AP CAL AB!!!! HELP. A ladder 10 feet long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall, and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ=π/3 ?

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{dx}{d\theta}=5\text{ ft/rad}[/tex]

Step-by-step explanation:

Please refer to the diagram below.

We can use the sine function. Recall that the sine function is the ratio between the opposite side and the hypotenuse. Hence:

[tex]\displaystyle \sin(\theta)=\frac{x}{10}[/tex]

We want to find how fast x changes with respect to θ. So, we want to find dx/dθ. Therefore, let's take the derivative of both sides with respect to θ:

[tex]\displaystyle \frac{d}{d\theta}[\sin(\theta)]=\frac{d}{d\theta}\left[\frac{1}{10}x\right][/tex]

Differentiate. Since it's with respect to θ, we can differentiate the left-hand side like normal. On the right, we will implicitly differentiate. This yields:

[tex]\displaystyle \cos(\theta)=\frac{1}{10}\frac{dx}{d\theta}[/tex]

Multiply both sides by 10. So, dx/dθ is:

[tex]\displaystyle \frac{dx}{d\theta}=10\cos(\theta)[/tex]

We want to find dx/dθ when θ is π/3. Thus, substitute π/3 for θ:

[tex]\displaystyle \frac{dx}{d\theta}=10\cos\left(\frac{\pi}{3}\right)[/tex]

Evaluate:

[tex]\displaystyle \frac{dx}{d\theta}=10\left(\frac{1}{2}\right)=5\text{ ft/rad}[/tex]

So, x is changing with respect to θ at a rate of 5 feet per radian.

AP CAL AB!!!! HELP. A Ladder 10 Feet Long Rests Against A Vertical Wall. Let Be The Angle Between The

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Which property is illustrated by the following statement?
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O A. Commutative Property of Addition
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O C. Commutative Property of Multiplication
O D. Associative Property of Multiplication

Answers

Answer:

Associative Property

Step-by-step explanation:

The associative property states that it doesn't matter where the parenthesis are put, the answer will always be the same

It should be Associative Property Of Multiplication

A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while. How many miles has the car traveled if it has 10 gallons of gas left in the tank?

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Answer:

Step-by-step explanation:

A rotating lawn sprinkler sprays water in a circular area of grass, as shown in the picture. The diameter of the circular area of grass is 16 ft.Which measurement is closest to the area in square feet that this sprinkler sprays with water?

Answers

The measurement that is closest to the area in square feet that this sprinkler sprays with water is 201.062 ft².

Area of Circle[tex]\rm{ Area\ of\ circle = \pi \times (radius)^2[/tex]Given to us,

Diameter of the circular area of grass, d = 16 ft.,

The radius of the circular area of grass, [tex]r = \dfrac{Diameter}{2} = \dfrac{16}{2} = 8\ ft[/tex],

Area of sprinkler sprays

Area in which the sprinkler sprays with water = Area of the circle

[tex]= \pi \times r^2\\= \pi \times 8^2\\=\pi \times 64\\= 201.0619\approx 201.062\ ft^2[/tex]

Hence, the measurement that is closest to the area in square feet that this sprinkler sprays with water is 201.062 ft².

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y=7 x=6 what is the value of y when x=12?

Answers

Answer:

Y = 14

Step-by-step explanation:

6 times 2 = 12

7 times 2 = 14

One angle of a triangle measures 40°. The other two angles are in a ratio of 5:9. What are the measures of those two angles?

Answers

Answer:

50 and 90

Step-by-step explanation:

(180-40)/(5 + 9) = 10

=> 50 and 90

Amber is traveling to he mom's house. The scale on the map is 2 inches=10 miles. She knows her mom lives 40 miles away. How far would that be on the map?

Answers

8 inches on the map. To approach this problem, just set up a proportion:

2in =10 mi x in =40 mi.

If we use that to set up an equation we get

80 =10x.

Answers

The ordered pairs that satisfy this function are (-3,-1) and (3,3)

help pleaseeeeeeeeeeeeee now

Answers

Answer: per 1 ticket sold it costs 10 dollars

Step-by-step explanation:

1 and ten meet on the graph constantly

A truckload of plastic soda bottles was finely shredded at a recycling center. The plastic shreds were placed into 55-liter drums. What it the mass of the plastic shreds inside one of the drums in kg? Assume lowest density within the range.

Answers

Answer:

75,900 g

Step-by-step explanation:

m=d×v

(1.38g/cm^3) × (55,000)

The mass of the drum is 75.9 kg.

What is the mass of the drum?

The mass of the drum is the product of the volume and density of the drum.

What are Arithmetic operations?

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have been given that the plastic shreds were placed into 55-liter drums.

We have to determine the mass of the plastic shreds inside one of the drums in kg.

Here density of the drum = 1.38g/cm³ and the volume of the drum = 55,000

The mass of the drum = (1.38g/cm³) × (55,000)

The mass of the drum = 75,900 g

The mass of the drum = 75.9 kg

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Answers

Answer:

55 dollars

Step-by-step explanation:

y = total cost, x = number of sessions attended

Non-members equation: y = 5x

Members equation: y = 3x + 25

y = 3(10) + 25

y = 30 + 25

y = 55 dollars

Hope this helps!

