Bob shoots off a small rocket from the balcony of his apartment. The balcony is 30 ft above the ground and the rocket travels at 40 ft/second. When does it reach the highest point? What is the highest point? When does it hit the ground (seconds)?

I'll do problem 9 to get you started.

Refer to figure 1 shown below. I've highlighted triangle AOB in red. This is an isosceles triangle with AO = OB as the congruent sides. These sides are congruent because they are radii of the same circle. Consequently, it means that the base angles opposite those sides are congruent.

I'll let x be the base angles. I'll let the remaining interior angle be y. Furthermore, z is adjacent to angle y.

For triangle AOB, and any triangle really, the interior angles add to 180 degrees.

A+O+B = 180

x+y+x = 180

2x+y = 180

y = 180-2x

Then we can say

(angle AOB) + (angle AOP) = 180

y + z = 180

180-2x + z = 180

z = 180+2x - 180

z = 2x

The punchline here is that angle ABP doubles to angle AOP.

angle AOP = 2*(angle ABP)

You'll repeat these same type of steps for triangle BOC in figure 2. The steps are effectively identical so there's not much for me to explain that I already haven't done so. You should find that r = 2m which shows angle PBC doubles to angle POC.

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

To wrap everything up for problem 9, we will combine the results we found for variables z and r.

angle AOC = z+r

angle AOC = 2x + 2m

angle AOC = 2(x+m)

angle AOC = 2*(angle ABC)

This concludes the inscribed angle theorem proof. Any inscribed angle doubles to get the corresponding central angle, where both subtend the same arc. In this case, they both subtend the arc APC.

[tex] \huge\rightarrow\sin( θ ) = \frac{ - 2 \sqrt{5} }{5} [/tex]

[tex] \huge\rightarrow\cos( θ ) = \frac{ \sqrt{5} }{5} [/tex]

We know that,

sine is the ratio of adjacent side over the hypotenuse.

[tex] \rightarrow\sin( θ ) = \frac{ - 2 \sqrt{5} }{5} = \frac{adjacent \: side}{hypotenuse} \\ [/tex]

also,

cosine is the ratio of base over the hypotenuse.

[tex]\rightarrow\cos( θ ) = \frac{?}{5} \\ [/tex]

[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{ {5}^{2} - ( - 2\sqrt{ 5} {}^{} ) {}^{2} } }{5} \\ [/tex]

[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{ {5}^{2} - {(2\sqrt{ 5})}^{2} } }{5} \\ [/tex]

[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{25 - 20} }{5} \\ [/tex]

[tex]\rightarrow\cos( θ ) = \frac{ \sqrt{5} }{5} \\ [/tex]

since ,cosine is always positive in the quadrant IV, option 3rd =√5/5 is correct ✓

Note:-

★theta to be used as A

[tex]\\ \rm\Rrightarrow sinA=\dfrac{-2\sqrt{5}}{5}[/tex]

Now

[tex]\\ \rm\Rrightarrow cosA=\sqrt{1-(dfrac{-2\sqrt{5}}{5})^2}[/tex]

[tex]\\ \rm\Rrightarrow cosA=\sqrt{1-\dfrac{20}{25}}[/tex]

[tex]\\ \rm\Rrightarrow cosA=\sqrt{\dfrac{25-20}{25}}[/tex]

[tex]\\ \rm\Rrightarrow cosA=\dfrac{\sqrt{5}}{5}[/tex]

Option C

A=πr²

where

π -> pi (3.14...)

r - radius

r² means you multiply r times itself

Hope it helps!

check the transformation template below, hmmm so to get the graph of "y" move to the right by 1 unit, we can simply make C = -1.

[tex]y=\stackrel{A}{1}\log_2(\stackrel{B}{1}x+\stackrel{C}{0})+\stackrel{D}{0}\qquad \qquad y=\stackrel{A}{1}\log_2(\stackrel{B}{1}x+\stackrel{C}{1})+\stackrel{D}{0} \implies y=\log_2(x-1)[/tex]

now, the x-intercept is simply where the graph touches the x-axis, and when that happens y = 0, so

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^{log_a x}=x\leftarrow \textit{let's use this rule} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{y}{0}~~ = ~~\log_2(x-1)\implies 2^0=2^{\log_2(x-1)}\implies 2^0=x-1 \\\\\\ 1=x-1\implies 2=x~\hspace{10em}\stackrel{x-intercept}{(2~~,~~0)}[/tex]

Answer:

Both of them are correct because if we simply the fraction of Edwin we will get the fraction of Tony

[tex] \frac{3}{6} [/tex]

