the log ride at an amusement park has a single hill with an incline of 127 feet and a decline of 93 feet. If the total horizontal distance between the start of the incline and end of the decline is 132 feet, find the maximum height of the ride
Answers
Answer:
85.02 feet
Step-by-step explanation:
In order to solve this we need to use Herons formula to discover the Area of the triangle and then solving the formula of the area to find the height.
Herons formula starts by calculating the semi-perimeter which is half the perimeter of the Triangle:
\(s=\frac{a+b+c}{2}\\ s=\frac{127+93+132}{2}\\s=176\)
Now that we knwo that s= 176 we need to use the second part of the formula:
\(A=\sqrt{(S-A)(S-B)(S-C)} \\\\A=\sqrt{(176-127)(176-93)(176-132)}\\A=\sqrt{176(49)(83)(44)} \\A=5612.02\)
So the area is 5612.02, with that we just have to solve the equation for area, which is \(A=\frac{B*H}{2}\)
So it would be 2A*B=H
H=2*5612.02*132
H=85.03
Related Questions
Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = 9 − x2 R: square with vertices (0, 0), (2, 0), (0, 2), (2, 2)
Answers
Answer:
The area of the surface over R is \(\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)
Step-by-step explanation:
From this study,
The surface area of f(x,y) is expressed by:
\(A = \iint_R \sqrt{1 +f^2_x+f^2_y}} \ dA\)
where
\(0 \leq x \leq 2 \ and \ 0 \leq y \leq 2\)
Given that:
f(x,y) = 9 - x²
Thus, \(f_x = -2x\) and \(f_y = 0\)
However, the area becomes:
\(A = \iint_R \sqrt{1+(-2x)^2+0^2} \ dxdy\)
\(A = \iint_R \sqrt{1+4x^2} \ dxdy\)
From above, replacing x with \(\dfrac{1}{2} \ tan \ u\)
then \(dx = \dfrac{1}{2} sec^2 \ udu\)
∴
\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint \sqrt{1 + 4u^2 } \ sec^2 \ udu\)
\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint sec^2 \ udu\)
\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} ( \sqrt{4x^2 + 1x} + \dfrac{1}{2} In \sqrt{4x^2 + 1}+2x)\)
Hence;
\(\mathsf{A = \int \limits ^2_0 \begin {bmatrix} \dfrac{1}{2}(\sqrt{4x^2 +1 x}+ \dfrac{1}{2} In ( \sqrt{4x^2+1}+2x \end {bmatrix}^2_0 \ dy}\)
\(\mathbf{A = 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)
Therefore, the area of the surface over R is \(\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)
Help me with this answer please
Answers
Answer:
There is 8 blue sweets and 4 red sweets.
Step-by-step explanation:
There is only blue and red sweets.
There is 12 sweets in total.
There is two times as many blue sweets as red sweets
There is 8 blue sweets and 4 red sweets.
Solve for y.
(4y + 5) (-2y + 3) = -3-7y - 8y2 +9y - 9
Answers
Step-by-step explanation:
hope this will help you......
Answer:
\((4y + 5)( - 2y + 3) =-3 -7y - 8 {y}^{2}+9y - 9 \\ - 8 {y}^{2} + 12y - 10y + 15 = - 12 + 2y - 8 {y}^{2} \\ - 8 {y}^{2} + 2y + 15 = - 12 + 2y - 8 {y}^{2} \)
value of y is getting cancelled outso value of y does not exist.Find the midpoint of the segment joining X(6,5) and Y(9,2). I'm lost geomerty
Answers
Answer:
Is there a graph?
Step-by-step explanation:
evaluating equations show your work 5x-5=6x+2
Answers
Answer:
-7
Step-by-step explanation:
Let's solve your equation step-by-step.
5x−5=6x+2
Step 1: Subtract 6x from both sides.
5x−5−6x=6x+2−6x
−x−5=2
Step 2: Add 5 to both sides.
−x−5+5=2+5
−x=7
Step 3: Divide both sides by -1.
