Applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.
What is the Tangent Ratio?Tangent ratio is part of the Trigonometry ratios, which is expressed as, tan ∅ = opposite side / adjacent side in a right triangle.
The information given would form a right triangle, where:
Reference angle = ∅ = 30°Opposite side = 14 ftAdjacent side = distance of the worm from the base of the tree = xApplying the tangent ratio, we would have:
tan 30 = 14/x
x = 14/tan 30
x = 24.2 ft.
Therefore, applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.
Learn more about tangent ratio on:
https://brainly.com/question/14169279
A Ferris wheel is 20 meters in diameter and completes 1 full revolution in 8 minutes.
A round Ferris wheel
A Ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.
a. Find the amplitude, midline, and period of h(t).
Enter the exact answers.
Amplitude: A= meters
Midline: h= meters
Period: P= minutes
b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t).
Hints:
What is the value of h(0)?
Is this the maximum value of h(t), the minimum value of h(t), or a value between the two?
The function sin(t) has a value between its maximum and minimum at t=0 , so can h(t) be a straight sine function?
The function cos(t) has its maximum at t=0, so can h(t) be a straight cosine function?
c. If the Ferris wheel continues to turn, how high off the ground is a person after 30 minutes?
Given that the Ferris diameter is 20 meters, with a rate of rotation of 1 turn in 8 minutes, we have;
a. Amplitude: A = 10 meters
Midline: h = 11 meters
Period, P = 8 minutes
b. h(t) = 10•cos((π/4)•t + π) + 11
c. 11 meters
How can the Ferris wheel be evaluated?The amplitude is the same as the radius of the Ferris wheel,
The radius of the Ferris wheel = 20 ÷ 2 = 10
Therefore;
Amplitude: A = 10 meters[tex]the \: midline \: = \frac{max \: height \: + min \: height}{2} [/tex]
Therefore;
[tex]midline \: = \frac{10 + 10 + 1 + 1}{2} = 11[/tex]
Midline: h = 11 metersThe period is the time to complete one rotation, therefore;
Period, P = 8 minutesb. h(t) = A•cos(B•t + C) + h
Where;
B = 2•π/P
When t = 0, h(t) = 1
Which gives;
h(0) = 1 = 10 × cos(B×0 + C) + 11
-10/10 = -1 = cos(C)
C = arcos(-1) = π
Therefore;
h(t) = 10•cos((π/4)•t + π) + 11h(0) = 1
h(0) is the minimum value of h(t)
h(t) cannot be a straight sine function because of the vertical shifth(t) cannot be a straight cosine function because at t = 0, is the minimum pointc. After 30 minutes, we have;
h(30) = 10•cos((π/4)×30 + π) + 11 = 11
The height of a person after 30 minutes is 11 metersLearn more about the Ferris wheel here:
https://brainly.com/question/86214
5
Solve for x. Round all answers to the nearest tenth.
X
32
14
O 11
O 11.7
O 10.2
O 11.9
Answer:
11.9
Step-by-step explanation:
Making sure your calculator is in degree mode, we have:
[tex] \cos(32) = \frac{x}{14} [/tex]
[tex]x = 14 \cos(32) = 11.9[/tex]
A line passes through (-4, 7) and has a slope of 3/2
Write an equation in slope intercept form for this line
Answer:
please see the photo above
CAN SOMEONE PLS ANSWER THIS QUESTION FAST
WILL MARK BRAINLIEST
Answer:
C. 9 miles/gallon
Step-by-step explanation:
Answer:
Maybe 10? I'm sure though
Step-by-step explanation:
Frank is surveying shoppers about their use of the new food court in a mall. Which question in his survey is a statistical question?
How many hours do you spend at the food court each month?
Where is the food court located in the mall?
How many restaurants are there in the food court?
Who is the manager of the food court?
Answer:
A How many hours do you spend at the food court each month? is a statistical question
Step-by-step explanation:
Because that can have many answers unlike where is the food court in the mall? that question is not statistical because there can only be one answer and so are all the other ones.
Answer:
How many hours do you spend at the food court each month?
Step-by-step explanation:
I just took test got 100% this answer is correct
How many hours do you spend at the food court each month?
Convert 68% As a fraction
Answer:
68/100
Step-by-step explanation:
It would be this because, with percentages, 100 is full. Therefore, we can just make 68 be out of 100. Hope this helps :)
I need help with this question!
