For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 400 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 20 ft/sec, starting at time t = 0, where t is time in seconds. Let θ be the angle between the line of your horizon and your line of sight to the elevator. 4 (a) Find a formula for h(t), the elevator's height above the ground as it descends from the top of the hotel. h(t) = (b) Using your answer to part (a), express θ as a function of time t. θ(t) = Find the rate of change of θ with respect to t. dθ dt = (c) The rate of change of θ is a measure of how fast the elevator appears to you to be moving. At what time does the elevator appear to be moving fastest? time = seconds At what height does the elevator appear to be moving fastest?

Answer:

[tex]\frac{p^2-25}{p^2-10p+25}[/tex]

We can factorise the numerator with the difference of squares formula:[tex]x^2-y^2=(x+y)(x-y)[/tex]

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

[tex]\frac{p^2-5^2}{p^2-10p+25} =\frac{(p+5)(p-5)}{p^2-10p+25}[/tex]

Now we can factorise the denominator:

[tex]\frac{(p+5)(p-5)}{p^2-10p+25} =\frac{(p+5)(p-5)}{(p-5)^2}[/tex]

[tex]\frac{(p+5)(p-5)}{(p-5)^2} =\frac{(p+5)(p-5)}{(p-5)(p-5)}[/tex]

Cancel out the common factor of (p-5):

[tex]\frac{(p+5)(p-5)}{(p-5)(p-5)} =\frac{(p+5)}{(p-5)}[/tex]

Answer:

Step-by-step explanation:

Answer: In the context of borrowing, principal is the initial size of a loan or a bond (the amount the bond issuer must repay). In the context of investing, principal is the original sum committed to the purchase of assets—independent of any earnings or interest.

Answer:

y + 2 = (11/17)(x - 8)

Step-by-step explanation:

Working with the x- and y-components of the given points, we see that the x component increases by 17 and the y-component decreases by 11.  Thus, the slope of this line is m = rise / run, or 11/17.

Start with the general point-slope form:  y - k = m(x - h) and use the coordinates of the 2nd point for h and k in this equation:

                                                                    y + 2 = (11/17)(x - 8)

                                                                     This is based on the point (-2, 8)

                                                                     and the slope 11/17.                                                                  

This result is the desired equation in point-slope form.  If we wish to reduce this, proceed as follows:

17(y + 2) = 11x - 88, or 17y + 34 = 11x - 88

This last result simplifies to 17y = 11x - 54, or y = (11/17)x -54/17 (which is in slope-intercept form).

I think you got your answer

Answer:

  1330.5 cm³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h . . . . . for radius r and height h

The radius of the given cylinder is 1/2(11 cm) = 5.5 cm. Filling in the formula values, we have ...

  V = π(5.5 cm)²(14 cm) = 423.5π cm³ ≈ 1330.5 cm³

The volume of the cylinder is about 1330.5 cm³.

Answer:

1330.5

Step-by-step explanation:

Radius is half of diameter (11), so 5.5 was the other number I plugged in.

Answer:

24.8

Step-by-step explanation:

Answer:

-1519 4/5

-1519.8

-7599/5

Step-by-step explanation:

Answer:

y° = 25°

Step-by-step explanation:

Given the diagram of a triangle, where it shows an exterior angle with a measure of ∠115°, and that an angle bisector bisects the triangle into two right triangles.  

According to the Exterior Angle Theorem, the measure of the exterior angle is equal to the sum of the measures of two non-adjacent interior angles.  In other words, the given exterior angle, m∠115° is equal to m∠y° + m∠90°.

Hence, we could simply solve for the value of y algebraically:

m∠y° + m∠90° = m∠115°

y° + 90° = 115°

Subtract 90° from both sides:

y° + 90° - 90° = 115° - 90°

y° = 25°

Verify whether we have the correct value for y by solving for x:

Since the exterior angle, ∠115°, and ∠x° are supplements, then it means that:

m∠115° + m∠x° = 180°

115° + x° = 180°

Subtract 115° from both sides:

115°- 115° + x° = 180° - 115°

x = 65°

According to the Triangle Sum Theorem, the sum of the measures of the interior angles of a triangle is 180°.

Hence:

m∠x° + m∠y° + m∠90° = 180°

65° + 25° + 90° = 180°

180° = 180° (True statement).

Therefore, the correct answer is: y = 25°. This measure represents either one of the ∠y.

Answer:

3 over5 multiplied by 320 equals 192

Answer:

The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g intersect. The solution of the inequality f(x) < g(x) is the set of all x for which the graph of f lies below the graph of g

Answer:

angle a = angle bac = 90 degrees

angle b = angle abc

angle c = angle acb

Answer:

We will use a Pythagorean identity and alegbra to prove this.

sin^2 + cos^2 = 1, dividing by cos^2 gives

tan^2 + 1 = sec^2.

Now, breaking down the fraction into parts and simplifying gives:

(1-sin^4)/cos^4 = 1/cos^4 - sin^4/cos^4 = sec^4 - tan^4

Now use difference of squares factoring from alegbra.

= (sec^2 + tan^2)*(sec^2 - tan^2)

By rewriting our Pythagorean identity to

sec^2 - tan^2 = 1 and tan^2 = sec^2 - 1,

we can finish the problem.

