A racetrack is in the shape of an ellipse, 180 ft long and 90 ft wide. What is the width 30 ft from a vertex?

Answer:

Step-by-step explanation:

Given point:

Slope-intercept form:

Use slope formula:

Use one of the points to find the y-intercept:

The line is:

Answer:

slope for y intercept={10--17)/(14--15)=27/29

Answer:

C. [tex]\frac{d^{2}f}{dt^{2}} = k\cdot \sqrt[3] {t}[/tex]

Step-by-step explanation:

Physically speaking, the acceleration is equal to the second derivative of the position of the vehicle in time. After a careful reading to the statement, we construct the following ordinary differential equation:

[tex]\frac{d^{2}f}{dt^{2}} = k\cdot \sqrt[3] {t}[/tex]

Where:

[tex]t[/tex] - Time, measured in seconds.

[tex]k[/tex] - Proportionality constant, measured in meters per second up to 7/3.

Therefore, the correct answer is C.

The differential equation that models the situation is:

[tex]\frac{d^2f}{dt^2} = k\sqrt[3]{t}[/tex]

Which is option C.

The position is the integral of the acceleration, with is the integral of the acceleration, hence, the relation between the position and the acceleration is:

[tex]\frac{d^2f}{dt^2}[/tex]

The acceleration is proportional to the cube root of the time since the start, hence:

[tex]\frac{d^2f}{dt^2} = k\sqrt[3]{t}[/tex]

In which k is the constant of proportionality.

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Answer:

Step-by-step explanation:

xhxj

Answer:

y+mx+b

Step-by-step explanation:

Answer:

A = 23°

B = 9.5

C = 14.7

Step-by-step explanation:

Right Answers :)

The missing values are:

A = 23°

b = 9.5

c = 14.72

"It is a triangle whose one of the angles measure greater than 90° and other two acute angles."

"The ratio of the length of a side of a triangle to the sine of the angle opposite to that side is the same for all sides and angles in a given triangle."

For given question,

We have been given an obtuse triangle ABC.

Here, ∠B = 32°

∠C = 125°

We know that the sum of all angles of  a triangle is 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A + 32° + 125° =180°

⇒ ∠A = 23°

Using the law of sines to triangle ABC,

[tex]\Rightarrow \frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC} \\\\\Rightarrow \frac{7}{sin23^{\circ}} =\frac{b}{sin32^{\circ}} =\frac{c}{sin125^{\circ}}[/tex]

Consider,

[tex]\Rightarrow \frac{7}{sin23^{\circ}} =\frac{b}{sin32^{\circ}} \\\\\Rightarrow \frac{7}{0.39} =\frac{b}{0.53} \\\\\Rightarrow 7\times 0.53=b\times 0.39\\\\\Rightarrow b = 9.5[/tex]

Now we find the length of the side AB.

[tex]\Rightarrow \frac{7}{sin23^{\circ}} =\frac{c}{sin125^{\circ}} \\\\\Rightarrow \frac{7}{0.39} =\frac{c}{0.82} \\\\\Rightarrow 7\times 0.82=c\times 0.39\\\\\Rightarrow c = 14.72[/tex]

Therefore, the missing values are:

A = 23°

b = 9.5

c = 14.72

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Answer:

5.3 is the amswer! Hope u pass

Answer:

A

Step-by-step explanation:

- 8 × - 3 = 24 ÷4=6

this is the right answer

Answer:

The equation of a direct proportion is: y=8x

So, the correct option is Option A.

Step-by-step explanation:

We need to find equation of direct proportion.

If y varies directly with x then:

[tex]y\:\alpha \:x\\y=kx[/tex]

Where k is constant of proportionality

So, Now Looking at all the options and comparing it with the general equation of direct proportion [tex]y=kx[/tex]

We get the correct option: y=8x

All other options are not according to direct equation

The equation of a direct proportion is: y=8x

So, the correct option is Option A.

Answer: i believe its 15

Step-by-step explanation:

it continues to go down by seven (if this is wrong I´m so sorry )

Answer:

the second plan should be purchased.

Step-by-step explanation:

school budget is $7200

plan 1: 241 students are $30 each is

241 × 30 = $7230 which is over budget with no money for parking for the vehicles.

plan 2: 241 students are $28 each is

241 × 28 = $6748

with a budget of $7200 for the trip the amount left for parking is

$7200 - $6748 = $452

plan 2: Parking is $15 per vehicle

Therefore the remaining $452 can be used to pay for 452 ÷ 15 = 30.13 vehicles

The school should purchase Plan 2 for the field trip.

The budget of $7200 can pay for 241 tickets for students and parking for 30 vehicles

The school should purchase the second plan.

School's budget = $7200

The cost for the first plan will be:

= 241 × $30

= $7230

This is more than the school budget of $7200

For the second plan, the cost will be:

= 241 × $28

= $6748.

This is below the school budget and therefore affordable.

The school should choose the second plan as there'll be more money available for parking.

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Answer:

a) $1.40   b) $9.35   c) $57.50

Step-by-step explanation:

a) The tax on the burger will be 3% of the cost of the burger.

This means 0.03 of 46.75 (0.03 x 46.75) = $1.40 tax

b) 20% of pre tax bill as tip would be:

0.20 of 46.75 (0.20 x 46.75) = $9.35 tip

c)Total cost of dinner including tax and tip would be:

Original Cost + Tax + Tip

= 46.75 + 1.40 + 9.35

= $57.50 total

Answer:

Each person will get 1/48 of a pound of spice

Answer:

1/48 pound

Step-by-step explanation:

You have to do 3/4 divided by 36, so you get

[tex]\frac{3}{4} / 36 = \frac{3}{4} * \frac{1}{36} = \frac{1}{48}[/tex]

Answer:

Base = 81 feet

Step-by-step explanation:

Given that,

Length of the ladder = 15 foot

Greg needed to clean his gutters which are 12 feet high from the ground.

