What to do: Complete each of the following problems involving ladders and walls by using trigonometric functions and inverse trigonometric functions to determine unknown lengths and angle measures.


Questions:

a) A ladder is placed against the wall of a building such that the bottom of the ladder is 3 ft from the bottom of the wall. If the ladder forms a 14 degree angle with the building, how high up the wall does the ladder reach?


b) A 15 foot ladder is leaned against a wall so that the bottom of the ladder forms a 75 degree angle with the ground. How far up the wall does the ladder reach?


c) You need to paint shutters on a window that is on the second floor of your house. You have a 20 foot ladder that you will use. There is a warning on the ladder that states the angle formed by the ladder and the ground must not be less than 70 degrees, or the ladder may slip and cause serious injury or death. You planned on placing the bottom of the ladder 3 feet from the base of the house.

Will the angle formed between the ground and the ladder be safe? What is the furthest possible distance the ladder can be placed to maintain a safe angle?


How you must answer:

- Sketch:

-We know:

-We want

-Rationale: Which ratio will you use and why?

-Solution


How do you answer:

= you must include an accurate sketch

= a statement identifying the known information - we know

= a statement that tells what you are solving for - we want

= the equation you used to solve the problem

Answer:

Philadelphia

Step-by-step explanation:

Philadelphia

San Diego

Houston

Phoenix

Explanation:

The top bar as a darker shade represents the population in 1990, and the lighter shade down below is the population for the year 2000.

The city of Dallas has its population increase because the lighter shaded bar is longer. This rules out choice A. Choices B and C are ruled out for similar reasoning (Phoenix and San Diego also show population growth).

Only Philadelphia experiences population decline during this time period.

Answer:

  17

Step-by-step explanation:

The geometry program that drew the circle through the three given points wrote this equation for the circle:

  (x -6)^2 +(y -11)^2 = 130

Compared to the standard form equation, ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . . circle with center (h, k) and radius r

we can see that the center is (h, k) = (6, 11).

The sum h+k is 6+11 = 17.

__

Additional comment

The center is at the point of intersection of the perpendicular bisectors of chords of the circle.

Here it is convenient to choose one of them as the horizontal segment with endpoints (3, 0) and (9, 0). The vertical line that bisects this segment is x=(3+9)/2 = 6. So, x=6 is the x-coordinate of the circle center.

We can use endpoints (-1, 2) and (3, 0) as another chord. Its midpoint is (-1+3, 2+0)/2 = (1, 1). The slope of this chord is (y2-y1)/(x2-x1) = (0-2)/(3-(-1)) = -1/2. So, the slope of the perpendicular bisector is -1/(-1/2) = 2, and the equation of that line is

  y -1 = 2(x -1)

For x=6, the point of intersection of the chord bisectors is ...

  y -1 = 2(6 -1) = 10

  y = 11

The coordinates of the circle center are (6, 11), so h+k = 6+11 = 17.

Answer:

Step-by-step explanation:

a)

The total amount coffee beans

b)

The total amount of market price

Answer:

a)   750a + 1200r = 1000000

b)   1065a + 876r = 1000000

Step-by-step explanation:

Define the variables:

Part (a)

Given:

If the plantation yields 1,000,000 kg of coffee:

⇒ 750a + 1200r = 1000000

Part (b)

Given:

If the price of Arabica beans is $1.42 per kg, and Arabica yields about 750 kg per hectare, then the price per hectare of Arabica coffee beans is:

⇒ $1.42 × 750 = $1065 per hectare

If the price of Robusta beans is $0.73 per kg, and Robusta yields about 1200 kg per hectare, then the price per hectare of Robusta coffee beans is:

⇒ $0.73 × 1200 = $876 per hectare

Therefore, if the plantation produces coffee worth $1,000,000:

⇒ 1065a + 876r = 1000000

Answer:

Length = 8+7 = 15

Width = 8

Step-by-step explanation:

                       New

Length = x+7 , x+4

Width = x ,x+2

(x+7) x = (x+4)( x+2)

expand and simplify x =8

The length of the shorter side length of original rectangle is 8 inches and of original rectangle longer side length is 15 inches.

Let l is the length and b is the breadth of the rectangle.

then the area of the rectangle is ab.

Given One side of a rectangle is 7 inches longer than another side.

then shorter side length is x and the large side length is 7+x.

then the area of the original rectangle is x(x+7)

Now calculate the sides of the new rectangle.

longer side of this rectangle decreases by 3 then new side is 7+x -3= 4+x

The shorter side increases by 2 inches then x+2.