3(10) + 25
=55 dollars

Gamers charges $8 to rent a video game. The Discount Club charges $4 to rent a video game after a membership fee of $10 is paid. For what number of video game rentals is Gamers less expensive than Discount Club? Write an inequality that represents this situation. (do not solve) How did you determine which inequality symbol to use for the situation?

Answers

Answer

8x>10+4x for x=>3

Just two games.

for the third game you would have paid $24 in total

Step-by-step explanation:

Given that

gamers charge $8

Discount Club charges $4 after a membership of $10

total for the Discount club is given by the expression

let x be the number of games rent

Y=10+4

So at the first rent, you will pay Discount Club

$14 and the second rent you would have spent

14+4= $18

and the third rent you would have spent

18+4= $22

the inequality is given as

for x=>3

8x>10+4x

20x3² - 4 ) divided by 50
Evaluate the expression.

Answers

Answer:

2/5x^9−2/25

Step-by-step explanation:

A train travels 540 miles in 12 hours.
Complete the table to represent the situation.

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1: 45
2: 90
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10: 450

A parent purchased a dictionary for $13.50 and a pack of printer paper for $4.50. The sales tax rate was 4%. What was the total bill, including the sales tax?

Answers

Answer:

C $18.72

Step-by-step explanation:

1. $13.50+$4.50= $18.00

2. $18.00* 4%=$0.72 sale tax

3. $18.00+$0.72= $18.72 your answer

Answer:

its c!

Step-by-step explanation:

$18.72

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Answers

Answer:

320 miles per hour

Step-by-step explanation:

Speed=800miles/2.5 hours

320milesperhour

8 + 6 + 12 = __ + 12 + 6

Answers

Answer:

The number 8 goes in the blank,

Step-by-step explanation:

Its basic commutative property.

Hope this helps!

I dont quite understand how to do this

Answers

Answer:

Step-by-step explanation:

substitute -3 in for x

f(-3)=(-3)²+1=

9+1=10

(You can ignore the g(x) part - it has nothing to do with this question.)

EXTRA POINTS * how do you graph y=2x + 1

Answers

Step-by-step explanation:

first u need to pick a random coordinate to substitute the X . example 0

y = 2(0) + 1

y =1 , X= 0

X= 1

y= 2(1) + 1

y= 3, X= 1

then you continue this same process and again until u have at least two points to draw a straight line. it kinda depended if u want to fill the entire graph.

Fill in the blanks 1. The degree of a linear equation is ? 2. The constant term has a degree ? 3. The solution of the equation ax + b = 0 is ? 4. If 2x - 3 = 0 then the value of x is ? 5. The value of x which satisfies the equation (- 8) = 2x + 4 is ? 6. The solution of the equation 10 - (x + 2) = 7x is ? 7. A linear equation in one variable has _________ solution ? 8. The sum of the two consecutive multiples of 10 is 210. The smallest multiple is 9. Convert the statement "adding 15 to 4 times x is 39" into an equation 10. Value of "S" in 1/3 + S = 2/5 is ?

Answers

Answer:

Step-by-step explanation:

A linear equation is of the form ax+b and the highest degree of x is 1. You can see that from the power of x which is 1.

The power of x is zero from the equating. It is not reflecting because anything raise to power if zero gives 1

To get the solution of the equation ax+b = 0

We will make x the subject of the formula

ax = -b

Divide both side's by a

ax/a = -b/a

x = -b/a

If 2x-3 = 0

2x = 0+3

2x = 3

2x/2 = 3/2

x = 3/2

Given -8 = 2x+4

2x = -8-4

2x = -12

x = -12/2

x = -6

A linear equation in one variable is known to have ONE solution. This is as demonstrated in the equation above, we cans see that the only solution is -6(just one solution)

Convert the statement "adding 15 to 4 times x is 39" into an equation 1

The product of 4 and x is 4x

Adding 15 to 4x will give

15+4x

If the resulting expression is equal to 39, the final equation will be;

15+4x = 39

10) given 1/3+S = 2/5, we are to find S

S = 2/5-1/3

S = 6-5/15

S = 1/15

Hence the value of S is 1/15

22x^3 y^4+28x^2 y^5+34xy^4

Answers

Answer:

2xy4 • (11x2 + 14xy + 17)

Step-by-step explanation:

(((22•(x3))•(y4))+((28•(x2))•(y5)))+(2•17xy4)

(((22•(x3))•(y4))+((22•7x2)•y5))+(2•17xy4)

(((2•11x3) • y4) + (22•7x2y5)) + (2•17xy4)

5.1 Pull out like factors :

22x3y4 + 28x2y5 + 34xy4 = 2xy4 • (11x2 + 14xy + 17)

Trying to factor a multi variable polynomial :

5.2 Factoring 11x2 + 14xy + 17

Final result :

2xy4 • (11x2 + 14xy + 17)

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