if the entrance ramp has an elevation of 15° with the vertical lift is 28 feet. what is the distance up the ramp?

(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ))

Recall that

tan(θ) = sin(θ) / cos(θ)

so cos²(θ) cancels with the cos²(θ) in the tan²(θ) term:

(sin²(θ) - 1) / (1 + cos(2θ))

Recall the double angle identity for cosine,

cos(2θ) = 2 cos²(θ) - 1

so the 1 in the denominator also vanishes:

(sin²(θ) - 1) / (2 cos²(θ))

Recall the Pythagorean identity,

cos²(θ) + sin²(θ) = 1

which means

sin²(θ) - 1 = -cos²(θ):

-cos²(θ) / (2 cos²(θ))

Cancel the cos²(θ) terms to end up with

(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ)) = -1/2

Answer:

math is hard :(

Step-by-step explanation:

Answer:The square root of 436149 is 660.41577812769

Answer:

4x^2+4x-4

Step-by-step explanation:

8x^2 + 3x - 4x^2 + x - 4

= 8x^2 - 4x^2 + 3x + x - 4

= 4x^2 + 4x - 4

Answer:

plug in the first equation into the second

Step-by-step explanation:

(4+y) -2y=10

Answer:

You need to plug in the first equation into the second

Step-by-step explanation:

(4+y) -2y=10

Answer:

7.99*10^7

is the answer to your question

Answer: 7.99×10[tex]x^{-7}[/tex]

Step-by-step explanation:

7.99 times 10[tex]x^{-7}[/tex] = 0.00000799

Answer: I think the answer is D

Step-by-step explanation:

Answer:

[tex]d \approx 19.42[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point (3, 8)

Point (7, -11)

Step 2: Find distance d

Answer:

Step-by-step explanation:

b

Answer:

Option b) 3x - 22 = 38 should be the correct answer.

Step-by-step explanation:

If we solve the equation, we get:

x = 20

So each bag had 20 apples. In total, 3 bags held 60 apples. If he gives away 22 apples to his friends, he has 38 remaining and this satisfies the discription given in the question.

Therefore, option B) 3x -22 = 38 should be your answer.

Answer:

1267-7

Step-by-step explanation:

1257-10-7

1247-7

1240

a.) The equation for profit is  - 0.5x² + 40x - 300

b.) The two values of x for profit = $300 are 20 and 60

c.) Profit of $15000 is not possible.

What is a profit?

Profit is defined as the total extent of benefit gained from selling some things. Mathematically, it is illustrated as the difference between the selling price and the cost price of an object.

Calculating the expression for profit

Given: the cost of producing x items = 55x + 300 and the revenue for selling x items is 95x - 0.5x²

a.) Profit = selling price/revenue - cost price

According to the question, we get,

Profit = 95x - 0.5x² - 55x - 300

= 40x - 0.5x² - 300

= - 0.5x² + 40x - 300                  —–— 1

b.) Finding two values of x, when profit is $300

Using equation 1, we get,

300 = - 0.5x² + 40x - 300

0.5x² - 40x + 600 = 0

0.5x² - 10x - 30x + 600 = 0

0.5x(x - 20) - 30(x - 20) = 0

(x - 20)(0.5x - 30) = 0

i.e. x = 20 or x = 60

Two values of x for profit = $300

c.) Let us consider the profit to be $15000

15000 = - 0.5x² + 40x - 300

0.5x² - 40x + 15300 = 0

Using the quadratic formula, x = (- b ± √b² - 4ac) / 2a, we get,

x = (40 ± √40² - 4(0.5)(15300)) / 2(0.5)

The roots of this equation will be imaginary. Thus, it can be said that profit can not be $15000.

Hence, a.) The equation for profit is  - 0.5x² + 40x - 300

b.) The two values of x for profit = $300 are 20 and 60

c.) Profit of $15000 is not possible.

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Question:

A 33 foot ladder leans against a building so that the angle between the ground and the ladder is 75º. How high does the ladder reach up the side of the building?

Round to 2 decimal places feet.

