A fountain on a lake sprays water in a parabolic arch modeled by the equation
y = −0.4x2 + 3x, where y is the height in feet and x is the horizontal distance. A beam of light is passed through the fountain to create a rainbow effect. If the beam is directed at an angle modeled by the equation -2.2x + 4.9y = 8.18, at what distance from the ground will the beam first touch the water spray?

A. 0.6 feet
B. 2 feet
C. 4.2 feet
D. 5.6 feet

Answers

Answer 1
Hello,

Answer B (2.0017868263...feet)

We must foind the intersection of the line and the parabola:

[tex]- \dfrac{4}{10} x^2+3x= \dfrac{22}{49}x+ \dfrac{818}{490}\\ ...\\ 196x^2-1250x+818=0\\ x= \dfrac{1250- \sqrt{921188} }{392}\approx0.7403433860\\ y=-0.4*0.74034...^2+3*0.74034...\approx2.0017868263... [/tex]


Related Questions

how many hours of training would you need to have a monthly pay of $2620

Answers

2620 /4 = 655 per week

 suppose you work 40 hours per week

655/40 = $16.38 per hour

that is a good pay, but training all depends on the actual job.

 some jobs don't require any training, some require 3 months or more.

 it also depends on your education

 

Jessica earns 3% commission selling computers she sold 37500 worth of computers last month how much commission did Jessica earn last month

Answers

Here,

3/100*37500
=1125

She earned total commission of 1125 last month

Type the number 3.14×103 in standard notation.

Answers

The answer is 3.14 x 10^3 

What is the area of the triangle in the diagram?

Answers

check the picture below.

Answer:

Option A is the answer.

Step-by-step explanation:

The area of the triangle is given as :

[tex]A=\frac{1}{2}\times base\times height[/tex]

Base will be given by :

[tex]\sqrt{(x1-0)^{2}+(y1-0)^{2}}[/tex]

= [tex]\sqrt{x1^{2}+y1^{2}}[/tex]

Similarly the height will be given by:

[tex]\sqrt{(x2-0)^{2}+(y2-0)^{2}}[/tex]

= [tex]\sqrt{x2^{2}+y2^{2}}[/tex]

Now, putting these dimensions in the formula we get:

[tex]\frac{1}{2}\times \sqrt{(x1^{2}+y1^{2})(x2^{2}+y2^{2})}[/tex]

Therefore, option A is the answer.

Rick is setting up a model train track that is 5 and 3 over 5feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone pole every 4 over 5foot apart. How many telephone poles does he need? (Input number values only)

Answers

That would be 5 3/5 divided by 4/5

= 28/5 / 4/5

= 28/5 * 5/4 

= 7  telephone poles

Answer:

1/2

Step-by-step explanation: man i needa level up... its not right i just need points lol

Ysidra paints a room that has 400 square feet of wall space in 2 and a half hours. at this rate, how long will it take her to paint a room that has 720 square feet of wall space?

Answers

1 hour 10 minutes /////

The time taken to paint a room which has a wall space of 720 feet² is equal to [tex]4\frac{1}{2}[/tex] hours.

What is the unitary method ?

The unitary method is a method in which you find the value of one unit and then the value of required no. of units.

It is given that room is painted that has wall space of 400 feet². The time taken to paint this space is 2 and half hours.

So , the wall space painted per hour will be :

= 400 ÷ [tex]2\frac{1}{2}[/tex]

= 400 ÷ [tex]\frac{5}{2}[/tex]

= 400 × [tex]\frac{2}{5}[/tex]

= 160 square feet per hour

We have to find out the time taken to paint a room which has a wall space of 720 feet². So , this will be calculated by dividing 720 square feet wall space by the per hour painted wall space that is equal to:

= 720 / 160

= 4.5 hours

or

= [tex]4\frac{1}{2}[/tex] hours

Therefore , the time taken to paint a room which has a wall space of 720 feet² is equal to [tex]4\frac{1}{2}[/tex] hours.

