A truck that is 11 feet tall and 7 feet wide is traveling under an arch. The arch can be modeled by:

y=-0.0625x+1.25x +5.75 where x and y are measured in feet.



a) Will the truck fit under the arch? Explain (with numerical details).

BIRD



b) What is the maximum width that a truck 11 feet tall can have and still make it under the arch?

Answers

Answer 1

Answer:

Yes

8 ft

Step-by-step explanation:

The equation of the arch is

[tex]y=-0.0625x^2+1.25x+5.75[/tex]

Differentiating with respect to [tex]x[/tex] we get

[tex]\dfrac{dy}{dx}=-2\times 0.0625x+1.25=-0.125x+1.25[/tex]

Equating with zero

[tex]0=-0.125x+1.25\\\Rightarrow x=\dfrac{-1.25}{-0.125}\\\Rightarrow x=10[/tex]

Double derivative of the equation

[tex]\dfrac{d^2y}{dx^2}=-0.125<0[/tex]

So, the function is maximum at [tex]x=10[/tex]

[tex]y=-0.0625x^2+1.25x+5.75=-0.0625\times 10^2+1.25\times 10+5.75\\\Rightarrow y=12[/tex]

The function is maximum at [tex](10,12)[/tex]

So, the truck's center should be below the point [tex](10,12)[/tex] for maximum width to pass through.

Now truck is 11 feet tall so [tex]y=11[/tex]

[tex]11=-0.0625x^2+1.25x+5.75\\\Rightarrow -0.0625x^2+1.25x-5.25=0\\\Rightarrow x=\frac{-1.25\pm \sqrt{1.25^2-4\left(-0.0625\right)\left(-5.25\right)}}{2\left(-0.0625\right)}\\\Rightarrow x=6,14[/tex]

The maximum width of the truck can be [tex]14-6=8\ \text{ft}[/tex] if it is 11 feet tall.

So, the truck which has a width of 7 feet can fit under the arch.


Related Questions

Need Help Asap! Thank you!

Answers

The answer should be option C, the one with the the graph labeled G.

(Need ASP)
Divide.


(4x3+2x+1)÷(x+1)



4x2−4x+6+5x+1


4x2+4x−6−5x+1


4x2−4x+6−5x+1


4x2+4x+6−5x+1

Answers

Answer:

Step-by-step explanation:

(4x^3+2x+1)÷(x+1)

Using synthetic division is

4x^2-4x+6- 5/x+1

4x2+4x−6−5x+1 is the solution for (4x3+2x+1)÷(x+1)

What is Division?

A division is a process of splitting a specific amount into equal parts.

We need to solve,

(4x3+2x+1)÷(x+1)

We use Synthetic division,  Synthetic division is a shorthand method for dividing a polynomial by a linear factor such as x + 3, and it's much simpler and faster.

Step 1: Set up the synthetic division.

Step 2: Bring down the leading coefficient to the bottom row.

Step 3: Multiply  by the value just written on the bottom row.

Step 4: Add the column created in step 3.

We get 4x2+4x−6−5x+1.

To learn more on Division click:

https://brainly.com/question/21416852

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Ahmed recorded the temperature outside his window one morning. On the second day, the temperature went up 7 degrees. On the third day, the temperature went down 10 degrees. On the fourth day, the temperature went down 6 degrees, and it was 1°F.What was the temperature on the first day?

Answers

Answer:

[tex]-2^{\circ}\text{F}[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the temperature on the first day

Second day temperature

[tex]x+7[/tex]

Third day temperature

[tex]x+7-10[/tex]

Fourth day temperature was [tex]1^{\circ}\text{F}[/tex]

[tex]x+7-10+6=1\\\Rightarrow x+3=1\\\Rightarrow x=1-3\\\Rightarrow x=-2^{\circ}\text{F}[/tex]

On the first day the temperature was [tex]-2^{\circ}\text{F}[/tex]

pleaseee help....leave an explanation if you can

Answers

Answer:

A and B

Step-by-step explanation:

Looking at A it is 2/8. If you divide both numbers by the top, which is two, it would become 1/4.

For B, if you divide both numbers by 4 it will also become 1/4.

Enter an equation in standard form to model the linear situation. A bathtub that holds 42 gallons of water contains 12 gallons of water. You begin filling it, and after 5 minutes, the tub is full.

