Mathematics College

The driver of a car traveling at 54ft/sec suddenly applies the brakes. The position of the car is s=54t-3t^2, t seconds afyer the driver applies the brakes.
How many seconds after the driver applies the brakes does the car come to a stop

Answers

Answer 1
  s = 60t - 3t^2 
v = ds/dt = 60 - 6t 

when it comes to rest, v = 0, 
so t = 10 sec 

now distance travelled = time taken x average velocity 
= 10 x (60 + 0)/2 
= 300 ft 

Answer 2

After time  [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.

What is time?

" Time is defined as the measurable slot of period in which required action is done."

Formula used

[tex]y = x^{n} \\\\\implies \frac{dy}{dx} = nx^{n-1}[/tex]

According to the question,

Position of the car [tex]'s' = 54t - 3t^{2}[/tex]

[tex]'s'[/tex] represents the distance

[tex]'t'[/tex] is the time in seconds

When driver applies break [tex]v= 0[/tex],

[tex]v = \frac{ds}{dt}[/tex]

Calculate the first derivative with respect to time we get,

[tex]'s' = 54t - 3t^{2}\\\\\implies \frac{ds}{dt} = 54- 6t[/tex]

As [tex]\frac{ds}{dt} =0[/tex] we get the required time as per given condition,

[tex]54-6t =0\\\\\implies 6t =54\\\\\implies t = 9[/tex]

Hence, after time  [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.

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Related Questions

which types of angels are not congruent?

Answers

same side exterior angles are not congruent

Each package of dried fruit contains 3/16 of a pound Mr. Lopez has 4 pounds of dried fruit How many packages can he fill

Answers

Final answer:

Mr. Lopez can fill 21 full packages of dried fruit, each containing 3/16 of a pound, with his 4 pounds of dried fruit.

Explanation:

The question asks how many packages of dried fruit Mr. Lopez can fill if each package contains 3/16 of a pound and he has 4 pounds of dried fruit. To answer this, we need to perform a division to find out how many 3/16 are in 4 pounds.

To solve this, we divide 4 pounds by 3/16 pounds per package:

4 ÷ (3/16) = (4/1) ÷ (3/16) = (4 × 16) / 3 = 64/3 = 21 with remainder 1.

Therefore, Mr. Lopez can fill 21 full packages of dried fruit and will have a little left over which is not enough to fill an additional full package.

Suppose θ is an angle in the fourth quadrant with cosθ=x/4. Find expressions for the other five trig functions in terms of x?

Answers

[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent} \\\\\\ % cotangent cot(\theta)=\cfrac{adjacent}{opposite} \qquad % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} \quad % secant sec(\theta)=\cfrac{hypotenuse}{adjacent}\\\\ -------------------------------[/tex]

now, we know the angle is in the IV quadrant, that means, the cosine is positive and the sine is negative, or "x" is positive whilst "y" is negative.

[tex]\bf cos(\theta )=\cfrac{\stackrel{adjacent}{x}}{\stackrel{hypotenuse}{4}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{4^2-x^2}=b\implies \stackrel{IV~quadrant}{-\sqrt{16-x^2}=b}\\\\ -------------------------------[/tex]

[tex]\bf sin(\theta)=\cfrac{-\sqrt{16-x^2}}{4} \qquad cos(\theta)=\cfrac{x}{4} \qquad % tangent tan(\theta)=\cfrac{-\sqrt{16-x^2}}{x} \\\\\\ % cotangent cot(\theta)=\cfrac{x}{-\sqrt{16-x^2}} \qquad % cosecant csc(\theta)=\cfrac{4}{-\sqrt{16-x^2}} \qquad % secant sec(\theta)=\cfrac{4}{x}[/tex]

now, for the cotangent and the cosecant, let's rationalize the denominator,

[tex]\bf cot(\theta)=\cfrac{x}{-\sqrt{16-x^2}}\cdot \cfrac{\sqrt{16-x^2}}{\sqrt{16-x^2}}\implies cot(\theta)=-\cfrac{x\sqrt{16-x^2}}{16-x^2} \\\\\\ csc(\theta)=\cfrac{4}{-\sqrt{16-x^2}}\cdot \cfrac{\sqrt{16-x^2}}{\sqrt{16-x^2}}\implies csc(\theta)=-\cfrac{4\sqrt{16-x^2}}{16-x^2}[/tex]

