If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, determine a quadratic model to represent the tunnel.
State a geometric model that could be used to represent a truck passing through the tunnel.
Answers
Answer:
TUNNEL:
f(x) = -2/4.9 [tex]x^{2}[/tex] + 9.8
TRUCK:
Width (m) < 9.8
Height (m) < -2/4.9 ( [tex]Width^{2}[/tex] /4 - [tex]4.9^{2}[/tex] )
Step-by-step explanation:
Please see attachment
If the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.
What is a quadratic function?Any function of the form[tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
It is given that, If the maximum height of the tunnel is the same as its maximum width, 9.8 meters.
We have to determine a quadratic model to represent the tunnel.
The quadratic function is formed as,
f(x) =K(x-x₁)(x-x₂)
x₁=width/2
x₁=9.8/2 = 4.9
x₂= -x₁ = -4.9
Substitute the obtained value as,
f(x) = K(x-4.9)(x-(-4.9))
f(x) =K(x²-4.9²)
f(0)=9.8
The value of K is obtained as a result,
K=-2×4.9/(4.9)²
K= -2/4.9
Substitute the value of K as,
f(x) = -2/4.9(x²-4.9²)
f(x) = (-2/4.9)x²+2×4.9
f(x)= (-2/4.9)x²+9.8
Thus, if the maximum height of the tunnel is the same as its maximum width, 9.8 meters, The quadratic model to represent the tunnel will be f(x)= (-2/4.9)x²+9.8.
Learn more about quadratic function here:
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Related Questions
If the principal is $612 and the rate of interest is 2.85%, what is the amount of interest after eight years?
Answers
Answer:
$766.28
Step-by-step explanation:
The equation for interest rate is as follows:
[tex]A = P(1 + r)^t\\[/tex]
A = The total amount
P = Initial amount
R = The interest rate
T = Time
Let's plug everything into the equation that is given in the question:
The initial amount = 612
Interest rate = 2.85
Time = 8 years
[tex]A = 612(1+.0285)^8[/tex]
***Just a reminder we move the decimal over twice when working with percents***
Now, lets solve for the total amount:
[tex]A = 612(1.0285)^8\\A = 612(1.252086602)\\A = 766.28[/tex]
Therefore, after 8 years the principal is $766.28.
I hope this helps!!
If you have any questions feel free to ask!
- Kay :)
The radius of a cone is decreasing at a constant rate of 5 centimeters per minute, and the volume is decreasing at a rate of 148 cubic centimeters per minute. At the instant when the radius of the cone is 222 centimeters and the volume is 21 cubic centimeters, what is the rate of change of the height? The volume of a cone can be found with the equation V=1/3πr^2h. Round your answer to three decimal places.
Answers
Answer:
The rate of change for the height of the cone is [tex]-2.849\times 10^{-3}[/tex] centimeters per minute.
Step-by-step explanation:
We derive an expression for the rate of change for the height of the cone by differentiating the volume formula given on statement:
[tex]\dot V = \frac{\pi}{3}\cdot (2\cdot r\cdot h \cdot \dot r + r^{2}\cdot \dot h)[/tex] (1)
Where:
[tex]\dot V[/tex] - Rate of change for the volume of the cone, measured in cubic centimeters per minute.
[tex]r[/tex] - Radius of the cone, measured in centimeters.
[tex]h[/tex] - Height of the cone, measured in centimeters.
[tex]\dot r[/tex] - Rate of change for the radius of the cone, measured in centimeters per minute.
[tex]\dot h[/tex] - Rate of change for the height of the cone, measured in centimeters per minute.
If we know that [tex]\dot V = -148\,\frac{cm^{2}}{min}[/tex], [tex]r = 222\,cm[/tex], [tex]V = 21\,cm^{3}[/tex], [tex]\dot r = -5\,\frac{cm}{min}[/tex], then the rate of change for the height is:
[tex]h = \frac{3\cdot V}{\pi\cdot r^{2}}[/tex] (2)
Where [tex]V[/tex] is the volume of the cone, measured in cubic centimeters.
[tex]h = \frac{3\cdot (21\,cm^{3})}{\pi\cdot (222\,cm)^{2}}[/tex]
[tex]h \approx 4.069\times 10^{-4}\,cm[/tex]
From (1):
[tex]\frac{3\cdot \dot V}{\pi} = 2\cdot r\cdot h\cdot \dot r + r^{2}\cdot \dot h[/tex]
[tex]r^{2}\cdot \dot h = \frac{3\cdot \dot V}{\pi}-2\cdot r\cdot h\cdot \dot r[/tex]
[tex]\dot h = \frac{3\cdot \dot V}{\pi\cdot r^{2}}-\frac{2\cdot h\cdot \dot r}{r}[/tex]
[tex]\dot h = \frac{3\cdot \left(-148\,\frac{cm^{3}}{min} \right)}{\pi\cdot (222\,cm)^{2}} -\frac{2\cdot (4.069\times 10^{-4}\,cm)\cdot \left(-5\,\frac{cm}{min} \right)}{222\,cm}[/tex]
[tex]\dot h = -2.849\times 10^{-3}\,\frac{cm}{min}[/tex]
The rate of change for the height of the cone is [tex]-2.849\times 10^{-3}[/tex] centimeters per minute.
