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3 years ago

Put the decimals in order from LEAST to GREATEST. 5.62, 9.4, 5.72, 3.1

Mathematics

1 answer:

Leni [432]3 years ago

5 0

Answer:

3.1, 5.62, 5.72, 9.4

Step-by-step explanation:

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Rewrite the product as a sum: 10cos(5x)sin(10x)

mote1985 [20]

Answer:

10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]

Step-by-step explanation:

In this question, we are tasked with writing the product as a sum.

To do this, we shall be using the sum to product formula below;

cosαsinβ = 1/2[ sin(α + β) - sin(α - β)]

From the question, we can say α= 5x and β= 10x

Plugging these values into the equation, we have

10cos(5x)sin(10x) = (10) × 1/2[sin (5x + 10x) - sin(5x - 10x)]

= 5[sin (15x) - sin (-5x)]

We apply odd identity i.e sin(-x) = -sinx

Thus applying same to sin(-5x)

sin(-5x) = -sin(5x)

Thus;

5[sin (15x) - sin (-5x)] = 5[sin (15x) -(-sin(5x))]

= 5[sin (15x) + sin (5x)]

Hence, 10cos(5x)sin(10x) = 5[sin (15x) + sin (5x)]

8 0

3 years ago

QUESTION 3 [10 MARKS] A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the nu

Harman [31]

Answer:

(a)Revenue function, $R(x)=580x-x^2$

Marginal Revenue function, R'(x)=580-2x

(b)Fixed cost =900 .

Marginal Cost Function=300+50x

(c)Profit, $P(x)=-35x^2+280x-900$

(d)x=4

Step-by-step explanation:

Part A

Price Function $= 580 - 10x$

The revenue function

$R(x)=x\cdot (580-10x)\\R(x)=580x-x^2$

The marginal revenue function

$\dfrac{dR}{dx}= \dfrac{d}{dx}(R(x))=\dfrac{d}{dx}(580x-x^2)=580-2x\\R'(x)=580-2x$

Part B

(Fixed Cost)

The total cost function of the company is given by $c=(30+5x)^2$

We expand the expression

$(30+5x)^2=(30+5x)(30+5x)=900+300x+25x^2$

Therefore, the fixed cost is 900 .

Marginal Cost Function

If $c=900+300x+25x^2$

Marginal Cost Function, $\frac{dc}{dx}= (900+300x+25x^2)'=300+50x$

Part C

Profit Function

Profit=Revenue -Total cost

$580x-10x^2-(900+300x+25x^2)\\580x-10x^2-900-300x-25x^2\\$Profit,P(x)=-35x^2+280x-900$

Part D

To maximize profit, we find the derivative of the profit function, equate it to zero and solve for x.

$P(x)=-35x^2+280x-900\\P'(x)=-70x+280\\-70x+280=0\\-70x=-280\\$Divide both sides by -70\\x=4$

The number of cakes that maximizes profit is 4.

6 0

3 years ago

F(b) = 7b^3 +8b and g(b) = b ^2+ b - 10. What is f(b)-g(b)?

Elden [556K]

Answer:

${ \bf{f(b) - g(b) : }} \\ { \tt{ = ( {7b}^{3} + 8b) - ( {b}^{2} + b - 10)}} \\ = ( {7b}^{3} - {b}^{2} + 7b + 10)$

7 0

3 years ago

Read 2 more answers

Option 1: Find x. Show all work.

Ronch [10]

Using law of cosines:

Cos(angle) = adjacent/ hypotenuse

Cos(22) = 12/x

Rewrite to get:

X = 12/cos(22)

Simplify:

X = 12.9424

Round the answer as needed.

5 0

2 years ago

Read 2 more answers

The mark up on an item is $3.75. If the mark up is 35%, what was the original price? Round

oksian1 [2.3K]

Answer:

$10.71

Step-by-step explanation:

$\frac{3.75}{y} =\frac{35}{100}$

y × 35 = 3.75 × 100

35y = 375

35y ÷ 35 = 375 ÷ 35

$y=10\frac{5}{7}$

y = 10.7142857143

10.7142857143 round to 10.71

5 0

3 years ago