A hair salon charges fixed rate of $25.00 for a haircut and then an additional $15.00 for any other services. Write a function to model cost of services there and then determine how many services you had if you were charged for $115.00

Answers

Fixed Cost: $25 Additional Cost: $15 per service To demonstrate how much a customer would have to pay for a trip to the salon, one can use the equation Total Cost = Fixed Cost + (Additional Cost x Number of services), or Total Cost = 25 + (15 x Number of services). If I were charged for $115, I would use the equation 115 = 25+(15xServices), and solve this to find that the number of services received was six.

Answer:

f(x) = 15x + 25; f(6) = 115

Step-by-step explanation:

the flat rate of $25 will be the y-intercept and the slope will be $15. since u are charged $115, plug that in for f(x) and solve for x. so the right answer is

f(x) = 15x + 25; f(6) = 115

Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.
If no money was deposited into or withdrawn from the account, how much money was in the account after ​3​ years?
Round your answer to the nearest cent.
Enter your answer in the box.

Answers

It would round out to about $329.19.

Answer: Its 329.18 just took a test.


The top of a 22-foot ladder rests against the top of an 18-foot wall. If the base of the ladder is on the same ground level as that of wall, what angle does the ladder form with the ground? Express your solution to the nearest degree.

Answers

use the sine ratio here:-   sin = opposite / hypotenuse so 
sin A =   18/22 

A =  54.9 degrees  

55 to nearest degree

Answer:

Step-by-step explanation:

Given that The top of a 22-foot ladder rests against the top of an 18-foot wall.

The ladder, the wall and the floor together make a right angled triangle with hypotenuse as ladder.

Thus we have a right triangle with hypotenuse = 22 ft

and the side of the wall = 18

The required angle is the angle  the ladder form with the ground.

Hence we have if x is the angle

[tex]sin x =\frac{Opposite}{Hypotenuse} =\frac{18}{22}[/tex]

From this we can find the angle X

X = sin inverse of 18/22

X=54.9

Round it off to X=55 degrees

Write each equation in slope intercept form 5x+3y=30

Answers

Get rid of x first -5x then divide the rest
Slope intercept form is: y = mx + b.

In order to get x to the other side, you subtract it on both sides.
3y = -5x + 30

But in slope intercept form, y can’t have any number in front of it. To get rid of the number, divide both sides by 3

y = -5x/3 + 6

What is a transformation and 3 types of transformations.

Answers

a transformation happen when the shape changes.
There are four transformations
translation
rotation
reflection
dilation

translation, rotation and reflection do not change the shape or the size of the shape and are known as rigid motions
A transformation is the movement or change in size of a shape on a graph.

The four types:
Dilation: Change of size.
Rotation: A clockwise turn in each of the four quadrants in a graph.
Translation: Simply relocating the shape.
Reflection: Mirroring the shape across either the y or x axis.

Hope that helps!

What's the Estimate of 615-342

Answers

Final answer:

To estimate the difference between 615 and 342, round each number to the nearest ten or hundred and subtract. Rounding to the nearest hundred gives an estimate of 300, while rounding to the nearest ten gives an estimate of 280.

Explanation:

To estimate the difference between 615 and 342, you can round each number to the nearest ten or hundred and then subtract the rounded numbers. Here's the step-by-step process:

Round 615 to the nearest hundred, which gives you 600.Round 342 to the nearest hundred, which gives you 300.Subtract the rounded numbers: 600 - 300 = 300.

This gives an estimate of the difference between 615 and 342 as 300.

If you prefer to round to the nearest ten instead, you'd get:

Round 615 to the nearest ten, which gives you 620.Round 342 to the nearest ten, which gives you 340.Subtract the rounded numbers: 620 - 340 = 280.

In this case, the estimate would be 280. You can choose the level of precision you want in your estimate based on how you round the numbers.

