ago
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