= (sec^2 + tan^2) * 1 = sec^2 + tan^2

= sec^2 + (sec^2 - 1) = 2*sec^2 - 1.

Step-by-step explanation:

if I understand this right, then you need paint and additional supplies.

but I don't see any information indicating how many gallons of paint I will need.

so, I can go only with the 1 gallon specified.

so,

1×30 + 60 = $90

we can save $45 per month.

then we need

90 / 45 = 2

months to have enough money.

please update the numbers to how many gallons you really need, and then take that result and divide it by the 45 savings per month.

Answer:

576 adults

Step-by-step explanation:

The 5 part of the ratio relates to 720 children, then

720 ÷ 5 = 144 ← value of 1 part of the ratio , then

4 parts = 4 × 144 = 576 ← number of adults

Answer:

576

Step-by-step explanation:

Adults : Children

      4  :  5

     x   :  720

Let the number of adults be x.

Use cross multiplication.

  [tex]4 : 5\\ x : 720\\[/tex]

[tex]4 *720=5*x[/tex]

[tex]\frac{4*720}{5} =\frac{5x}{5}[/tex]

4 × 144  = x

576 = x

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

Converting m to mm

=> 1 m = 1000 mm

=> 8 m = 8000 mm

Therefore,

The wire will be 8000 mm long.

Hope it helps you...

Please mark as brainlliest!!!

Answer:

0.38 < 0.70

Step-by-step explanation:

Answer: D. 16.33

Step-by-step explanation:

Answer:

16.8

Step-by-step explanation:

s = ∅ × r

= 2π/3 × 8

= 16/3 * π

= 16.75516

= 16.8

Answer:

C.) 16.8 is your answer

Step-by-step explanation:

Answer:

3/12 percent

Step-by-step explanation:

Answer:

50+90+3x+1=180.....................

Answer:

0.5256

Step-by-step explanation:

X ~ B(10,0.75)

q = 1 - 0.75 = 0.25

Answer:

20

Step-by-step explanation:

4*5 = 20%

Answer:

21. 2x + 28

22. 18a - 17b

23. He flipped the numerator and denominator, 6.4 with 7.2 and he added the exponents instead of subtracting.

24. 8.8888888888889 × 10^{0}

Step-by-step explanation:

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today!

We can solve this problem in two steps, one is Comprehending and another is Solving. I'll start off with Comprehending.

Comprehending

We can start off by looking at the problem, it wants us to find the percentage increase from 36 to 48. We can then find difference between 48 and 36; that would be 12.

Now that we know the increase from 36 to 48 is 12. We need to find how much percent 12 is of 36.

Now that we know what we have to do, we can start solving.

Solving

We can solve the problem by setting up and equation, but we can also just use our logic in finding it out.

Since we know that we need to find how much 12 is of 36, we can just solve for that and we will get our answer.

We can do that with one step.

[tex]\frac{12}{36}=0.33[/tex]

Since it is a percent, we can multiply 0.33 by 100 and we get our answer of 33%

Answer:

86 quarts

Step-by-step explanation:

If you took away 28 quarts and were left with 58 quarts then you add the two numbers to get 86 quarts which is what you started with.

Answer:

Ok I don't know waht you mean but the answer is

Step-by-step explanation:

Answer:

x=3/2±(√11)2

x=1.5+1.65831i

x=1.5−1.65831i

Find the Solution for

2x^22−6x+10=0

using the Quadratic Formula where

a = 2, b = -6, and c = 10

x=(−b±√(b^2−4ac))/2a

x=(−(−6)±√((−6)2−4(2)(10)))2(2)

x=(6±√(36−80))/4

x=(6±√−44)/4

The discriminant b^2−4ac<0

so, there are two complex roots.

Simplify the Radical:

x=(6±2√11 i)/4

x=6/4±(2√11 i)4

Simplify fractions and/or signs:

x=3/2±(√11)2

which becomes

x=1.5+1.65831i

x=1.5−1.65831i

[tex]LHS \\ = 8 + 7 - {2}^{2} \\ = 8 + 7 - 4 \\ = 15 - 4 \\ = 11[/tex]

[tex]RHS \\ = {3}^{2} + 2 \\ = 9 + 2 \\ 11[/tex]

So, LHS = RHS

=

Hope it helps.

Do comment if you have any query.

Answer:

Below!

Step-by-step explanation:

Let's try the 'equal' sign for this equation.

Remember, when it comes to simplifying, exponents come first. This means that we need to simplify the exponents first.

Since the LHS and the RHS are equal, the 'equal' sign will fit into the equation. Hence, this is proven as true. Let's try the 'not equal' sign.

Now, this is a definite false. The 'not equal' sign is used when two values are not equal to each other, however, in this situation, 11 does equal 11. In between them is a 'not equal' sign. Hence, this is proven false.

We can conclude that the sign you are looking for is an 'equal' sign.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

A

Step-by-step explanation:

x from 0 < x < 2 is wrong because < means goes to but does not equal that value, and [tex]\leq[/tex] means it INCLUDES that value. Because the function includes it (not an open hole), you should choose A.