So new rectangle area is (x+4)(x+2)

Both rectangle area is equal then

(x+4)(x+2) = x(x+7)

x² +2x+4x+8 = x²+7x

x²+6x+8 = x²+7x

x²-x²+7x-6x = 8

x = 8

Since a shorter side length is 8 inches and a longer side length is 8+7 =15 inches.

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Answer:

Step-by-step explanation:

Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

So:

[tex]9^2+13^2=c^2[/tex]

[tex]250 = c^2[/tex]

[tex]\sqrt{250} = \sqrt{c^2}[/tex]

[tex]c = 15.8113883[/tex]

OR (rounded)

[tex]c = 15.8[/tex]

Answer:

D, assuming that the function continues past the line shown

Step-by-step explanation:

There is no reason that the X is ending on either side. There should be arrows on both ends of the graphed function though.

Answer:

6x³ - 15x² - 1

3x divided by 3x is 1

So, here we are to simplify the polynomial :

[tex] \\ \longrightarrow \sf \qquad6x^3 - 15x^2 - \frac{3x}{ 3x}\\ \\[/tex]

We can simplify it as,

[tex]\\ \longrightarrow \sf \qquad6x^3 - 15x^2 - 1 \\ \\[/tex]

Some points to know :

Answer:

140 child tickets were sold

Step-by-step explanation:

a = number of adult tickets

c = number of child tickets

a+c = 350

6.50 c + 8.50a = 2695

Multiply the first equation by -8.50 together

-8.50c  -8.50c =-2975

Add this to the second equation to eliminate a

-8.50c  -8.50c =-2975

6.50 c + 8.50a = 2695

---------------------------------

-2c   + 0a = -280

Divide by -2

-2c/-2 = -280/-2

c = 140

Answer:

Radius of sphere =1unit

SurfaceareaVolume=4πr234πr3=34π(1)3×4π(1)21=31

∴V:S=1:3 cm

Step-by-step explanation:

Hope this helps. If any questions, please ask in comments.

Answer:

I'm talking about the boxes:

1st-false, there are 7/19, which is not more

2nd-true, there are 12/19 which is the most

3rd-true, 12/20 of the women like dancing

4th-false, 7/20 like dancing

5th-true, 13/20 don't like dancing

Answer:

Given:

< or > = open circle

≤ or ≥ = closed circle

So we are looking for:

Therefore, the attached is the correct answer.

Answer:

Rational:2.1,2.2

Irrational:[tex]\sqrt{5},\sqrt{6}[/tex]

Step-by-step explanation:

Trial and error

its b i know

Step-by-step explanation:

It's a geometric sequence

Formula:&

[tex]\\ \sf\longrightarrow a(n)[/tex]

[tex]\\ \sf\longrightarrow ar^{n-1}[/tex]

[tex]\\ \sf\longrightarrow 1.3125(4)^{n-1}[/tex]

Answer:

Step-by-step explanation:

(i)

PQRS is a parallelogram (given)

      ∴ QT = TS (Diagonals of a parallelogram bisects each other)

also,   QT = RM (given)

      ∴TS = RM

PQRS is a parallelogram,

     ∴RT = PT (Diagonals of a parallelogram bisects each other)

also, SM = PT (given)

    ∴RT = SM

TS = RM

RT = SM

∴ RTSM is a parallelogram (both pairs of opposite sides are equal in length)

(ii)

QP // RS (Opposite sides of a parallelogram are parallel)

∴ ∡RQP = ∡NRS (Corresponding ∡s)

RTSM is a parallelogram(Proved above)

∴MS // RT (Opposite sides of a parallelogram are parallel)

∴NS//RP

∴∡RNS = ∡ QRP (Corresponding ∡s)

in ΔPQR and Δ NSR,

QP = RS (Opposite sides of a parallelogram are equal)

∡RQP = ∡NRS (Proved above)

∡RNS = ∡ QRP(Proved above)

∴ ΔPQR≡ΔSRN (AAS)

Corresponding sides of ≡ Δs are equal, ∴QR = RN

Answer:x=4 (0,0)

Step-by-step explanation:

Determine the zeros of function,factor the functions. Set the factored function equal to 0 and solve. Then find the y-y-intercept of the given function by setting x equal to 00and Solving for y.