One species of fish in a fishery had an initial population
of 255 fish and after 9 seasons, the population had grown to
480 fish. A second species that was being overfished started
with an initial population of 450 fish, and after the same 9
seasons, it had a new population of 90 fish. Assuming a
linear growth, write the equations for the population of
•each species. Graph your equations in the coordinate plane.
Find the point in the graph which represents when the two
populations will have the same number of fish. After how
many seasons will the second population be eliminated?
Answers
9514 1404 393
Answer:
y = 25x +255y = -40x +450(3, 330)11 1/4 seasonsStep-by-step explanation:
The 2-point form of the equation of a line is useful for these problems. It is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
__
a) The two points are (0, 255) and (9, 480). The equation is ...
y = (480 -255)/(9 -0)(x -0) +255
y = 25x +255
__
b) The two points are (0, 450), (9, 90). The equation is ...
y = (90 -450)/(9 -0)(x -0) +450
y = -40x +450
__
c) The point where both populations are the same is (3, 330).
__
d) The second population will be eliminated after 11 1/4 seasons.
Please help need this fast I’m timed.
-28
-3
3
15
Answers
Answer:
-28
Step-by-step explanation:
-28
Explanation: you have to use PEMDAS
From each of the following sets make all possible ordered pairs,
(a) P= {x,y)
(b) X= {1, 2, 3)
Answers
Answer:
All possible ordered pairs are as follows:
{(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)}Step-by-step explanation:
In an ordered pair (x, y),
x is called the first component y is called the second component.Let
P = {x, y}
X = {1, 2, 3}
The number of elements in the set P = n(P) = 2The number of elements in the set X = n(X) = 3So, the number of possible ordered pairs = 2 × 3 = 6
Therefore, all possible ordered pairs are as follows:
{(x, 1), (x, 2), (x, 3), (y, 1), (y, 2), (y, 3)}can anyone help me with this problem
Answers
Answer:
third option
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
[tex]\frac{1}{4}[/tex] [tex](2)^{k-1}[/tex] ← is in this form
with a₁ = [tex]\frac{1}{4}[/tex] and r = 2
in 2011, there were 3223 sea otters in monterey Bay is approximately 77 square miles. to the nearest whole number, what was the density of the sea otter population? (explain your answer)
Answers
Answer:
42 sea otters per mi2
{(2,2),Is this a function?
Answers
As Jupiter revolves around the sun, it travels at a speed of approximately 8 miles per second. Convert this speed to kilometers per second. At this speed, how
many kilometers will Jupiter travel in 15 seconds? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers
Answers
Answer:
Speed is 12.8km/sec. Jupiter will travel 192km in 15 sec.
Step-by-step explanation:
[tex]\frac{8mi}{1sec} * \frac{1.6km}{1mi} = 12.8km/sec[/tex]
[tex]\frac{12.8km}{1sec} * 15sec = 192km[/tex]
POSSIBLE POINT
Ms. Gomer-Weyh loves to ski! She joined a local ski club which is featuring a special $20 registration fee plus $30 per visit for up to 4 visits.
Write the equation and make a graph that models the situation.
Answers
Answer:
I can only make an equation
20+30(4)+y(z)=X
Step-by-step explanation:
SO we know the registration fee is 20 dollars so that can’t change
We know that its 30 dollars for up to 4 visits so 30*4
THe Y is for the amount it take to ski after the 4 times
The Z is for the amount of times you went after the 4 times
So yeah
How many \frac{1}{3} 3 1 inch cubes does it take to fill a box with width 22 \frac{2}{3} 3 2 inches, length 33 \frac{1}{3} 3 1 inches, and height 22 \frac{1}{3} 3 1 inches?
Answers
Answer:
560Step-by-step explanation:
First we need to find the volume of the cube;
Volume = Length * Width * height
Given;
Length = 3 1/3 in
Width = 2 2/3 in
Height = 2 1/3 in
Volume = 3 1/3 * 2 2/3 * 2 1/3
Volume = 10/3 * 8/3 * 7/3
Volume = 560/3 in^3
To know thw amount of 1/3 in^3 it takes to fill the box, we will take the ratio of the volume to the unit volume;
Ratio = 560/3÷1/3
Ratio = 560/3 * 3/1
Ratio = 560
Hence it will take 560 1/3 in^3 to fill a box with that volume
from 2000 to 2010, the population of Florida increased by 23.5%. the population in 2000 was 15,982,378
Answers
Answer:
ok
Step-by-step explanation:
ANSWER PLSSS!!!!!!