Answers

Answer:

5x+12y= 42

Step-by-step explanation:

9x + 11 = 110
what is x ?

Answers

Answer:

x = 11, lucky you, this stuff is easy

Step-by-step explanation:

110 - 11 = 99

9 x 11 = 99

99 + 11 = 110

Answer:

x = 11

Step-by-step explanation:

9x + 11 = 110

- Pass the 11 to the other side of the equation (grouping similar terms) and then perform the following operation:

9x = 110 - 11

9x = 99

- Now we have to obtain x by dividing 9 on both sides of the equation:

(9/9)x = 99/9

x = 99/9, which is divisible by 11.

3/4 divided by 2/3 in simplest form

Answers

9/8 because in dividing you multiply by the reciprocal so 3/4 x 3/2= 9/8

Answer:

1 1/8

Step-by-step explanation:

1. Keep, change, flip

3/4 x 3/2

2. Multiply

3/4 x 3/2= 9/8

3. Simplify

9/8= 1/18


These two triangles are similar what is the measure of angle M?

Answers

Answer:

30

Step-by-step explanation:

We can ignore the fact they are similar altogether. It's known that all 3 angles of a triangle add up to 180, so:

180=102+48+m

180=150+m

30=m

Answer:

A. 30 degrees

Step-by-step explanation:

They are similar aka the same or congruent and since you know all three angles you just match them up.

Your science teacher tells you that the next test is worth $0 points and contains 19 problems. Multiple-choice
questions are worth 2 points each and short answer questions are worth 5 points. Find how many of each type of
question will show up on the test.

Answers

Answer:

The test had

30

multiple choice questions, and

8

word problems.

Step-by-step explanation:

Angelina paid $6.60 for a dozen cupcakes for a birthday party. What is the unit cost for each cupcake? *

Answers

Answer:

the answer would be 1.82

Step-by-step explanation:

it is this answer because you have to see how much money goes into one cupcake which to put stuff into different places you have to divide 12/6.60

Answer:

$0.55 Hope this helps!!!!!!!

Step-by-step explanation:

Remember that is that a dozen is equal to 12.

12x= 6.60

/12     /12

x=.55

Determine the number that can be used in place of the question mark to make the equation true.

(1/5)^?= 25
The solution is

Answers

(1/5)^x = 25
x = -2
Since when it’s a fraction, the result is negative.
The solution is -2

What is 83 1/3% of 30

Answers

answer: 25

step by step explanation:
yw
hope this helps
give brainliest plz

Is 78 − –5 positive or negative?

Answers

Answer: it would be a positive

Answer:

the answer is positive because 78 is bigger than -5

Step-by-step explanation:

what is the slope of the line that passes through the points
(5,1) and (2,-7)
A.) 3/8
B.) -8/3
C.) 8/3
D.) -3/8

Answers

Slope is the change in y over the change in x:

Slope = (-7 - 1) / (2 - 5)

Slope = -8/-3

Slope = 8/3

(y2-y1)/(x2-x1)
(-7-1)/(2-5) = -8/-3
It would be C. 8/3

What theorems can be used to prove the triangles are congruent?
SSS
ASA
AAS
HL​

Answers

Answer:

1.) SAS | 2.) HL | 3.) HL | 4.) SSS (Not too sure about this one)

Step-by-step explanation:

When I bought my car it was $25,000. My car’s value is now $11,000. What percentage is my car now from its original price?

Answers

Answer:

56% should be the answer

how many 4-digit number are divisible by 7,8,10 and 25​

Answers

9514 1404 393

Answer:

  7

Step-by-step explanation:

In order for a number to be divisible by all of 7, 8, 10, and 25, it must be a multiple of the least common multiple of those numbers.

  LCM(7, 8, 10, 25) = 7×8×25 = 1400

There are floor(10,000/1,400) = 7 4-digit numbers divisible by 7, 8, 10, and 25. They are ...