Answer:

10 years

Step-by-step explanation:

Simple interest formula:

AV=PV(1+it)

13200=8000(1+.065t)

1.65=1+.065x

.65=.065x

10=x

Answer:

The fully factored form of the function f(x) is : (x+5)(x-1)(x-3)

Step-by-step explanation:

Answer:

v > - 78

Step-by-step explanation:

Version 1.

   v

-----------  < 92

-6 + 79

    v

------------  <  92

    73

    v

------------  <  92(73)

    73(73)

v < 6716

-------------------------------------

Version 2

    v

------------ + 79 <  92

    -6       -79      -79

        v

(-) ------------  <  13(6)

        6(6)

-v < 78

÷-1   ÷-1

v > -78

I hope this helps!

yes it is true and second is false

Answer:

Formula of Mean= Efx/n

Formula of Median=n+1/2

I think it will help you

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's use section formula ~

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{mx_2 + nx_1}{m + n} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{my_2 + ny_1}{m + n} [/tex]

And since mid point divides a line segment Into two equal parts, m : n = 1 : 1

so, take m = n = 1

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{(1 \times - 1)+(1 \times - 2)}{ 1+ 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{- 1- 2}{ 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{ - 3}{ 2} [/tex]

Now, let's find y - coordinate ~

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{(1 \times - 5) + (1 \times - 4)}{1 + 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{ - 5 - 4}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{ - 9}{2} [/tex]

So, coordinates of midpoint is ~

[tex]\qquad \sf  \dashrightarrow \:( - \dfrac{3}{2} ,- \dfrac{9}{2} )[/tex]

Answer:

When dissolved, bases release hydroxide ions, OH-(aq) into solution.

Step-by-step explanation:

Water is the product of an acid and base reacting. Chemists say that the acid and base cancel or neutralise each other, hence the reaction is known as "neutralisation"

Answer: It increases the concentration of OH- in solution.

Step-by-step explanation:

Answer: 45

Step-by-step explanation: 2 1/4 = 2hr and 15 min

1/3 of 2hr and 15 min = 45

Amount of time spent by Nathan's family watching the video is 3/4 hour or 45 minutes.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Given that,

Nathan’s family spent 2 and 1/4 hours visiting national monument near their home.

They watched a video in the visitor center for 1/3 of that time.

Total time spent by Nathan's family in the monument = 2 + 1/4 hours

                                                                                         = 9/4 hours

Fraction of time spend in watching the video = 1/3

Time spend in watching the video = 1/3 × 9/4

                                                         = 3/4 hour

                                                         = 45 minutes

Hence the time spent is 3/4 hour.

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Tony deposited three checks as given in deposite ticket. The amount of the third check that Tony deposited is given by: Option B: $105.20

Resultant deposited amount = Deposited amount - The amount deducted.

We subtract the amount deducted from the amount deposited to get the resultant deposite amount that will go in bank.

Well, it might be that we deduced more than what we deposite, in that case net deposite will come as negative, indicating that there is deduction instead of deposite.

The missing image of the deposite ticket is attached below.

From that image, we can see that:

Thus, the net deposited amount is:

Net deposite = deposited amounts - deduced amounts

686.04 = 491.6 + 157.68 + x - 68.44 (all in dollars)

[tex]686.04 = x+ 491.6 + 157.68 - 68.44\\686.04 = x + 580.84\\\\\text{Subtracting 580.04 from both the sides} \\\\686.04 - 580.84 = x\\x = 105.20 \: \rm dollars[/tex]

Net deposite = 105.20 (in dollars).

Thus, the amount of the third check that Tony deposited is given by: Option B: $105.20

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Answer:

Step-by-step explanation:

49

Answer: 5/3

Step-by-step explanation:

1. 3/x = 5/y

2. Cross multiply

3y = 5x

3. Dividing the sides by 3

y = 5x/3

4. Dividing the sides by x

y/x = 5/3

Answer:

Step-by-step explanation:

Use a simple interest formula.

Simple interest formula:

→ 2000*4.6%4

You have to convert 4.6% into a decimal form.

→ 4.6%=0.046

→ I=2000*0.046*4

Solve.

Multiply the numbers from left to right.

→ 2000*0.046*4=368

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

7.8

Step-by-step explanation:

3.2 + 4.6 = 7.8 because 6+2 equals 8 and 4+3 equals 7 so 7.8

Answer: 96

Step-by-step explanation: formula for volume is lwh. 2 times 8 times 12 equals 192. divide that by 2 because there is only half left.