What is Ann's speed at 7 mins? give a reason to support your answer
Answers
Answer:
She drove 4 minutes
Step-by-step explanation:
| 18| - | - 10| what is the absolute value
Answers
Answer:
16
Step-by-step explanation:
Answer:
Step-by-step explanation:
the absolute value of 18 is 18 because absolute value is the distance from zero. the calculate value of -10 is 10. 18-10=8
|18| - |-10| =
18 - 10 = 8
15t +95 + 5 - 9
i need help asap
Answers
A jar contains 444 red marbles, 444 green marbles, and 555 blue marbles.
If we choose a marble, then another marble without putting the first one back in the jar, what is the probability that the first marble will be blue and the second will be green?
Answers
Answer:
5/39
Step-by-step explanation:
Write a Proof statement,
Answers
Answer:
Step-by-step explanation:
Given:
MO bisects ∠KMN and LO bisects ∠KLN
To prove:
LK ≅ LN
Statements Reasons
1). MO bisects ∠KMN 1). Given
2). LO bisects ∠KLN 2). Given
3). ∠KLM ≅ ∠NLM 3). Definition of angle bisector
4). ∠KMO ≅∠NMO 4). Definition of angle bisector
5). ∠KMO + ∠KML = 180° 5). Linear pair postulate
6). ∠NMO + ∠NML = 180° 6). Linear pair postulate
7). ∠KMO + ∠KML = ∠NMO + ∠NML 7). Transitive property of equality
8). ∠KMO + ∠KML = ∠KMO + ∠NML 8). Substitution property
9). ∠KML = ∠NML 9). Subtraction property of equaity
10). LM ≅ LM 10). Reflexive property
11). ΔLKM ≅ ΔLNM 11). ASA property of congruence
12). LK ≅ LN 12). CPCTC
Which list shows these numbers in order from least to greatest?
Answers
It would be
B since it is in least to greatest order
Answer:
-3,-2,0,2,3 [c]
Step-by-step explanation:
I had that quiston on my warm up [edge 2021] and got it right
i first tried b and that didnt work
After w weeks , a student has saved 100 + 15w dollars. How much money has the student saved after 3 weeks ?
A$105
B$65
C$120
D$145
Answers
Answer:
The student will have $145
Step-by-step explanation:
The student would already have $100 and if you take 15 times the number of weeks, 3 weeks. 15 times 3 is $45. $100 + $45 = $145
Answer:
D. $145
Step-by-step explanation:
In order to find out the answer to the equation 100 + 15w = ? we have to multiply 15 by the 3 weeks the student has saved up 15 dollars to get the total money they have saved by saving 15 dollars per week:
15 * 3 = 45
we then add the 100 dollars that was already saved up to 45
100 + 45 = $145
So after 3 weeks $145 have been saved up
Hope this helps!!!
Let p(x)=x^3+15x^2-8x+2. What is the remainder when p(x) is divided by x-2?
Answers
Answer:
Step-by-step explanation:
Using synthetic division, the zeros goes into the box, which would be -1
-1 | 1 -3 -1 24
-1 4 -3
1 -4 3 21
The remainder is 21
Renee spent 1/8 of the day landscaping around the house. She spent half of the time pulling weeds. What fraction of the day did rehne spend pulling weeds?
Answers
Answer:
The fraction of the day Rehee spent pulling weeds = 1/16
Step-by-step explanation:
Let us take the fraction representing a whole day to be a whole number - 1
Renee spent 1/8 of the day landscaping around the house.
This means she spent 1/8 X 1 landscaping around the house = 1/8
She spent half of the time pulling weeds.
This means she spent 1/2 of 1/8 of 1 landscaping around the house = 1/16
1/2 X 1/8 X 1 = 1/16
The fraction of the day Rehee spent pulling weeds = 1/16
can someone plz help me with this question ASAP. drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. the organizers of a founders day festival on main street surveyed local businesses to see if they would be offering any promotions to customers during the festival. the table contains the data gathered.
Answers
Answer:
hello the geinus has arrived
What is the surface area of the rectangular prism?
3 in.
12 in.
9 in
A
358 in
B
342 in?
315 in
D
306 in
Answers
Answer: the answer is b
Step-by-step explanation:
Answer:
Oh im doing my star 360 test rn too!