  1400, 2800, 4200, 5600, 7000, 8400, 9800

-3y-3x=-3




plz help me​

Answers

Answer:

y = -x + 1

Step-by-step explanation:

-3y - 3x = -3

Add 3x

-3y = 3x - 3

Divide by -3

y = -x + 1

If you’re trying to solve for x the answer is x=1-y ... hopefully that helped :)

ASAP please i need helppp

Answers

HAHAHHAH UR IN EXAM can I answer now?
I think it’s the first one

write the linear equation

Answers

Answer:

y = 3/5 +2

Step-by-step explanation:

I thought a bleep who lost the baddest bleep said sum

Answers

Answer:

i did say something boo boo

Step-by-step explanation:

Answer:

They did, I believe bleep's last words were "One day all this will fade away."

Step-by-step explanation:

May I have brainliest please? :)

What is the scale factor?*
A
7
6
5
5
30
С
3
3
2.
В"
-10
2
3
5
6
78
9 10 11 12 13
-2
-3

Answers

Answer:

Scale factor is 3

Step-by-step explanation:

The distance in A and B is 2

The distance in A' and B' is 6

6/2=3

A scientist used 786 milliliters of an liquid for an experiment. How many liquids of liter did the scientist to use for this experiment?

Answers

Answer:

0.786 L

Step-by-step explanation:

1000 ml to 1 L

(786 ml) / (1000 ml) = 0.786 L

0.786 L liquids of liter did the scientist to use for this experiment

What is division?

Division is the process of splitting a number or an amount into equal parts.

here, we have,

A scientist used 786 milliliters of an liquid for an experiment.

we know,

1000 ml to 1 L

so, we get,

(786 ml) / (1000 ml) = 0.786 L

Hence, 0.786 L liquids of liter did the scientist to use for this experiment.

To learn more on division click:

brainly.com/question/21416852

#SPJ2

Question 5 : CONSUMER MATH

Answers

Answer:

23.1345 is the answer I am not that sure though

Juan reads 300 pages 5 days which reading rate is equivalent

Answers

60 pages per day!

It is shown that One is reading 300 pages in five days so we need to find a reading rate which would be the total number of pages one reads over the number of days so the substitute does values by doing 300/5 you would get 60 pages per day

b The lines are translations of each other
The lines are reflections of each other
d They have the same y-intercept
e a
Both lines have a positive slope.
с

Answers

Answer:

A, B, E

Step-by-step explanation:

The slope is the same (1/4x)

it is a translation given the y intercept moved it 5 units

they are both positive

Aidan had 13 tropical fish and gave 8 of them to his brother then Aidan bought 6 more from the pet store each fish cost $9.45 how many fish does Aidan have now

Answers

Answer:

11 fishes

Step-by-step explanation:

Answer:27

Step-by-step explanation: add all the answers

A family has completed 50% of a trip and they have traveled 10 miles. How long is the trip?

Answers

Answer: 20 miles? lol

Step-by-step explanation:

Answer is 20

Explanation:

50% of 20 is 10.

10 + 10 = 20.

3. Determine whether these two lines are parallel, perpendicular, or neither. 1 point
8x + y = 7, 4x + 3y = 12 *
parallel,
perpendicular or
neither

Answers

Answer:

The two lines are neither

Step-by-step explanation:

Parallel lines have equal slopes and different y-interceptsPerpendicular lines have a product of their slopes = -1The slope of a line whose equation is ax + by = c is m = [tex]\frac{-a}{b}[/tex]

∵ The equations of the lines are

8x + y = 7 ⇒ 1st4x + 3y = 12 ⇒ 2nd

∵ In the 1st equation a = 8 and b = 1

m1 = [tex]\frac{-8}{1}[/tex] = -8

∴ The slope of the 1st line is -8

∵ In the 2nd equation a = 4 and b = 3

m2 = [tex]\frac{-4}{3}[/tex]

∴ The slope of the 2nd line is [tex]\frac{-4}{3}[/tex]

→ By using the facts above

m1 ≠ m2

∴ The two lines are not parallel

∵ m1 × m2 = -8 × [tex]\frac{-4}{3}[/tex] = [tex]\frac{32}{3}[/tex]

m1 × m2 ≠ -1

∴ The two lines are not perpendicular

The two lines are neither parallel nor perpendicular

A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = y minus 11 equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus 7 right-parenthesis.(x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.

Answers

Answer:

A and D

Step-by-step explanation:

I took the assignment

Answer:

a, d

Step-by-step explanation:

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