What is the value of the 4 in 24,659

Answers

4000

Place values are according to the digits...

So...
20000+4000+600+50+9=24,659

The value of 4 in the given number is 4000.

The given number is 24,659.

What is the place value?

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

In the given number 24,659, 4 is in thousands place.

So, the value of 4 is 4000

Therefore, the value of 4 in the given number is 4000.

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Which is the better estimate of the weight of a football helmet

Answers

Hey there,
Probably 3 - 5 pounds.

Hope this helps :))

~Top

The Fenton College Cougars made 40 field goals in a recent basketball game some 2 pointers and the rest 3 pointers. Altogether the 40 baskets counted for 89 points. how many of each type of field goal was made?

Answers

x = 2 pointers, y = 3 pointers

x + y = 40.....x = 40 - y
2x + 3y = 89

2(40 - y) + 3y = 89
80 - 2y + 3y = 89
-2y + 3y = 89 - 80
y = 9 <=== there were 9 three-point shots

x = 40 - y
x = 40 - 9
x = 31 <=== there were 31 two-point shots

Take apart an addend to solve 35+27

Answers

Using take apert, we have

       35      +    27

=  32 + 3   +    27

=  32 + 30

=  62

what is the exact of the expressions square root of 180 - square root of 125 + square root of 5

Answers

[tex]\bf \sqrt{180}-\sqrt{125}+\sqrt{5}\qquad \begin{cases} 180=2\cdot 2\cdot 3\cdot 3\cdot 5\\ \qquad 2^2\cdot 3^2\cdot 5\\ \qquad (2\cdot 3)^2\cdot 5\\ \qquad 6^2\cdot 5\\ 125=5\cdot 5\cdot 5\\ \qquad 5^2\cdot 5 \end{cases} \\\\\\ \sqrt{6^2\cdot 5}-\sqrt{5^2\cdot 5}+\sqrt{5}\implies 6\sqrt{5}-5\sqrt{5}+\sqrt{5}\implies 2\sqrt{5}[/tex]

The exact value of the expression √180 - √125 + √5 simplifies to 2√5, by combining like terms after simplifying each square root separately.

The exact value of the expression [tex]\sqrt{180}[/tex] - [tex]\sqrt{125}[/tex] + [tex]\sqrt{5}[/tex] can be calculated by simplifying each square root separately. Firstly, the [tex]\sqrt{180}[/tex] can be simplified to 6√5, because 180 = 36 × 5, and 36 is a perfect square whose square root is 6. Similarly, the [tex]\sqrt{125}[/tex] simplifies to 5√5, since 125 = 25 × 5 and the [tex]\sqrt{25}[/tex] is 5. The [tex]\sqrt{5}[/tex] remains as it is because it cannot be simplified further.

The expression then becomes 6√5 - 5√5 + √5. Now, we combine like terms. Since all terms involve the [tex]\sqrt{5}[/tex], we can combine them as follows: (6 - 5 + 1)√5, which simplifies to 2√5. Therefore, the exact value of the expression is 2√5.

Cell phones can weigh as little as 2 ounces. How many pounds can the cell phone weigh?

Answers

16 ounces in a pound. 

2/16= .125

.125 pounds
Final answer:

A cell phone weighing 2 ounces translates to 0.125 pounds, since there are 16 ounces in one pound.

Explanation:

Cell phones can weigh as little as 2 ounces. The first step in determining how much a cell phone can weigh in pounds is to know the conversion factor between ounces and pounds. Since there are 16 ounces in one pound, you can divide the weight of the cell phone in ounces by 16 to convert it to pounds. For a cell phone that weighs 2 ounces:

Divide the weight in ounces by 16 to convert to pounds: 2 ounces ÷ 16 = 0.125 pounds.

Therefore, a cell phone that weighs 2 ounces is equivalent to 0.125 pounds.

What is the value of mc016-1.jpg?
-20
-4
4
20

the pic is the .jpg

Answers

(4-2)^3 -3*4 =

(4-2) = 2, 2^3 = 8

3*4 =12

 so you have 8-12 = -4

 Answer is -4

Explanation:

This question's it's about the order of operations. It stands for parenthesis, exponents, multiply, divide, add, and subtract. It can also go left too right. (PEMDAS)

First, do parenthesis.