−x
−1
=
7
−1
x=−7
Hey guys, I actually really need your help right now. Is it possible if you guys can provide instructions please?
Answers
Answer:
a. (-6,4)
b. minimum
c. zero roots
Answer:
a. The coordinates of the vertex are (-6, 4)
b. The vertex is a minimum
c. There are 0 real roots
Step-by-step explanation:
a. The coordinates of the vertex are represented by (h, k) in the vertex form equation: y = a(x-h)^2 + k. Therefore, the coordinates of the vertex are (-6, 4).
b. Since the coefficient value of a is positive, the graph is a minimum.
c. The graph is a minimum with a positive y coordinate for the vertex, which means that there are zero real roots because the graph never intersects the x-axis.
Which statements are true? Select each correct answer. Responses Only some triangles are plane figures. Only some triangles are plane figures. All triangles are polygons. All triangles are polygons. All triangles have 3 right angles. All triangles have 3 right angles. All triangles are closed figures. All triangles are closed figures. All triangles have 3 straight sides.
Answers
The three true statements are as follows:
All triangles are polygons.All triangles are closed figures. All triangles have 3 straight sides.What are the true statements?In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.
A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.
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A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The survey reported a confidence interval that between 22% and 32% of the residents supports the plan. What is the margin of error on the survey? Do not write ± ± on the margin of error.
Answers
Answer:
\(\Huge \bold{\boxed{\boxed{\text{5\%}}}}\)
Step-by-step explanation:
To calculate the margin of error for the survey, we need to use the formula:
\(\large \text{Margin of error} = \large \text{$\frac{\text{Range of values}}{2}$}\)
The range of values is the difference between the upper and lower bounds of the interval. In this case, the lower bound is 22% and the upper bound is 32%, so the range of values is:
\(\large \text{Range of values = 32\% - 22\% = 10\%}\)
Substituting this value into the formula, we get:
\(\large \text{Margin of error = $\frac{10\%}{2}$ = 5\%}\)
Therefore, the margin of error on the survey is 5%.
birth weights for a simple random sample of 195 boys were recorded. the mean weight calculated for this sample was 3.04 kilograms and the standard deviation was 0.71 kilograms
Answers
Answer:
The sample mean birth weight for the 195 boys is 3.04 kilograms and the sample standard deviation is 0.71 kilograms.
Step-by-step explanation:
Select the correct answer.
A figure shows the inscribed triangle ABC with center point O which bisects BO. An angle of C is 50 degrees.
In the diagram,
is a diameter of the circle with center O. If m∠
= 50°, what is m∠
?
A.
50°
B.
40°
C.
80°
D.
100°
Reset Next
Answers
Answer: C
Step-by-step explanation:
PLEASE HELP ILL GIVE BRAINLIEST AND FOLLOW using y=mx+b form
Answers
Answer:
y=1+5
Step-by-step explanation:
b is the y intercept and 1 is the slope gradient
Analyn is heating a solution in her chemistry lab. The temperature of the solution starts at 10°CShe turns on the burner and finds that the solution's temperature increases by 4°C every minute. This graph shows the temperature change.
Answers
Answer:
D
Step-by-step explanation:
if you go 6x and 34 y you get a point on the line.
PLEASE HELP! ( Question attached below! )
Answers
Since the diagonals of the quadrilateral are equal , it is either a square or rectangle
How do we know a quadrilateral by diagonal?The diagonals of the square bisect each other at 90° The two diagonals of the square are equal to each other.
The diagonals of the rectangle bisect each other. Both diagonals of the rectangle are equal in length.
The Rhombus is a quadrilateral, where diagonals bisect each other and are not equal.
The diagonals here are BD and AC
therefore BD = √ -3-(-1)² + 10-2)²
BD = √ 2²+8²
BD = √ 4+64
BD = √ 68
AC = √ 2-(-6)² + 7-5²
AC = √8²+4²
AC = √ 64+4 = √68
AC = BD = √68
therefore since the diagonals are equal in length, the quadrilateral will either be a square or rectangle.
