Answer:
3
Step-by-step explanation:
Parabola Equations - Algebra
Please explain working clearly.
Help greatly appreciated,
Thanks!
Answer:
[tex]\displaystyle h=-\frac{1}{6}x^2+2x[/tex]
Step-by-step explanation:
We are given that the height of the tunnel is modeled by:
[tex]h=rx^2+tx[/tex]
Where r and t are constants.
We are also given that the maximum height of the tunnel h is six meters.
And at ground level, the width is 12 meters.
And we want to determine the equation of the parabola.
First, since this is a quadratic, our maximum height h will occur at the vertex of our equation.
Recall that the vertex is given by the formulas:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In our case, we have the function:
[tex]h=(r)x^2+(t)x[/tex]
Hence, a = r; b = t; and c = 0.
Therefore, the x-coordinate of our vertex is:
[tex]\displaystyle x = -\frac{t}{2r}[/tex]
Therefore, if we substitute this back into our equation, the result should be six since six is the maximum height. Hence:
[tex]\displaystyle (6)=r\left(-\frac{t}{2r}\right)^2+t\left(-\frac{t}{2r}\right)[/tex]
Simplify:
[tex]\displaystyle 6=r\left(\frac{t^2}{4r^2}\right)-\frac{t^2}{2r}[/tex]
Simplify:
[tex]\displaystyle 6=\frac{t^2}{4r}-\frac{t^2}{2r}[/tex]
Subtract:
[tex]\displaystyle 6=\frac{t^2}{4r}-\frac{2t^2}{4r} = -\frac{t^2}{4r}[/tex]
Multiply:
[tex]\displaystyle 24r=-t^2, \, r\neq 0[/tex]
Solve for r:
[tex]\displaystyle r=-\frac{t^2}{24}[/tex]
Next, we are given that the width is 12 meters at ground level.
Hence, when h = 0, the difference of our roots is 12:
We have:
[tex]0=rx^2+tx[/tex]
Factor:
[tex]0=x(rx+t)[/tex]
By the Zero Product Property:
[tex]x=0\text{ or } rx+t=0[/tex]
Hence, the first zero is 0.
Therefore, the second zero must be 12 to ensure that our width is 12.
Let's isolate the second zero. Subtract t from both sides:
[tex]rx=-t[/tex]
Divide both sides by r:
[tex]\displaystyle x=-\frac{t}{r}[/tex]
We know that this zero must be 12. Thus:
[tex]\displaystyle 12=-\frac{t}{r}[/tex]
We have previously solved for r. Substitute:
[tex]\displaystyle 12=-\frac{t}{-\dfrac{t^2}{24}}[/tex]
Simplify:
[tex]\displaystyle 12=\frac{24}{t}[/tex]
Take the reciprocal of both sides:
[tex]\displaystyle \frac{t}{24}=\frac{1}{12}[/tex]
Multiply. Hence, the value of t is:
[tex]t=2[/tex]
Find r. Recall that:
[tex]\displaystyle r=-\frac{t^2}{24}[/tex]
Therefore:
[tex]\displaystyle r=-\frac{(2)^2}{24}=-\frac{4}{24}=-\frac{1}{6}[/tex]
Then in conclusion, our equation will be:
[tex]\displaystyle h=-\frac{1}{6}x^2+2x[/tex]
A special blend of coffee beans is going to be sold in cylindrical canisters whose dimensions always have a height that is two more inches than the radius. The table shows various volumes, V(r), for the given radii, r.
Answer:
Option C, V(r)=πr^3+2πr^2
Step-by-step explanation:
did on edge
Please help quick
Screenshot Below ( WILL mark as brainliest )
Answer:
-1/3
Step-by-step explanation:
Our points are as follows:
x1= 0
y1= 2
x2= 3
y2= 1
Now we use the slope formula rise/run and we plug in the numbers
1-2= -1
3-0= 3= -1/3
Pls it’s really importa I need help !!
Answer:
i cant see the picture clearly it is blury sorry cant help if it is like that!!!!
Step-by-step explanation:
Can someone please help!!! I’ll give brainlest!!