Answer:

[tex]H = 31.88[/tex]

Step-by-step explanation:

The question is illustrated using the attachment as a sketch.

We have that

[tex]Ladder = 33ft[/tex]

[tex]\theta = 75[/tex]

Required

Determine how high the ladder is to the building

Represent the length of the ladder with L and how high the ladder is on the building with H.

The relationship between L, H and [tex]\theta[/tex] is"

[tex]Sin\theta = \frac{H}{L}[/tex]

Substitute values for L and [tex]\theta\\[/tex]

[tex]Sin(75) = \frac{H}{33}[/tex]

Make H the subject

[tex]H = 33 * Sin(75)[/tex]

[tex]H = 33 * 0.9660[/tex]

[tex]H = 31.88[/tex]

Hence, the height to which the ladder reaches is approximately 31.88ft

Answer:

Makayla got the highest

Step-by-step explanation:

if you do 100÷15=answer×12=80%

if you do 100÷35=answer×27=77%

Answer:

y = 3x

Step-by-step explanation:

A proportional relationship should be represented by an equation in this format:

y = kx

Answer:

y < 3/4x

Step-by-step explanation:

Answer:

B. Time(length)

Step-by-step explanation:

The function that would be represented as a good name for a function for the length of the race and the return the time required to finished it

here the independent variable or the INPUT is the length while the output would be the time that required to finish it

Hence, the correct option is B,

Therefore all the other options would be incorrect

Answer:

64%

Step-by-step explanation:

divide 80 by 125 and get .64

Answer:

64

I already did this in school

Answer:

15x + 9

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

12x + 14 + 3x - 5

Step 2: Simplify

Given:

The quadratic equation is

[tex]0=-3x^2-4x+5[/tex]

To find:

The simplest radical form of the solution.

Solution:

Quadratic formula:

If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have,

[tex]0=-3x^2-4x+5[/tex]

Here, a=-3, b=-4 and c=5. Putting these values in the quadratic formula, we get

[tex]x=\dfrac{-(-4)\pm \sqrt{(-4)^2-4(-3)(5)}}{2(-3)}[/tex]

[tex]x=\dfrac{4\pm \sqrt{16+60}}{-6}[/tex]

[tex]x=\dfrac{4\pm \sqrt{76}}{-6}[/tex]

[tex]x=\dfrac{4\pm 2\sqrt{19}}{-6}[/tex]

Taking 2 common, we get

[tex]x=\dfrac{2(2\pm \sqrt{19})}{-6}[/tex]

[tex]x=\dfrac{(2\pm \sqrt{19})}{-3}[/tex]

[tex]x=-\dfrac{(2\pm \sqrt{19})}{3}[/tex]

Therefore, the correct option is A.

Answer:

6/10

Step-by-step explanation:

2 groups of 3/10 =

2 × 3/10 =

6/10

Option ' B ' [ sin 35° = cos 55° ] is true!

- Used a calculator ! The value is shown in the calculator in the attached picture!

-------- Happy LearninG <3 ------

Answer:

im not sure if this is right but -0.358

Step-by-step explanation:

do y2-y1 over x2-x1 then subtract your y values then subtract your x values then you get your numbers then divide those numbers from top divided by bottom.

Answer:

HERE FOR POINTS SORRY

Step-by-step explanation:

Answer: See attached

Step-by-step explanation:

5/9 will give a repeating decimal 0.55555. You would write it as 0.5 with a "bar" line over the 5. See attached file of how it looks

The total number of different pizzas that Sarah can order is 42. The correct option is C.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given the following choices for selecting a pizza. Therefore, we can write,

Number of choices for size = 2

Number of choices for toppings = 7

Number of choices for crust = 3

Total number of choices available with Sarah = Number of choices for size × Number of choices for toppings × Number of choices for crust

Total number of choices available with Sarah = 2 × 7 × 3 = 42

Hence, the total number of different pizzas that Sarah can order is 42.

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Answer:

-24

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

Answer:

193.27

Step-by-step explanation:

Answer:

$193.27 left on his gift card