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Find the total surface area of the prism.
7 ft
8 ft
5 ft
5 ft
Answers
Answer:
The total surface area of triangular prism
A = 232 foot²
Step-by-step explanation:
Explanation:-
Given bases of prism 5 f t , 5 f t , 7 f t
The perimeter of the sum of the bases
P = 7 + 5 +5 = 17 f t
Lateral surface area =perimeter X height
= 1 7 × 8
= 136 f t²
Base area of the triangular prism = \(\frac{1}{2} h ( b_{1} + b_{2} ) = \frac{1}{2} 8 ( 5 +7) =48\)
The total surface area of triangular prism
\(A = p h + 2 Base Area\)
\(A = p h + 2 Base Area = 136 + 2 ( 4 8 ) = 232\)
The total surface area of triangular prism
A = 232 foot²
In major need of help ‼️
Answers
Given: 140 students have I-Phones
Find: How many students have other types of phones
Variable: Independent variable- Survey, Dependent variable- Types of phones
Equation: 140 divided by 4
Solution: is
4/140
4/14= 3
4/20= 5
4/140 = 35
-----------------------------------------------------
I just want to write this just in case (you dont have to read this) Many people like myself have alot of problems with math, its really hard! Just keep on trying, I know that everybody says that but please take it into consideration. Work hard, have a nice day!
twice the sum of J and 4
Answers
Answer:
2(j+4)
Step-by-step explanation:
Answer:
\(\huge\boxed{\sf 2(J+4)}\)
Step-by-step explanation:
The sum of J and 4 = J + 4
Twice the sum of J and 4 = 2(J+4)
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807What is the horizontal asymptote of j(x)=14x^3+45/2x^3+x+9
Answers
Answer:
It's C! y = 7
Step-by-step explanation:
Anna volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday, 382 people went to The Youth Wing, 461 people went to Social Issues, and 355 went to Fiction and Literature. On Sunday, the library had 800 total visitors. Based on what Anna had recorded on Saturday, about how many people should be expected to go to The Youth Wing? Round your answer to the nearest whole number.
Answers
Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.
Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:
\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)
Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)
Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:
\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)
Calculating the proportion:
\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)
Calculating the estimated number of visitors to The Youth Wing on Sunday:
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)
Simplifying the equation:
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)
Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:
\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)
Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
find the average speed of a man that travel in 120km in 5hrs
Answers
Answer: 24 km/hour
Step-by-step explanation: 120/5= 24
If Richmond is 5cm from Santa Fe, what is the distance between the two cities in miles?
Answers
Using the scale factor
\(1\operatorname{cm}=125\text{miles}\)use the conversion to find the distance in miles
\(5\operatorname{cm}\cdot\frac{125\text{miles}}{1\operatorname{cm}}=625\text{miles}\)Simplify the expression:
7r–3r+9r
Answers
Answer:
13r
Step-by-step explanation:
-First, collect like terms by calculating the sum or difference of their coefficients.
(7-3+9)r
-Then, calculate the sum or difference and you get..
13r.
Hope this helps! :)
Answer:
13r
I think it is correct but just try making sure oater sorr if I a wrong though
A rectangular prism with a square base has a height of 17.2cm and a volume of 24.768cm². What is the length of its base?
Answers
The formula for the volume of a rectangular prism is:
V = lwh
where V is the volume, l is the length, w is the width, and h is the height.
We know that the height of the rectangular prism is 17.2 cm, and the volume is 24.768 cm³. We also know that the base is a square, so the length and width are the same. Let's call the length of the base x.
Then, we can write:
V = lwh
24.768 = x * x * 17.2
24.768 = 17.2x²
x² = 1.44
x = 1.2
Therefore, the length of the base of the rectangular prism is 1.2 cm.
The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.
In this problem, we know that the height is 17.2 cm, and the volume is 24.768 cm³. We also know that the base is a square, so the length and width are the same.