Answer:
1750 calories
Step-by-step explanation:
2000 on average
1750 for his diet
2000 x 7 = 14,000
1750 x 7 = 12,250
14,000 - 12,250 = 1750
Which line is parallel to y = 3x - 1? *
y = 4x - 1
y = -3x + 5
y = 3x
y = -3x + 6
Answer:
y=3x
Step-by-step explanation:
parallel means same x value when talking about graphs
Answer:
y=3x
Step-by-step explanation:
because parallel line mean they got same slope and in y=3x-1 equation the slope is 3x. so, the same slope is 3x.
don´t forget to brainllest!:)
NEED ANSWER ASAP ONLY 4 min
Answer:
A
Step-by-step explanation:
-4x-10≤2
-4x≤12 Add 10 on both sides
-x≤3 Divide by 4 on both sides
x≤-3 put a negative on both sides
Hope this helps :D Please mark brainliest if correct :D
Answer:
[tex]x \geqslant - 3[/tex]
it's b
Which models best illustrates the inequality and its graph?
t is at most 55
t is 55 or more
t is at least 55
t is less than 55
Mr. Smith went to buy a refrigerator. He had $346. The refrigerator cost $783.
Part A
About how much more money does Mr. Smith need in order to buy the refrigerator?
Round your answer to the nearest hundred dollars.
Part B
After visiting the bank ,Mr.Smith paid $800 for the refrigerator.How much change did he receive Mr.Smith receive in change ?
Answer:
Part A- $400
Part B- $17
Step-by-step explanation:
Answer:
A- 400.00 more dollars.
B- 17 dollars in change.
Step-by-step explanation:
783-346 and then round up.
800-783 for change
Steve can run 1 2/9 miles in 10 minutes. How many miles can he run in 30 minutes?
Answer:
3 2/3
Step-by-step explanation:
remember to give me brainliest cause I helped you
what is the distance between -48 and 17 on a number line
Answer:
65
Step-by-step explanation:
Answer:65
Step-by-step explanation: this may or may not be right just draw out a number line and count the spaces
5x + 2x =
can i get help fast please
Answer:
7x
Step-by-step explanation:
You add the two numbers and bring over your variable.
John writes the proof below to show that the sum of the angles in a triangle is equal to 180 degrees
Which would John NOT need to use in his proof?
A.The sum of the angles on ore side of a straight line is 180
B. If a statement about a is true and a = b statement formed by replacing a with b is also true.
C.When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
D. When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent
Answer: A
Step-by-step explanation:
The proof that is not needed John's proof is When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent
The following proof are needed.
When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. This is why ∠4≅∠1 and ∠5≅∠3. The sum of the angles on one side of a straight line is 180. That is why m∠4 + m∠2 + m∠5 = 180°If a statement about a is true and a = b statement formed by replacing a with b is also true.m∠4 + m∠2 + m∠5 = 180° (sum of angles on a straight line)
∠4≅∠1 and ∠5≅∠3 (alternate interior angles)
Therefore,
∠1 can replace ∠4 and ∠3 can replace ∠5
m∠1 + m∠2 + m∠3 = 180°
Therefore, When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent is not needed.
read more: https://brainly.com/question/19633821?referrer=searchResults
A popular news article currently has 50,600 page views, and that number is rising 36% every hour. How many page views will the article have in seven hours? If necessary round your answer to the nearest whole number
Answer: 320,172 views
Step-by-step explanation: To figure this out first multiply 50,600 by .36, finding out what the 36% increase is, the get the answer which is 68,816. Then you continue and do that six more times to get the answer of 320,172.45573 which rounded is 320,172 views.
Hudson and know are running a race. Know got a 30 foot head start. Hudson is running at 8.8 feet per second. Know is running at 6.3 feet per second. How many seconds until know and Hudson are at the same place.
Answer:
It will take 12 seconds to be at same distance Step-by-step explanation:
hope it helps
!!!HELP ME WITH THIS QUESTION PLEASE!!!
Answer:
-6
Step-by-step explanation:
f(4)=2(4)-14
=8-14
=-6
What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation? What number would you multiply the first equation by in order to eliminate the y-terms when adding to the second equation?
Answer:
1. Multiply (2) by 2 to eliminate the x-terms when adding
2. Multiply (2) by 3 to eliminate the y- term
Step-by-step explanation:
Use this system of equations to answer the questions that follow.
4x-9y = 7
-2x+ 3y= 4
what number would you multiply the second equation by in order to eliminate the x-terms when adding the first equation?
4x-9y = 7 (1)
-2x+ 3y= 4 (2)
Multiply (2) by 2 to eliminate the x-terms when adding the first equation
4x-9y = 7
-4x +6y = 8
Adding the equations
4x + (-4x) -9y + 6y = 7 + 8
4x - 4x - 3y = 15
-3y = 15
y = 15/-3
= -5
what number would you multiply the second equation by in order to eliminate the y- term when adding the second equation?
