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Los ciclistas se encuentran aproximadamente 140 segundos después de partir.

En este problema asumimos que cada ciclista se mueve a rapidez constante, de modo que la rapidez angular de cada uno se define como sigue:

ω = 2π / T         (1)

Donde:

A su vez, la posición de cada ciclista es descrita por las siguientes dos ecuaciones paramétricas:

x / R = cos ωt   (2)

y / R = sin ωt    (3)

Donde:

Primero, determinar la rapidez angular de cada ciclista:

ω₁ = 2π / 105 s

ω₁ ≈ 0.060 rad / s

ω₂ = 2π / 60 s

ω₂ ≈ 0.105 rad / s

Segundo, procedemos a graficar cada función paramétrica y determinamos el primer punto de intersección. Los resultados se encuentran en las imágenes adjuntas. Nótese que las curvas verde y púrpura se basan en la ecuación (2), mientras las curvas azul y rojo lo son de la ecuación (3).

Los dos ciclistas se encuentran por primera vez si las cuatro ecuaciones tienen el mismo valor t. En consecuencia, los ciclistas se encuentran aproximadamente 140 segundos después de partir.

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Natural number multiplication is commutative.

The given number is commutative as -

7.4.1.5 = 5.1.4.7

The answer will always be same irrespective of the order in which it is multiplied

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The device numbers should be less than 18.

Given, internet service provider is charging a rate of $175 per month.

The new plan would charge $94 plus an additional $4.50 per device connected to the network.

we need to find the number of devices for which the cost of the new plan is less than the cost of the current plan.

old plan = $175

New plan = $94 plus $4.50 per device

let us suppose 'x' devices can be connected.

so, 94 ₊ 4.5x < 175

4.5x < 175 ₋ 94

4.5x < 81

x < 81/4.5

x < 18

less than 18.

Hence there should be less than 18 devices connected for the new plan.

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Answer:

A.

B.✅

C.✅

D.✅

E.

F.✅

Step-by-step explanation:

[tex](4x-1)² = 11 \\ 4x-1 = \sqrt{11 } \\ 4x = \sqrt{11} + 1 \\ x = \frac{ \sqrt{11} + 1 }{4} [/tex]

Answer:

13/4

Step-by-step explanation:

_______________________________

The larger of the two integers is 18 and the smaller integer is 17.

Integers are collection of whole numbers and negative numbers. Integers are not fractional numbers or decimal. Some examples of integers are -5,-25,0,13,9 .

Let us consider the smaller integer be x.

As the integers are consecutive, the larger integer is (x+1).

Now according to the given condition:

Twice the large integer=2(x+1)

15 less than the 3 times the smaller integer=3x-15

Now the value of these two expressions is equal.

Therefore: [tex]2(x+1)=3x+-15[/tex]

Solving the above equation to find the value of x:

[tex]or,2(x+1)=3x-15\\or,2x+2=3x-15\\or,2x-3x=-15-2\\or,-x=-17\\or,x=17[/tex]

Therefore the smaller integer is 17.

Larger integer(x+1) : 17+1=18

Therefore the integers are 17 and 18.

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Answer:

35

Step-by-step explanation:

Step-by-step explanation:

the slope is (y coordinate change / x coordinate change) when going from one point on the line to another.

the direction does not matter, but it is essential that once a direction is picked for one coordinate, we use the same one then also for the other.

I prefer to go from left to right, so (-5, 0) to (-4, 2) :

x changes by +1 (from -5 to -4).

y changes by +2 (from 0 to 2).

so, the slope is +2/+1 = 2/1 = 2.

Answer:

y ≥ 5

Step-by-step explanation:

[tex]\frac{6y}{6}\ge \frac{30}{6}\\\frac{30}{6} = 5\\y \ge 5[/tex]

Hope this helps.

Dividing the number 5 by 4 gives a rational number 5/4.

The word 'rational' comes from the word 'ratio.'

For the given expression;

When 5 is divided by the number 4, 4 will not completely divide the number 5 as 5 is not the multiple of 4.

Thus, dividing 5 by 4 gives the rational number 5/4.

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Answer:

13/25

Step-by-step explanation:

hope this helps :)

Answer:

It has 1 line off symmetry.

Step-by-step explanation:

it has one straight from the top point all the way down.