Therefore, we can write the equation:
24.768 = x² * 17.2
To solve for x, we can divide both sides by 17.2, and then take the square root of both sides:
x² = 24.768 / 17.2
x² = 1.44
x = sqrt(1.44)
x = 1.2
Therefore, the length of the base of the rectangular prism is 1.2 cm.
Poppy gets semi-monthly paycheck of $2,375. What is her annual income?
Answers
Answer:
57,000
Step-by-step explanation:
(2375*2)*12
not sure what semi monthly is but i assume it’s 2 times every month, times 12 months in a year, boom
Someone please help me
Answers
Answer:
13
Step-by-step explanation:
6 doubled is 12 plus one is 13
15. Kate has 63 pens. She gives all the pens to her 9 friends. Each friend gets
the same number of pens.
Kate said that when she divided the number of pens that each friend got by 9,
the answer was equal to 63. Her friend Margo said that when the number of
pens each friend got was multiplied by 9, the answer was equal to 63.
Which girl is correct? Explain your answer. I will mark as brainlist and vote if you answer
Answers
The girl which is correct between kate and her friend Margo is Margo.
The correct answer option is option B
How to multiply?Number of pens Kate has = 63Number of Kate's friends = 9If each friend gets the same number of pens;
Number of pens each friend get = Number of pens Kate has / Number of Kate's friends
= 63 / 9
= 7
Check:
Number of pens each friend get × Number of Kate's friends = Number of pens Kate has
7 × 9 = 63
Therefore, Kate's friend, Margo is correct.
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A shipping box is 36 inches by 24 inches by 18 inches
how many cubic feet can it hold
Answers
Answer:
To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.
Given:
Length = 36 inches
Width = 24 inches
Height = 18 inches
Converting the dimensions to feet:
Length = 36 inches / 12 inches/foot = 3 feet
Width = 24 inches / 12 inches/foot = 2 feet
Height = 18 inches / 12 inches/foot = 1.5 feet
Now, we can calculate the volume of the box by multiplying the length, width, and height:
Volume = Length * Width * Height
Volume = 3 feet * 2 feet * 1.5 feet
Volume = 9 cubic feet
Therefore, the shipping box can hold 9 cubic feet.
Step-by-step explanation:
First convert the units because it's asking for the cubic feet but they give us the measurements in inches.
To convert inches to feet we divide the number by 12.
36 ÷ 12 = 3
24 ÷ 12 = 2
18 ÷ 12 = 1.5
Now to find the volume, we multiply it all together.
3 × 2 × 1.5 = 9
It can hold 9 cubic feet.
Hope this helped!
A gardener made a scale drawing of a lawn with a scale
factor of 1:4. The dimensions of her drawing are 15 inches
long by 10 inches wide. Her partner plans to make another
scale drawing of the lawn, but with a scale factor of 1:20.
What are the dimensions of her scale drawing?
A. The length is 3 inches and the width is 2 inches.
B. The length is 50 inches and the width is 75 inches.
O c. The length is 2 inches and the width is 3 inches.
O D. The length is 75 inches and the width is 50 inches.
Answers
Answer: A.
Step-by-step explanation:
I just took the exam
can i get brainlyiest?
the candle was 1 inches long when new.Each half hour 3/4 inch of the candle burned away.After 4 hours,how long was the candle
Answers
After 2 hours, the candle would have burned away another 1.5 inches (4 half-hour periods * 3/4 inch burned in each period), leaving it with a length of 0 inches. At this point, the candle has completely burned down.
Therefore, after 4 hours, the length of the candle would be 0 inches.
An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be 95% confident that the sample mean is within 4 IQ points of the true mean.
What is the required sample size?
Answers
Answer:
55
Step-by-step explanation:
\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)
Make sure to always round up the required sample size to the nearest integer!
-750 DEGREE TO RADIAN
Answers
2pi = 360 degree
If we divide 360 by 2
Pi = 180 degrees
To find 1 radian in degree
180/pi
Cause
Pi = 180 degree
/pi /pi
1 radian = 189/ pi