4x-9y = 7 (1)
-2x+ 3y= 4 (2)
Multiply (2) by 3 to eliminate the y- term
4x - 9y = 7
-6x + 9y = 12
Adding the equations
4x + (-6x) -9y + 9y = 7 + 12
4x - 6x = 19
-2x = 19
x = 19/-2
= -9.5
x = -9.5
Answer:
3 and 2
Step-by-step explanation:
i did the thing
Four friends purchase a pineapple for $2.89 and 18.4 pounds of peaches. The peaches cost $1.75 per pound. The friends share the total cost equally.
What amount does each person pay?
$8.77
$9.31
$21.34
$35.09
Answer:
$8.77
Step-by-step explanation:
Total cost = 2.89 + 18.4*1.75
= 2.89 + 32.2
= $35.09
Amount paid by each person = $35.09/4
= $8.77
Answer:
Four friends purchase a pineapple for $2.89 and 18.4 pounds of peaches. The peaches cost $1.75 per pound. The friends share the total cost equally.
What amount does each person pay?
$8.77
$9.31
$21.34
$35.09 The right answer is A. 8.77 I took the quiz and I got 100%
Step-by-step explanation:
b. (6.91 X 10-2) + (2.4 x 10-3)
Answer:
91.82
Step-by-step explanation:
Download the free app Socratic. The app looks like a picture of an owl. It can help you with at least 98% percent of your math problems. Hope this helped :)
Find the inverse of the function.
y = 4x
Answer: f-1 (x) = x/4
Step-by-step explanation:
Write the slope-intercept form of the equation of the line given the slope and the y-intercept.
8
Slope = -
y-intercept = 4
3
Answer:
The answer is y=-8/3x + 4
Step-by-step explanation:
There is this format called linear function where it looks like this
y=mx + b
where m is the slope and b is the y-intercept
pls mark me as brainliest
PLEASE HELP NEED FAST
Answer:60
Step-by-step explanation:
Answer:
45 hope this helps! If its wrong let me know!
Helppp!! evaluate (-6)^3
Answer:
-216
Step-by-step explanation:
Answer: the equation would be -6 x -6 x -6 = 216
Step-by-step explanation:
-3.2 < -3 Is this true or false?
Answer:true
Step-by-step explanation: because -3.2 is smaller than -3 because negatives get smaller the bigger the negative
Which set of numbers form a right angle? Choose ALL that apply.
A. 1,2,3
B. 3, 4, 5
C. 15, 20, 25
D. 6, 8, 10
E. 8, 15, 18
Answer:ABCDEF
Step-by-step explanation:
The table represents the speed of a car in a northern direction over several seconds.
A 2-column table with 5 rows. The first column labeled Column 1 has entries 0, 2, 4, 6, 8, 10. The second column labeled Column 2 has entries 5, 10, 15, 20, 25, 30.
Column 1 would be on the x-axis, and Column 2 would be on the y-axis. Which best lists the titles of each column?
Column 1 should be titled “Time,” and Column 2 should be titled “Velocity.”
Column 1 should be titled “Velocity,” and Column 2 should be titled “Time.”
Column 1 should be titled “Time,” and Column 2 should be titled “Acceleration.”
Column 1 should be titled “Acceleration,” and Column 2 should be titled “Time.”
Answer:
Column 1 should be titled “Time,” and Column 2 should be titled
“Velocity.” ⇒ 1st answer
Sorry for being super late
what is the slope of (16,2) and (32,4)
Answer:
0.125
Step-by-step explanation:
Please help! I’ll give brainliest :)
X = ___ ??
Y = ___ ??
Answer:
X=60 degrees Y=30 degrees
Step-by-step explanation:
simplify completely 1/2 +1/4
Answer:
1/2+1/4
4/8+2/8
6/8
3/4
Step-by-step explanation:
Answer:
The answer is 3/4.
Step-by-step explanation:
1/2+1/4
First we want to get a common denominator so that they can be added together.
1/2 * 2/2 = 2/4
We multiplied 1/2 by 2/2 so that both terms have a denominator of 4. Note that we also multiplied the top and bottom of 1/2 because we have to keep the value of the fraction the same.
Now we just add the fractions together.
2/4 + 1/4 = 3/4
So 3/4 is the answer. It is already in its simplest form meaning it cannot be simplified further.
“Ms. Kits works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kits sold a total of 110 CDs over the 2 weeks. How many CDs did she sell last week and this week?” How do I write this as 2 equations with 2 variables?
Answer:
Ms kits sold 336 CDS
Step-by-step explanation:
I cant help with the last part sorry dont listen to my answer