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James ran at a rate of 11.5 km per hour. What was james' speed in miles per hour? (NOT TO BE SOLVED. Needs to be an equation)

Answers

1km = 0.621371 miles

 so equation  is

total miles per hour = 11.5km * 0.621371

1. After a 12% increase the cost of a new cooker is £190.40

Work out the original price of the cooker.
[3 marks]



Answer £



2. A running club has 270 members.
There are 25% more men than women in the running club.

2. (a) How many men are in the running club?
[2 marks]




Answer


2. (b) 40% of the men and 30% of the women also belong to a cycling club.

Work out the percentage of the whole membership that belong to a cycling club.
[2 marks]



Answer %

Answers

1
X+.12*x=190.40
X(1+.12)=190.40
X=190.40/1.12=170

2a
X+x+25=100
2x=75
X=37.5%

Men=.375*270=101

2b

The required cost of the cooker after a 12% increase in the cost is given as  £213.248.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

1.
Let the cost of the cooker be x,
According to the question,
x = 1.12 × 190.40
x =  £213.248

Thus, the required cost of the cooker after a 12% increase in the cost is given as  £213.248.

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If angleA and angleB are vertical angles, and angleA = 38°, find the measure of angleB. A. B = 7° B. B = 57° C. B = 38° D. B = 142°

Answers

Angle B = 38° (option C)
This is because vertical angles are congruent

Hope this helps!! :)

Answer:

C. B = 38°

Step-by-step explanation:

A vertical angle is created when two lines intersect, and are a pair of two non adjacent angles that are opposite from the origin, so both angles are going to measure the same.

Since both vertical angles are the same, both measure 38º.

Vertical angles are shown in the image:In this case the angle A would be the omega, and the B is the alfa.

If NO = 17 and NP = 5x -6, find the value of X. Then find NP and NO.

Answers

Since NO=NP (as seen by the 2 lines next to each other), we get 
17=5x-6. Adding 6 to both sides, we get 23=5x and by dividing 5 on both sides we get x=23/5

If a person wanted to purchase their dream car, and keep it for many years, should they lease or buy? Why? (Site 1)

Answers

Buying an asset or a vehicle means paying off the entire sum of money that is the cost of the asset at the time of its purchase.

Leasing an asset means purchasing an asset by not paying the entire sum of money at the time of purchasing, rather paying in the form of rent over the period of time.

If a person wants to purchase his dream car for keeping for many years, then Buying Option is better because the payment of the overall cost in buying will be less than leasing.

This will also provide benefit that at the time of sale the owner will be paid off higher value of car as compared to car taken on lease.

For more information about leasing and buying, please refer to the link:

https://brainly.com/question/19843028

Final answer:

If a person wants to purchase their dream car and keep it for many years, it is generally recommended to buy rather than lease. Buying a car provides long-term ownership, customization options, and potential resale value, while leasing offers lower monthly payments but no ownership.

Explanation:

If a person wants to purchase their dream car and keep it for many years, it is generally recommended to buy rather than lease. Here are the reasons why:

Ownership: When you buy a car, you become the owner and have the freedom to modify or personalize the vehicle as you wish. Leasing, on the other hand, only provides temporary possession of the car.Long-term cost: Buying a car may have higher upfront costs, such as a down payment and monthly loan payments, but in the long run, you will own the vehicle. Leasing involves lower monthly payments, but you will not own the car at the end of the lease term.Resale value: Owning a car allows you to build equity over time. You can sell the car later and recoup some of the cost. Leasing does not provide this opportunity.

In conclusion, buying a car is a better option if you want long-term ownership and the ability to customize the vehicle. Leasing may be suitable for those who prefer lower monthly payments and don't want to commit to long-term ownership.

Joan works on commission

Answers

for a future store..

What is 4h-3 expression factored

Answers

Greetings!

This is not factor-able.
-No Common Factors, other than "1"
-Not a difference in squares
-Can't group

You can factor:
1(4h-3)
But, this is useless.

Hope this helps.
-Benjamin

Find an equation of the set of all points equidistant from the points a(−1, 6, 3) and b(4, 3, −2).