[tex] = \frac{1}{2} [/tex]

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

Answer:

slope = 4/5

Step-by-step explanation:

Take any two points:

(5, 1) & (10, 5)

The slope

[tex]m=\frac{5-1}{10-5} =\frac{4}{5}[/tex]

Hope this helps

Answer:

4/5 is the slope of the line

Using the slope concept, supposing the horizontal distance is of 1500 feet, the angle of depression will be of 37º.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we suppose an horizontal distance of 1500 feet, with a vertical distance of 2000 feet, hence:

[tex]\tan{\alpha} = \frac{1500}{2000}[/tex]

[tex]\alpha = \tan^{-1}{\left(\frac{1500}{2000}\right)}[/tex]

[tex]\alpha = 37^\circ[/tex]

The angle of depression will be of 37º.

More can be learned about the slope concept at https://brainly.com/question/18090623

Answer:

10.5 ft

Step-by-step explanation:

This problem is using scaling.

Basically:

2.5(RV) = WZ

Meaning our scale factor is 2.5.

Multiply 4.2 * 2.5

Your answer is 10.5 ft.

Answer:

204, there is no remainder.

Step-by-step explanation:

Answer: 204 Rem 2

Step-by-step explanation: Use long division

Answer:

Step-by-step explanation:

The line perpendicual to a reference line will have a slope that is the negative inverse of the reference line.  In this case, the reference line is y= -(1/3)X+8, with a slope of -(1/3).  The negative inverse would be 3.  So the new line would have the form:

y = 3x + b

To find b, the y-intercept, use the given point and solve for b:

y = 3x + b

or 8 = 3*3 + b for the point (3,8)

8=9+b

b= -1

Thje equation of the line perpendicualr to the reference line and going through point (3,8) is:

y = 3x - 1

See attached graph.

Answer:

I give answers I think their correct but as humans we make mistakes so there may be errors

You have to multiply the Diameter, times Pi.(3.14)

7. 21.98

8. 62.8

9.75.36

10. 59.66
11. 84.78
12. 3082.2

 I dunno the last one. I probably do but
Hope This Helped!

Answer:

see explanation

Step-by-step explanation:

using the sine ratio in the right triangle.

sin23° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{7}[/tex] ( multiply both sides by 7 )

7 × sin23° = x , then

x ≈ 2.7 ( to the nearest tenth )

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

using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{27}{17}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{27}{17}[/tex] ) ≈ 57.8° ( to the nearest tenth )

Answer: A

Step-by-step explanation:

1/2=.5

1/3=.3 repeated

3/18=0.16 6 repeated

No b,c,

1/2>3/18

so a is correct

Answer:

it doesnt say any statement at all can you add them

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

Here we go ~

According to given figure,

[tex]\qquad \sf  \dashrightarrow \:x + 68 = 174[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 174 - 68[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 106 \degree[/tex]

Answer:

x < 15

Step-by-step explanation:

1)  Regroup terms.

⇒ x - 50 < - 35

2) Add 50 to both sides.

x < - 35 + 50

3) Simplify - 35 + 50 to 15.

x < 15

Answer:

x < 15

Step-by-step explanation:

-50 + x < -35

+50          +50

________________

x < 15

Hope this helps :)

Answer:

They both have H hoel

Step-by-step explanation:

\

Answer:

See below

Step-by-step explanation:

(a+c)^2 = t

(a+c) = sqrt t

c = sqrt(t) - a

Answer:

[tex]f(n)=f(n-1) + 4(3)^{n-2}[/tex]

[tex]\textsf{where}\quad f(1)=4[/tex]

Step-by-step explanation:

Given sequence:  4, 8, 20, 56, 164

First, work out the difference in the terms:

[tex]4 \underset{+4}{\longrightarrow} 8 \underset{+12}{\longrightarrow} 20 \underset{+36}{\longrightarrow} 56 \underset{+108}{\longrightarrow} 164[/tex]

As the first differences are not the same, work out the second differences:

[tex]4 \underset{\times 3}{\longrightarrow} 12 \underset{\times 3}{\longrightarrow} 36 \underset{\times 3}{\longrightarrow} 108[/tex]

Therefore, the term-to-term rule is:

[tex]f(n)=f(n-1) + 4(3)^{n-2}[/tex]  

[tex]\textsf{where}\quad f(1)=4[/tex]

[tex]f(2)=f(1) + 4(3)^{2-2}=4+ 4(3)^{0}=4+4=8[/tex]

[tex]f(3)=f(2)+4(3)^{3-2}=8+4(3)^1=8+12=20[/tex]

[tex]f(4)=f(3) + 4(3)^{4-2}=20+4(3)^2=20+36=56[/tex]

[tex]f(5)=f(4) + 4(3)^{5-2}=56+4(3)^3=56+108=164[/tex]

The number that can not represent the probability of an event is -0.5.