Step-by-step explanation:
Pls answer if u know :)
This is a very important homework and i was gone for days so idk
Answers
Answer:
Option B
Step-by-step explanation:
Slope of the line is calculated by the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\[/tex]
We have the points ( -2 , 4) and (3 , -5) so plug in the values in the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-5-4}{3-(-2)}\\\\m=\frac{-9}{5}\\[/tex]
so the slope(m) equals -9/5
The radius of a circle is 6 yards. What is the circle's area?
Use 3.14 for PI
Answers
Answer:
113.04
Step-by-step explanation:
To calculate a circle's area, the formula is Pi R Squared. R is radius. Radius squared would be 36. (6*6) Now, multiplied by Pi, the area would be: 113.04. (36*3.14)
Answer:
113.04
Step-by-step explanation:
The radius of a circle is 6 yards. What is the circle's area?
r=6 yd
Use 3.14 for .
square yards
You answered:
113.1
square yards
remember
Use this formula to find the area from the radius.
A=r2
Use 3.14 as an approximation for .
≈3.14
solve
The radius is 6 yards. Replace r by 6 in the formula.
A
= r2
≈ 3.1462
≈ 3.1466
≈ 113.04
The area is about 113.04 square yards.
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Javier often orders party trays from his favorite Mexican food restaurant for company events. For a recent company event, he spent $259 on 4 burrito platters and 2 taco platters. For a company meeting, he spent $284 on 4 burrito platters and 4 taco platters. How much does each type of platter cost?
and
Jeff is a shoe salesman, and he works on commission. This week, there is a special incentive to sell shoes and boots by a certain company. Yesterday, Jeff sold 8 pairs of shoes and 7 pairs of boots, earning $188 in commission. Today, he sold 8 pairs of shoes and 6 pairs of boots, earning a total commission of $168. How much does Jeff earn for the sale of each type of footwear?
Answers
Answer:
1. 1 Burrito Platter = $58.50 , 1 Taco platter = $12.50
2. One pair of boots = $20 , One pair of shoes = $6
Step-by-step explanation:
1. Let the cost of one burrito platter be x and one taco platter be y.
4x + 2y = 259 --- Equation 1
4x + 4y = 284 --- Equation 2
Equations 2-1: 4x + 4y - 4x - 2y = 284 - 259
2y = 25
y = 25 ÷ 2
y = 12.50 (Taco platter)
Substitute y = 12.50 into Equation 1:
4x + 2y = 259
4x + 2(12.50) = 259
4x + 25 = 259
4x = 259 - 25
= 234
x = 234 ÷ 4
x = 58.50 (Burrito platter)
2. Let the cost of one pair of boots be x and one pair of shoes be y.
7x + 8y = 188 --- Equation 1
6x + 8y = 168 --- Equation 2
Equations 1-2: 7x + 8y - 6x - 8y = 188 - 168
x = 20 (Boots)
Substitute x = 20 into Equation 2:
6x + 8y = 168
6(20) + 8y = 168
120 + 8y = 168
8y = 168 - 120
= 48
y = 48 ÷ 8
y = 6 (Shoes)
Marley got 18 questions right on her lastest math test. When she checked her score in Aspen she saw that was 90%. How many questions were on the test?
Answers
Answer:
20 questions were on the test
Step-by-step explanation:
18 questions = 90%1 question = 5%20 questions = 100%Therefore, there were 20 questions on the test.Which equation represents a line which is perpendicular to the line y = 4/3x-6
Answers
Last month you spent $40 on clothing. This month you spent 120% of what you spent last month. Set up a proportion to model this situation. How much did you spend this month?
Answers
Answer:
$48
Step-by-step explanation:
Given that:
Money spent on clothing last month = $40
Money spent this month is 120% of the spending of the last month.
To find:
A proportion to model this situation.
And the spending done this month?
Solution:
Let us have a look at 120% first.
[tex]120\%= \dfrac{120}{100} = \dfrac{6}{5}[/tex]
[tex]\frac{6}{5}[/tex] of [tex]x[/tex] can be found by comparing [tex]x[/tex] with 5, then we have to find the equivalent of 6.
Here, [tex]x[/tex] is 40.
5 parts are equivalent to 40
1 part is equivalent to [tex]\frac{40}{5} = 8[/tex]
6 parts are equivalent to [tex]8\times 6 = 48[/tex]
OR
simply:
[tex]40 \times \dfrac{120}{100} = 48[/tex]
What was the difference in the starting temperature and the ending temperature
Answers
Answer:
You subtract the final temperature from the starting temperature to find the difference. So if something starts at 50 degrees Celsius and finishes at 75 degrees C, then the change in temperature is 75 degrees C – 50 degrees C = 25 degrees C. For decreases in temperature, the result is negative.
Step-by-step explanation: really not sure how to explain but in my understood thats my answer