Answers

hello :
the set of all points M (x,y) equidistant from the points A(−1, 6, 3)
and B(4, 3, −2): 
MA = MB  or  MA² = MB²
an equation is : 
(x+1)²+(y -6)²+(z - 3)² = (x - 4)² +(y -3)² + (z+2)²

Standard printer paper has a thickness of 0.1mm. write an equation for a function that should approximately the thickness of a sheet of paper after nn folds. f(n)=f(n)=

Answers

Folding a paper will make it thickness become double from it before.
Unfolded paper has 1 thickness
1 times folded paper has 2 thickness
2 times folded paper has 4 thickness
3 times folded paper has 8 thickness

From here it is clear that the pattern is [tex] 2^{n} [/tex]. SInce the paper is 0.1mm, then the function would be:
f(n)= [tex] 2^{n} [/tex] x 0.1mm

The bakers healthy bakery can make 160 bagels in 5 hours. a.how many can they make in 1 hour? B.How many can they make in 12 hours?

Answers

A) Think of the amount as a fraction or ratio: 160/5 now, we want the denominator to be equivalent to 1 hour so we divide 5 by 5 to get 1. What we do to the bottom, we do to the top, so we do 160 divided by 5 = 32 bagels in 1 hour.
B) Now take 160/5 and set the denominator equal to 12. 5 times 2.4 equals 12, so then multiply 160 times 2.4 = 384 bagels in 12 hours. Hope this helps!

I believe it would be 32 in 1 hour. A: 160÷5=32
For the second part you multiply B: 32x12=384
so 384 bagels in 12 hours.

Change the line 3x − 8y = 5 into slope-intercept form.

Answers

slope is y=mx+b
m=slope
b=y intercept

solve for y basically


3x-8y=5
minus 3x both sides
-8y=-3x+5
divide both sides by -8
[tex]y=\frac{3}{8}x-\frac{5}{8}[/tex]

True or False
The sum of two trinomials is ALWAYS a trinomial

Answers

true because it is two triomials and it stay trinomials

Answer:

True.

Step-by-step explanation:

If the two trinomials are given as

x³ + 2x² + 4 = 0

and

2x³ + x² - 3 = 0

Then by adding these trinomials we get

(x³ + 2x² + 4) + (2x³ + x² - 3) = 0

3x³ + 3x² + 1 = 0

Which proves that sum of two trinomials is ALWAYS a trinomial.

So the answer is True.

The perimeter of a rectangular garden is 290 feet. If the length of the garden is 84 feet, what is its width?

Answers

Since the formula for the perimeter is 2l+2w=290 (given that the length=l and the width is w), we plug 84 in for l to get (2)(84)+2w=290. Next, we multiply it out to get 168+2w=290 and we subtract 168 from both sides to get 122=2w. Dividing 2 from both sides, we get 61=w. 
the width would be 61 ft

What is the scientific notation for 12,400,000?

Answers

1.24 x 10
hope i can help even though its late

Suppose point e has a coordinate of 11​, and eg= 8. what are the possible coordinates of point​ g?

Answers

So I will be assuming that EG = 8 is the length of the line segment EG. If that's the case, therefore the coordinates of G would simple be:

G =11 ± 8

G = 11 – 8, 11 + 8

G = 3, 19 

So G can have a coordinate of 3 or 19.

Andrea wants to deposit money into a bank account that earns 4.5% simple interest. Use the formula l=Prt to find the ammount of money that she should deposit so that she earns $2800 after 4.5 years. Show and explain your work.

Answers

The formula is
I=prt
I interest earned 2800
P amount deposited. ?
R interest rate 0.045
T time 4.5 years
Solve the formula for p by dividing both sides by rt to get
P=I/rt
P=2,800÷(0.045×4.5)
P=13,827.16 round your answer to get 13827

Hope it helps!

Help plz someone give me an answer

Answers

Greetings!

"Solve for x: [tex]7x-4+x=12[/tex]"...

Add like terms.
[tex]8x-4=12[/tex]
Add 4 to both sides.
[tex](8x-4)+4=(12)+4[/tex]
Simplify.
[tex]8x=16[/tex]
Divide both sides by 8.
[tex](8x)/8=(16)/8[/tex]
Simplify.
[tex]x=2[/tex]

The variable is equal to 2.

Hope this helps.
-Benjamin

(-4,7),(6,-1) what is the answer

Answers

(y+1)=-8/10 (x-6)
5y+5=-4x+24
5y=-4x+19
if you are finding a slope you must use the formula    y2-y1 / x2-x1

-1-7             -8           -4
-------  =     ------  =   -----
6--4            10            5


now to find the y intercept you need to plug either (-4,7) or (6,-1) into y=mx+b

7 = -4/5(-4) + b
7 = 3.2 + b
3.8 = b

the equation is        y = -4/5x + 3.8

What conjecture can you make about the twentieth term in the pattern A, B, A, C, A, B, A, C?

Answers

Answer:

c

Step-by-step explanation:

ABACABACABACABACABAC

Final answer:

The pattern A, B, A, C repeats every four terms. Dividing the term number (20) by the length of the repeating sequence (4) yields 5 with no remainder, indicating the twentieth term will be the same as the fourth term - which is 'C'.

Explanation:

The given pattern A, B, A, C, A, B, A, C is a repeating sequence that occurs in sets of four (A, B, A, C). To ascertain the twentieth term in this pattern, divide the term number by the length of the repeating sequence. That would be 20 divided by 4, which equals 5 with no remainder. That suggests the twentieth term will be the same as the fourth term in the sequence, which is C.

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Next school year, 2 out of every 7 students plan te take an elective computer course. if there are 2464 students at the high school, how many computer students should the school plan for?

Answers

2 out of every 7 students plan to take the course....that means 5 out of every students do not plan to take it. So 2/7 of the total students plan to take it and 5/7 of the total students do not plan to take it.

so 2/7 of 2464 plan to take the course.....2/7(2464) = 4928/7 = 704 students ...the school need to plan for 704 students <==

A problem states: " there are 3 more baseballs than bats in a dugout. There are 15 bats and baseballs in the dugout in all. How many bats are in the dugout?" Let b represent the number of bats. Which expression represents the situation?

Answers

9 baseballs and 6 bats

Answer:

The required equation is 2b+3=15.

Number of bats = 6

Number of baseballs = 9

Step-by-step explanation:

Let b be the number of bats.

It is given that there are 3 more baseballs than bats in a dugout.

Number of baseballs = b + 3

Number of bats and baseballs in the dugout in all is

[tex]Total=b+(b+3)[/tex]

[tex]Total=(b+b)+3[/tex]

[tex]Total=2b+3[/tex]

There are 15 bats and baseballs in the dugout in all.

[tex]2b+3=15[/tex]

The required equation is 2b+3=15.

Subtract 3 from both sides.

[tex]2b=15-3[/tex]

[tex]2b=12[/tex]

Divide both sides by 2.

[tex]b=6[/tex]

The value of b is 6. So, the number of bats is 6 and number of baseballs is 6+3=9.

What is 4 7/8 as a improper fraction

Answers

The answer is 39/8. You had to multiply 4 by the denominator, you'd get 32; and add the numerator. which would get you 39. Simply place the 39 over 8, the denominator, and Voila! you get 39/8
[tex]a \frac{b}{c} = \frac{ac+b}{c} [/tex]


[tex] \frac{4 x 8 + 7}{8} = \frac{39}{8} [/tex]  <--- Answer

What is the largest decimal value that can be represented by a 16 bit number?

Answers

i dont know bro sorry

Distributive property 3(-7-8n)

Answers

3 (-7-8n)
3 x -7= -21
3 x -8n= -24n
-21-24n= 45n

Answer:

- 21 - 24 n.

Step-by-step explanation:

Given  : 3(-7-8n)

To find : Solve by  Distributive property .

Solution : We have given 3(-7-8n).

Distribute 3 over -7 and - 8n .

3 * - 7+ 3 * -8n .

- 21 + ( -24 n).

- 21 - 24 n.

Therefore, - 21 - 24 n.

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