Option A is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The probability of an event always lies between 0 and 1 (inclusive), where 0 represents an impossible event and 1 represents a certain event.

Therefore, any number outside this range cannot represent the probability of an event.

Probabilities are always non-negative values between 0 and 1 (inclusive). The value 0 represents an impossible event, meaning that the event cannot occur.

The value 1 represents a certain event, meaning that the event will definitely occur. Any value between 0 and 1 represents the likelihood that the event will occur, where a value closer to 0 represents a low probability and a value closer to 1 represents a high probability.

Negative numbers cannot represent probabilities since probabilities are always non-negative values between 0 and 1.

Thus,

The number that can not represent the probability of an event is -0.5.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ7

each number has its place on the number line so true

Step-by-step explanation:

and 5 is one place to the left in 15.2

Answer:

48

Step-by-step explanation:

5(x2+y)+y2

5 x (3 x 2 + 6) + 6 x 2

5 x 6 + 6 + 6 x 2

30 + 6 + 6 x 2

30 + 6 + 12

36 + 12 = 48

Answer: the answer is D

Step-by-step explanation:V = pi (d/2)^2  *  h

V =  pi  (d^2  / 4)   * h

 h =  4V  /  ( pi  * d^2)       (meters) 

Mr. Red's salary is an illustration of an arithmetic sequence

The explicit rule of Mr. Red's salary is an = 500n + 29500

Mr. Red's salary is an arithmetic sequence with the following parameters:

First term, a1 = 30000

Common difference, d = 500

The explicit rule is calculated as:

an = a1 + (n - 1) * d

This gives

an = 30000 + (n - 1) * 500

Evaluate the product

an = 30000 - 500 + 500n

This gives

an = 29500 + 500n

Rewrite as:

an = 500n + 29500

Hence, the explicit rule of Mr. Red's salary is an = 500n + 29500

Read more about arithmetic sequence at:

https://brainly.com/question/6561461

sin U= |TS| / |US|

-> |US| = |TS| / sinU

-> x= 0.6 / sin 37°

-> x≈1,0

Answer:

The answers are D and then B.

Step-by-step explanation:

The first question asks which team has the youngest members on average. This is easily answered because the "mean" is simply the average of all the ages. Therefore the youngest "mean" age will also have the youngest members on average.

The second question asks what team has the most variability in ages. Range is the difference between the highest and lowest number. Therefore the team with the highest range should, logically, also have the most variability.

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(12)\implies \log_5(4\cdot 3)\implies \log_5(2^2\cdot 3) \\\\\\ \log_5(2^2)~~ + ~~\log_5(3)\implies 2\log_5(2)~~ + ~~\log_5(3)[/tex]

Answer:Samsung Galaxy Z Fold3 5G 256GB Phantom Black Smartphone

USD 1343

a) All the plans have a base service charge of $23 per month plus the cost of the phone. Write an expression to represent the service charge.

1343 + 23m

b) There are three unlimited plans, and each plan incorporates the service charge. Translate each plan into an algebraic expression using the service charge expression from the above question.

Plan 1: $8 less than twice the amount of the service charge.

(service charge is 23 per month so)

1343 + 2(23m– 8)

Plan 2: The quotient of the service charge and 2 increased by a fee of $50 per month.

1343 + (23m/2 + 50m)

Plan 3: The sum of half the number of months cubed and a third of the service charge.

1343 + (1/2m3 + 1/3(23m))

c) Which plan would be most cost effective for a 2-year contract? Show all calculations that led to your results. Explain your results comparing the 3 plans.

Plan 1: 1343 + (24(23 – 8) = 1703

Plan 2: 1343+ (24x61.5) = 2819

Plan 3: 1343 + (1728 + 552) = 3623

Plan 1 is the most cost effective because it is the cheapest

d) Sharaf Digital is having a special promotion by challenging customers to create their own plan. Customers must write a verbal expression that must include the service charge and at least two operations. The operations to choose from are listed below.

If the plan is within $15 per month of one of the original 3 plans then the customer could choose that plan.

Create a 4th plan and show all calculations that led to your results.

Operations: product, more than, less than, double, sum, divided by, square

The product of 3.5 and the total cost divided by 4

3.5(1343 + (24(23 – 8))/4 = 1490.13

Plan 4 = 1490.13/24 = 62.09

Plan 1: 1703/24

70.95

Step-by-step explanation: