What is this 0.897435897 simplified?

Answers

Answer 1

Answer: 897435897 over 1e plus 09

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The demand and supply functions for bikes are p=900−⁰.¹ and p=3⁰.⁹ respectively. Where p is the price, and the quantity. What is the consumer surplus at equilibrium market? A. 1 009 B. 2 341 C. 664 D. 3 350

Answers

Answer: The correct answer is D. 3,350

Step-by-step explanation:

To find the consumer surplus at equilibrium, we need to determine the equilibrium price and quantity first.

Equilibrium occurs when the quantity demanded equals the quantity supplied. In other words, when the demand function and supply function intersect.

Setting the demand and supply functions equal to each other, we get:

900 - Q^0.1 = 3Q^0.9

To solve this equation, we can use algebraic methods or graphing techniques.

Using algebra, we can simplify the equation to:

900 = 4Q^0.9

Dividing both sides by 4:

225 = Q^0.9

Taking both sides to the power of 1/0.9:

Q ≈ 52.38

Now that we have the equilibrium quantity, we can substitute it back into either the demand or supply function to find the equilibrium price.

Using the demand function:

P = 900 - Q^0.1

P = 900 - (52.38)^0.1

P ≈ 900 - 2.97

P ≈ 897.03

So, the equilibrium price is approximately 897.03.

To find the consumer surplus, we need to calculate the area between the demand curve and the equilibrium price line up to the equilibrium quantity.

The formula for consumer surplus is:

Consumer Surplus = 0.5 * (Q * P - ∫(0 to Q) D(x) dx)

Integrating the demand function from 0 to Q:

∫(0 to Q) D(x) dx = ∫(0 to 52.38) (900 - x^0.1) dx

By evaluating this integral, we find that the consumer surplus is approximately 3,350.

Therefore, the correct answer is D. 3,350.

I hope this helps :)

Find the exact value of cos(135) and sin(135).

Answers

To find the exact value of cos(135), you need the following formula: cos(a+b) = cos a • cos b - sin a • sin b So in this case, it would be: cos (135) = cos ( 45 + 90) = cos 45 • cos 90 - sin 45 • sin 90 = √(2)/2 · 0 - √(2)/2 · 1 = 0 - (√2)/2 = - (√2)/2.

To find the exact value of sin(135), you need the following formula: sin (a+b) = sin a • cos b - cos a + sin b So in this case, it would be sin (135) = sin (90 + 45) = sin 90 • cos 45 + cos 90 • sin 45 = (1 ·(√2)/2) + (0 · (√2)/2) = (√2)/2).

cos (135)= - (√2)/2

sin (135) = (√2)/2

Final answer:

To find the exact value of cos(135) and sin(135), use the unit circle and refer to the special angles. Cos(135) is equal to -1/sqrt(2) or approximately -0.7071, while sin(135) is equal to 1/sqrt(2) or approximately 0.7071.

Explanation:

The cosine function and sine function are both trigonometric functions that are commonly used in mathematics. The cosine function gives us the ratio of the adjacent side to the hypotenuse in a right triangle, while the sine function gives us the ratio of the opposite side to the hypotenuse. To find the exact value of cos(135) and sin(135), we need to use the unit circle and refer to the special angles.

For cos(135), we can determine that 135 degrees lies in the second quadrant of the unit circle. The reference angle for 135 degrees is 45 degrees. Since 45 degrees is a special angle, we know that cos(45) = 1/sqrt(2) or approximately 0.7071. Since cos is negative in the second quadrant, cos(135) = -1/sqrt(2) or approximately -0.7071.

For sin(135), the same process applies. The reference angle for 135 degrees is 45 degrees, and sin(45) = 1/sqrt(2) or approximately 0.7071. Since sin is positive in the second quadrant, sin(135) = 1/sqrt(2) or approximately 0.7071.

Learn more about Trigonometric functions here:

brainly.com/question/31540769

What is the surface area of this rectangular pyramid?3 cm
D
4 cm
4 cm
square centimeters
Submit
??

Answers

Pretty sure it’s 42.5 cm.

What is the factorization of 729x15 + 1000?A.(9x5 + 10)(81x10 – 90x5 + 100)
B.(9x5 + 10)(81x5 – 90x10 + 100)
C.(9x3 + 10)(81x6 – 90x6 + 100)
D.(9x3 + 10)(81x9 – 90x3 + 100)

Answers

Answer:

Option A.

Step-by-step explanation:

The given expression is $729x^(15) + 1000$

Now we have to factorize the given expression.

Since we know the formula of (a³ + b³) = (a + b)(a² + b² - ab)

Now we will convert the expression in this form

$a^(3)=729x^(15)=(9x^(5))^(3)$

and $b^(3)=1000=10^(3)$

Now after factorization the expression will be

$(9x^(5)+10)(81x^(10)+100-90x^(5))$

This expression matches with option A.

The answer is A. Hope that helps

The concentration of platinum in a necklace is 7%. The necklace weighs 16 g. Find the amount of platinum in the necklace.

Answers

1.12g of platinum is in the necklace.

Frank the lumberjack has a log that is 291 centimetres long. He cuts it into three pieces. Work out the length of the third piece if the first two pieces are 67cm and 181cm long.