Answer:
B
Step-by-step explanation:
Guys please help! i will mark brainliest to the right answers
Note: in order for me to mark a brainliest 2 people need to answer
Answer:
look at the picture i have attached and tell me what you think???
Step-by-step explanation:
parallel is two lines that go like this \\ or like this =
perpendicular is two lines that go like this +
which is it?
Answer:
they are parallel as gradient is the same because in first equation coefficient of x is -2 and in second equation after rearranging equation in form of y= mx + c, m is -2
19. Given that angle BFC = 58°. Angle BXG = 48° and angle CBF 22 Find () 2BGX (iv) BCG (i) 2BGF (iv) ZBFG (ii) BCF H EE 58 48° D C 220 A- Figure 5.74
The unknown angles in the cyclic quadrilateral is as follows:
∠BGX = 74° (sum of angles in a triangle)
∠BGF = 180° (opposite angles of cyclic quadrilateral are supplementary)
∠BCF = 100°(sum of angles in a triangle)
∠BCG = 26°
∠BFG = 22°
Cyclic QuadrilateralA cyclic quadrilateral has all its angles equal to 360 degrees. The sum of angles in a cyclic quadrilateral is equals to 360 degrees.
Let's find the missing angles as follows:
∠BGX = 180 - 48 - 58 = 74° (sum of angles in a triangle)
∠BGF = 180 - 100 = 80° (opposite angles of cyclic quadrilateral are supplementary)
∠BCF = 180 - 22 - 58 = 100°(sum of angles in a triangle)
∠BCG = 100 - 74 = 26°
∠BFG ≅ CBF = 22°(alternate angles)
learn more on angles here: https://brainly.com/question/19430381
In a popular online role playing game, players can create detailed designs for their
character's "costumes," or appearance. Eli sets up a website where players can buy
and sell these costumes online. Information about the number of people who visited
the website and the number of costumes purchased in a single day is listed below.
314 visitors purchased no costume.
68 visitors purchased
exactly one costume.
17 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase
exactly one costume as a fraction in simplest form.
Answer:
Submit Answer
attempt 2 out of
The probability that the next person will purchase exactly one costume is given by: 68/399
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
The total number of visitors to the website is 314 + 68 + 17 = 399.
Out of these 399 visitors, 68 purchased exactly one costume.
Therefore, the probability that the next person will purchase exactly one costume is given by:
68/399
This fraction cannot be simplified any further, so the final answer is:
68/399.
To learn more about probability from the given link:
https://brainly.com/question/30034780
#SPJ1
A deck of cards contains
52 cards. two decks
are put together, how
many cards will be left
over if 7 people divide
them evenly?
Answer:
6
Step-by-step explanation:
52+52=104
104/7=14.8
7*14=98
104-98=6
Please help and I'll mark brainliest
Answer:
the answer is 60
Step-by-step explanation:
brainliest please
Answer:
B.) I'm not 100% sure
Step-by-step explanation:
Hope this helped
29
= 30
31
An amount of $32,000 is borrowed for 6 years at 6.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must
paid back
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$32000\\ r=rate\to 6.25\%\to \frac{6.25}{100}\dotfill &0.0625\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &6 \end{cases} \\\\\\ A=32000\left(1+\frac{0.0625}{1}\right)^{1\cdot 6}\implies A=32000(1.0625)^6\implies A\approx 46038.78[/tex]
WHEN THE WHOLE IS THE SAME, HOW MANY 8THS DOES IT TAKE TO EQUAL 1\4. DRAW A MODEL TO SHOW YOUR ANSWER.
Answer: 4
Step-by-step explanation:
4 times 2 is 8 if you make 4 eighths you will get 1/4 a
Find the area of the figure
Answer:
88 cm²
Step-by-step explanation:
88 cm² is your answer
. Find the angle between the given vectors to the nearest tenth of a degree. u = <2, -4>, v = <3, -8> (2 points)
Answer:
6.0
Step-by-step explanation:
practice many times
A container holds 4 gallons of lemonade. How much is this in pints
Answer:
i think I'd be / the answer is 46
To visit the top of the Empire State Building, a ticket cost $ 4.00 in 1999. In 2009, the price rose to $ 20.00. What was the percent charge
Answer:
500%
Step-by-step explanation:
500% is 500/100 which is just 5*4=20
Find the area of the trapezoid
insurance that pays for damages to houses or businesses is called
Answer:
Homeowners insurance
Step-by-step explanation:
Homeowners insurance is designed to protect your home from what are called "perils." A peril is your exposure to risk or something that causes loss or destruction. … Homeowners 2 (HO2): This policy protects your property against 18 perils (including 11 perils from Homeowners 1). Typical homeowners insurance policies offer coverage for damage caused by fires, lightning strikes, windstorms and hail. But, it's important to know that not all natural disasters are covered by homeowners insurance. For example, damage caused by earthquakes and floods are not typically covered by homeowners insurance.