We need to find how far away does Greg need to place the ladder from the base of the house to reach the gutters. Let it is b.

Here, hypotenuse = 15 feet, height = 12 feet and base = b

We can use Pythagoras theorem to find b.

[tex]b^2+h^2=H^2\\\\b^2=H^2-h^2\\\\b^2=15^2-12^2\\\\b^2=225-144\\\\b=81\ \text{feet}[/tex]

So, the ladder should be placed at a distance of 81 feet from the base of the house to reach the gutters.

Answer:

a

Step-by-step explanation:

rn rn m rn... rn

rn rn rn

rn em rn rnnn

Answer:

[tex]\left \{ {{x=3} \atop {y=-7}} \right.[/tex]

Step-by-step explanation:

We can directly substitute y of the first equation to the second equation.

-2x - 1 = 3x - 16

5x = 15

x = 3

Substituting back to any of the two equations, we get y = -2(3)-1 = -7.  If you check with the second equation, y = 3(3)-16 = -7 as well.

Therefore [tex]\left \{ {{x=3} \atop {y=-7}} \right.[/tex].

Answer:

118

Step-by-step explanation:

Distribute 5 through the parentheses

-5 - 5 - 2(-1 - 1) - 62(-1 - 1)

distribute -2 through the parentheses

-5 - 5 + 2 + 2 -62(-1-1)

distribute -62 through the parentheses

-5 - 5 + 2 + 2 + 62 + 62

calculate the sum & differences

118

Answer:

[ -3 4 ]

Step-by-step explanation:

Answer:

12 f

Step-by-step explanation:

2k + 5

2k + 5 = 0

       -5

2k       =    -5

2k ÷ 2  -5  ÷ 2

k = 2.5 or 5/2

Answer:

4.44444444444 or 40/9

Step-by-step explanation:

i searched it up

8 divided by 1 4/5 in fraction form will be 40 / 9. Then the faction number 40 / 9 in the decimal form will be 4.4444.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The mixed fraction number is converted into a faction number.

⇒ 1 4/5

⇒ 1 + 4/5

⇒ (5 + 4) / 5

⇒ 9/5

Then the quotient of the numbers 8 and 9/5 will be given as,

⇒ 8 / (9/5)

⇒ 8 x 5 / 9

⇒ 40 / 9

The faction number 40 / 9 in the decimal form will be 4.4444.

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Answer:

Step-by-step explanation:

Like terms have same variables. Combine like terms.

2) (-4x + 6) + (x - 5) = -4x + 6 + x - 5

                              = -4x + x  + 6 - 5

                             =   -3x + 1

4) (-2x + 10) + (-8x - 1) =  -2x + 10 - 8x - 1

                                 = - 2x - 8x + 10 - 1

                                = - 10x + 9

6) (8x + 9) + (-6x - 1) = 8x + 9 - 6x - 1

                                = 8x - 6x + 9 - 1

                                = 2x + 8

Answer:1.2

Step-by-step explanation:

The height of the 6th bounce of the ball will be 1.2 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

[tex]T_{n} =ar^{n-1}[/tex]

Where,

[tex]T_{n}[/tex] is the nth term.

r is the common ratio

a is the first term

According to the given question.

During the first bounce, height of the ball from the ground, a = 6 feet

And, the each successive bounce is 72% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

= 72% of 6

= [tex]\frac{72}{100} (6)[/tex]

= 0.72 × 6

= 4.32 feet

During the third bounce, the height of ball from the ground

= 72% of 4.32

= [tex]\frac{72}{100} (4.32)[/tex]

= 3.11 feet

Like this we will obtain a geometric sequence 6, 4.32, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.72

Therefore,

The sixth term of the geometric sequence is given by

[tex]T_{6} = 6(0.72)^{6-1}[/tex]

[tex]T_{6} =6(0.72)^{5}[/tex]

[tex]T_{6} = 6 (0.193)[/tex]

[tex]T_{6} = 1.16 feet[/tex]

[tex]T_{6} = 1.2[/tex] feet

Hence, the height of the 6th bounce of the ball will be 1.2 feet.

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Answer:

10

Step-by-step explanation:

Answer: If, on earth, your mass is 30kg, then your weight is m*g which is mass (30kg) times Earth gravity (9.8m/s^2) = 294 N.

Step-by-step explanation:

The weight of a girl would be 294 N on Earth with a mass of 30 Kg.

Arithmetic operations can also be specified by the addition, subtract, divide, and multiply built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

The weight on Earth of a girl would be the product of the mass and acceleration due to gravity on Earth

So the required solution would be:

⇒ weight  = mass × acceleration due to gravity on Earth

⇒ weight  = 30 × 9.8

⇒ weight  = 294 N.

Hence, the weight of a girl would be 294 N on Earth with a mass of 30 Kg.

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Answer:

Sixty-three percent is the statistic and 39% is the parameter.

Step-by-step explanation:

The statistic and the parameter are to be considered as 63% is the statistic and 39 % is the parameter.

Here the parameter represent the fixed measure that explained the overall population that share the related and common attributes.

And, the statistic means the attribute of the sample or the portion of the target population.

Hence, Sixty-three percent is the statistic and 39% is the parameter.

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