[tex](4-2)=2[/tex]

[tex]2^3-3*4[/tex]

Then exponents.

[tex]2^3=2*2*2=8[/tex]

[tex]8-3*4[/tex]

Multiply left to right.

[tex]3*4=12[/tex]

Subtract left to right.

[tex]8-12[/tex]

[tex]12-8=4[/tex]

It change positive to negative sign.

Answer: → [tex]\boxed{=-4}[/tex]

*The answer must have a negative sign.*

Hope this helps!

Thank you!

-Charlie

There are 117 staff members in your school. 1/3 of them are going away for the Thanksgiving holiday. How many staff members are not traveling?
This was the main question but i didnt get how to solve it.. (wasnt sure if subtraction was thr right way)

Answers

117/1 * 1/3 = 117/3 = 39

117 - 39 = 78

78 staff members are not leaving for Thanksgiving.

Find three points that solve the equation , -5x-3y=-7

Answers

To find three points, we can literally plug x values in a solve for y. To make this a little easier, we can solve for y to start. First, we can add 5x to both sides (addition property of equality) to get 7+5x=-3y. Next, we can divide both sides by -3 to get 
[tex]- \frac{7+5x}{-3} =y[/tex]

To make this really simple, we can make 7+5x equal to factors of -3. For example, -3*2=-6. If we have 7+5x=-6, we can subtract 7 to both sides to get -13=5x. Next, we can divide both sides by 5 to get x=-13/5. Since 7+5x=-6, we can plug that into 
[tex]- \frac{7+5x}{-3} =y[/tex]
to get (-6)/(-3)=2=y. I challenge you to find the other two points on your own - good luck!

Choose the best answer. Which of the following is not a type of savings account? A.passbook account
B.statement account
C.club account
D.automatic account

Answers

Hello!

I believe the best answer to this question would be D. Club account, because there was something called "Christmas club account" during the Great Depression. Now, it's a savings program, so you could save that it's technically not a savings account.

I really hope this helped you! :)

Answer with explanation:

Saving Account →A savings account is a type of bank account in which you can keep extra money possessed by you in an institution, which is most safest place,The money you get  as an interest  is proportional to amount of money deposited in that institution.

A. Passbook Account :  A Passbook Savings account is also a saving account,in which you get interest for your deposit and also get a passbook for easy record keeping.

B.Statement account : It is also a saving account,in which you get statement for your credit and debit in your account.

C. Club Account: In this type of Saving account, you deposit money for your future investment or for any future purpose by a group.You have to deposit and withdraw money within a certain time frame.

D. Automatic account: In this type of account , money is transferred to it's customers automatically in their accounts by a certain process. It is not a saving Account.

Option 4→: Automatic Account : is the type of account which is not a saving Account.

Texaschic101
Help please

Answers

So what this is, is the range from 0 - 4, not including 4, or the range from 5 - 9, not including 9.

Obviously the mean and median aren't shown.

So in this case it would be the first one, since the second bar isn't including 9, so it wouldn't include 9, so we wouldn't know how many of 10-14 are 9s, so we don't know that.

So it would have to be the first one.

Area of 100 3/4 feet x 75 1/2 feet?

Answers

100 3/4 x 75 1/2
25 x 3 x 75 1/2. (Divided by 4 to 100 and 4 to get 25)

25 x 3 x 75 1/2 ( multiple everything on top)

5625/2 ( then divided normally)

2812.5 or 2812 1/2

Can someone help me if anyone know. Please, thanks

Answers

6 and 8/15 inches. Take the 1/5 and 1/3 and find a common denominator. Then Subtract the smaller number from the bigger number. Bam
I simplified the numbers. Then the subtract his height at birth from his height when he was a year old.

The depths of water, at the edge of a pier, at different times of day, are represented by the table below. Which of the following functions best models the depths of the water?