What is the perfect square of the root 3x^4
Answer:
the perfect square is 9x²
Step-by-step explanation:
√(3×)⁴
=(3x)²
=9x²
Find the product. (6y - 2)2
A. 36y2 - 24y + 4
B. 36y2 + 24y = 4
C. 36y2 + 4
D. 12y2 - 16y + 4
Answer:
A. 36y² - 24y + 4Step-by-step explanation:
Use identity
(a ± b)² = a² ± 2ab + b²Here we have a = 6y, b = 2
(6y - 2)² = (6y)² - 2(6y)(2) + 2² = 36y² - 24y + 4Correct choice is A
a man buys a vehicle at a cost prize of R60 000 from Cape Town. He transported the vehicle from cape town to Gauteng province, where he stays, at a cost prize of R4 500. at what prize must he sell the car to make an overall profit of 25% ?
Answer:
R80625
Step-by-step explanation:
Total Cost : 60000 + 4500 = 64500
To make 25% profit: 64500 X 1.25 = 80625
l need help with this pls
Answer:
50°
Step-by-step explanation:
In a parallelogram opposite angles have the same measure. Angle ABC has then the same measure of angle ADC, which is 38°+12°=50°
Express 100,000 as a power of 10
Answer:
10^5
Step-by-step explanation:
10 multiplied by itself five times (10*10*10*10*10) is 100,000.
For what values of x is x3+23x2+162x+360=0 a true statement?
Answer:
Step-by-step explanation:
x³+23x²+162x+360=0
x³+12x²+11x²+132x+30x+360=0
x²(x+12)+11x(x+12)+30(x+12)=0
(x+12)(x²+11x+30)=0
(x+12)[x²+6x+5x+30]=0
(x+12)[x(x+6)+5(x+6)]=0
(x+12)(x+6)(x+5)=0
x=-12,-6,-5
What is an equation of the line that passes through (0, 4) and (2,8)?
Answer:
y=2x+4
Step-by-step explanation:
Hi there!
We are given the points (0, 4) and (2,8)
We want to write the equation of the line that passes through these two points
There are 3 ways to write the equation of the line, but the most common way is with slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
So, to use this way, we need to find the slope of the line
The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We are already given the points needed to find the slope, but let's label them to avoid any confusion
[tex]x_1=0\\y_1=4\\x_2=2\\y_2=8[/tex]
Now substitute these values into the formula.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{8-4}{2-0}[/tex]
Subtract
m=[tex]\frac{4}{2}[/tex]
Divide
m=2
The slope of the line is 2
Here is the equation of the line so far:
y=2x+b
Now we need to find b
As stated before, b is the y intercept of the line, which is the point in where the line passes through the y axis; the value of x at this point is 0
One of the points we were given earlier is actually the y intercept of the line; that point is (0, 4) *notice how x=0 at this point
The value of b is the value of y at the y intercept; in this case, the value of b is 4
Substitute 4 as b into the equation
y=2x+4
Hope this helps!
See more on this topic here: https://brainly.com/question/27172025
Is the table a linear or exponential function?
The table represents linear because the x represent the exponential functions
Jeremiah has a mailing cylinder for posters that measures 12 inches long and 8 inches in diameter. What approximate volume can it hold? Use 3.14 for pi. Do not round. SHOW YOUR WORK.
Answer:
The cylinder can hold 508.68 in³
Explanation:
The volume of a cylinder can be calculated using the following rule:
Volume of cylinder = πr²h cubic units
where r is the radius of the cylinder and h is its height
Now, we are given that:
height of cylinder = 18 in
diameter of cylinder = 6 in which means that the radius of the cylinder is 3 in
π is 3.14
Substitute with the givens in the above equation to get the volume of the cylinder as follows:
Volume of cylinder = πr²h
Volume of cylinder = 3.14 * (3)² * 18
Volume of cylinder = 508.68 in³
expand the following
1. ( m+n)(10m-4n)
2.(6x+y)
hope it helps....!!!!!