Answers

The best answer is C) y=4.75 * cos(0.52x - 2.08) + 7.65

Unfortunately, the two only ways to solve this problem are to either graph all the options or plug in time values for x and see which agrees the most with the tide chart. Both are time-consuming, but I chose to graph each one with a graphing application. 
Plugging in a few values for x confirms that C is the best function. 
12pm (x=0)
y = 4.75 * cos(0 - 2.08) + 7.65
y = 5.334
2pm (x=2)
y= 6.5
4pm (x=4)
y=12.4
It is not a perfect representation, but the shape of the graph and closeness to the points given is the best of the four options provided. 

Which of these is equivalent to 3-23-2?

Answers

Answer:

-22

Step-by-step explanation:

This is a case of directed numbers. The numbers 23 and 2 carry negative signs like this:

- 23

- 2

Therefore, adding these negative numbers gives -23 - 2 = -25

Adding the sum to 3 gives: 3 - 25 = -22

Name the triangle with the following characteristics. Sides: 5 cm, 5 cm, 7 cm.
A. scalene triangle B. acute triangle C. isosceles triangle D. right triangle

HELP ASAP

Answers

i belive it might be a right triangle
Isosceles triangle since two sides are equal

The complement of 17% is

Answers

38% :)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Answer:

73%.

Step-by-step explanation:

Let x be the complement of 17%.

We are asked to find the complement of 17%.

We know that two angles are complementary when they add up-to 90 degrees. So we can set an equation as:

[tex]17\%+x=90\%[/tex]

[tex]17\%-17\%+x=90\%-17\%[/tex]

[tex]17\%-17\%+x=73\%[/tex]

Therefore, the complement of 17% is 73%.

What is 5.8×2.4?

Show your work
What grade if u like this you will get 24 points
.


.

Answers

13.92 is the answer because 5.8x2.4=13.92
the answer is 13.92. steps are.
1.     put 5.8*2.4 into a standard algorithm.  which will look like this.
   5.8
x 2.4
---------
   232
+1160
--------
    13.92  hope that helped

What is the molar solubility of magnesium fluoride in a solution that is 0.40 m f− ions? the ksp of mgf2 is 6.4 × 10−9. hints what is the molar solubility of magnesium fluoride in a solution that is ions? the of is . 8.0 × 10−9 8.0 × 10−5 1.6 × 10−8 4.0 × 10−8?

Answers

Answer: MgF2 ====⇒ Mg+2 + 2F- Ksp = [Mg+2][F-]^2 Let S = molar solubility of MgF2 [Mg+2] = S ; [F-] = 2s Since the [F-] is initially 0.40 M, then [F-] = 0.40 + 2S 6.4 x 10^-9 = (S) (0.40 + 2S)^2 ; one can neglect the 2S in the 0.40 + 2S expression since it is very, very small compared to the 0.40 already present. 6.4 x 10^-9 = S(0.40)^2 S = 4.0 x 10^-8 Molar solubility = 4.0 x 10^-8
Final answer:

The molar solubility of magnesium fluoride in a solution with a concentration of 0.40 M fluoride ions is 0.80 M.

Explanation:

The molar solubility of magnesium fluoride in a solution with a concentration of 0.40 M fluoride ions can be calculated using the solubility product constant (Ksp) of MgF2, which is 6.4 × 10-9.

First, write the dissolution equation for MgF2: MgF2(s) ⇌ Mg2+(aq) + 2F-(aq)

Since the stoichiometry of the dissolution equation is 1:2 between magnesium ions and fluoride ions, the molar solubility of MgF2 is twice the concentration of fluoride ions.

Therefore, the molar solubility of MgF2 in a solution that is 0.40 M fluoride ions is 2 × 0.40 M = 0.80 M.

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A surveyor took the following measurements from two irregularly shaped pieces of land. Some of the lengths and angle measures are missing. Find all missing lengths and angle measures. Round lengths to the nearest tenth and angle measures to the nearest minute

Answers

Part A:

To find angle D, we make use of the rule of Sines because we know the measure of the side opposite angle D and we also know the meansure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle D as follows:

[tex] \frac{62}{\sin{D}} = \frac{51}{\sin{53^o}} \\ \\ \Rightarrow \sin{D}= \frac{62\sin{53^o}}{51}} \\ \\ = \frac{49.5154}{51} =0.9709 \\ \\ \Rightarrow D=\sin^{-1}{0.9709} \\ \\ =76.14^o=76^o8'[/tex]

Therefore, angle D is 76°8'



Part B:

To find angle E, recall that the sum of the angles in a triangle is 180°.

Thus, 53° + 76°8' + E = 180°

E = 180° - 53° - 76°8' = 50°52'

Therefore, angle E is 50°52'



Part C:

To find the measure of side e, we apply the cosine rule as follows:

[tex]e^2=51^2+62^2-2(51)(62)\cos{50^o52'} \\ \\ =2,601+3,844-2,098.85=3,991.25 \\ \\ \Rightarrow e=\sqrt{3,991.25}=63.18[/tex]

Therefore, the measure of side e is 63.2



Part D

To find angle G, we make use of the rule of Sines because we know the measure of the side opposite angle G and we also know the measure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle G as follows:

[tex]\frac{80}{\sin{G}} = \frac{62}{\sin{49^o}} \\ \\ \Rightarrow \sin{G}= \frac{80\sin{49^o}}{62} \\ \\ = \frac{60.3768}{62} =0.9738 \\ \\ \Rightarrow G =\sin^{-1}{0.9738}=76.86^o=76^o52'[/tex]

Therefore, angle G is 76°52'



Part E:

To find angle H, recall that the sum of the angles in a triangle is 180°.

Thus, 49° + 76°52' + H = 180°

H = 180° - 49° - 76°52' = 54°14'

Therefore, angle H is 54°14'



Part F:

To find the measure of side a, we apply the cosine rule as follows:

[tex]a^2=80^2+62^2-2(80)(62)\cos{54^o14'} \\ \\ =6,400+3,844-5,798.10=4,445.90 \\ \\ \Rightarrow a=\sqrt{4,445.90}=66.68[/tex]

Therefore, the measure of side a is 66.7



Part G:

To find angle A, we make use of the rule of Sines because we know the measure of the side opposite angle A and we also know the measure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle A as follows:

[tex]\frac{66.7}{\sin{A}} = \frac{30}{\sin{25^o54'}} \\ \\ \Rightarrow \sin{A}= \frac{66.7\sin{25^o54'}}{30} \\ \\ = \frac{29.1347}{30} =0.9712 \\ \\ \Rightarrow A =\sin^{-1}{0.9712}=76.21^o=76^o12'[/tex]

Therefore, angle A is 76°12'



Part H:

To find angle B, recall that the sum of the angles in a triangle is 180°.

Thus, 25°54' + 76°12' + B = 180°

B = 180° - 25°54' - 76°12' = 77°53'

Therefore, angle B is 77°53'



Part I:

To find the measure of side b, we make use of the rule of sines

Thus, we find side b as follows:

[tex]\frac{b}{\sin{77^o53'}} = \frac{30}{\sin{25^o54'}} \\ \\ \Rightarrow b= \frac{30\sin{77^o53'}}{\sin{25^o54'}} \\ \\ = \frac{29.3317}{0.4368} =67.15[/tex]

Therefore, the measure of side b is 67.2
Final answer:

To find the width of the river, use trigonometry and the tangent function. The width of the river is approximately 67.1 meters.

Explanation:

To find the width of the river, we can use trigonometry. The surveyor measured an angle of 35° from the baseline to the tree on the opposite bank. We know the distance along the river is 100 m. Let's denote the width of the river as 'x'.

We can use the tangent function to solve for 'x'. The tangent of the angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 'x' (the width of the river) and the adjacent side is 100 m (the distance along the river).

So, the equation becomes:

tan(35°) = x/100

To find the value of 'x', we can multiply both sides by 100:

x = 100 * tan(35°)

Using a calculator, we can find that x is approximately 67.1 m. Therefore, the width of the river is approximately 67.1 meters.

An audio cable is 15.7dm long. How long is the cable in meters?

Answers

The answer should be 1.57m
Other Questions
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