Answer:the answer is 4 kg

Step-by-step explanation:

i can¡ explane u i see the rpta

Answer:

D.)

Step-by-step explanation:

The price of the perpetuity is $2200

The present value of a perpetuity is determined by simply dividing the amount of the regular cash flows by the discount rate. A growing perpetuity includes a growth rate that increases the cash flows received each period going forward.

Given:

coupon=$55

yield to maturity=2.5%

As, we know price of the perpetuity is determined by dividing the coupon by the yield to maturity.

So,

price=coupon/yield to maturity

price=$55/2.5%

price=$2200

Hence, the price of the perpetuity is $2200

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Answer:

Multiplicative inverse or reciprocal.

Step-by-step explanation:

Multiplicative inverse or reciprocal.

Taking into account the definition of speed, Monica will complete the triathlon in 12.62 hours.

Speed can be defined as the amount of space traveled per unit of time with which a body moves and can be calculated using the expression:

speed= distance traveled÷ time

In this case, you know

Replacing these values ​​in the speed definition:

Solving:

Swim: 1.8 mph×time to swim= 2.4 miles

time to swim= 2.4 miles÷ 1.8 mph

time to swim= 1.33 h

Ride a bike: 19.2 mph× time to ride a bike = 112 miles

time to ride a bike= 112 miles÷ 19.2 mph

time to ride a bike=5.83 h

Run: 4.8 mph× time to run= 26.2 miles

time tu run= 26.2 miles÷ 4.8 mph

time to run= 5.46 h

The time to complete the triathlon is the sum of each of the stages:

Total time= time to swim + time to ride a bike + time to run

Total time= 1.33 h + 5.83 h + 5.46 h

Total time= 12.62 h

In summary, Monica will complete the triathlon in 12.62 hours.

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Answer: 7.49

Step-by-step explanation:

7 is above 5, so we round up from .48 to .49.

Answer:

(-5,3)

Step-by-step explanation:

That's the coordinates of it being reflected over X axis for point P.

Answer:

Step-by-step explanation:

where is the swan?

Answer:  First graph

Step-by-step explanation:

We first rewrite the equation in slope-intercept form y = ax + b, where a is the slope and b is the y-intercept(where x is equal to 0).

24x + 64y = 384

         64y = -24x + 384

             y =  [tex]-\frac{24}{64}[/tex]x + 6

The y-intercept for this graph is equal to 6. Only the first graph satisfied the slope of the linear equation that we are looking for. In the first graph, when x was equal to 0, y was equal to 6.

Answer:

21.78 m^2

Step-by-step explanation:

9.9 x 4.4 / 2 = 21.78 m^2

L = 1.3245 is  the legnths of the pen's sides .

What is area and perimeter?

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)

So W = 30 - 2L.

Area = L x W = L (30 - 2L) = 30L - 2L^2.

This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .

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Answer:

Mark them in a gtaph paper.

Step-by-step explanation:

Tke a graph paper and draw the x and y axis in the middle of the graph.

If u hv learned coordinates mark the points and count the boxes in between.

That will be ur answer

Thank me later

The grade level is treated as categorical when a principal wants to know the number of students from each grade will be participating in a performance.

Variables can be classified into quantitative and categorical. Quantitative variables are those which carry numerical values. Even though a person's grade in school is generally identified by a number, it is a categorical variable. Categorical variables classify data into different groups as the grade level. The grade level categorizes students into different grades and each grade level represents a particular grade only.

Any variable which is partly qualitative and represents groups of data are called categorical variables. Also grade level is ordinal. An example of a situation in which grade level is treated as categorical is when a principal wants to know how many students from each grade will be participating in a performance. Other examples of categorical variables are race, gender, age group, etc.

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Answer:

y=-x+13

Step-by-step explanation:

m=-1

m is slope

point is (9, 4)

first use point slope equation

y-y1=m(x-x1)

y-9=-1(x-4)

distribute

y-9=-x+4

isolate the y variable

y=-x+13

If shareholders in an electronics company were informed that the company's market share increased from 4.5% to 5.4%, a rise of 0.9 percentage points. The percent increase in sales that this represent is: 20%.

Using this formula

Percentage increase= Percentage increase in share price / Initial percentage x 100%

Let plug in the formula

Percentage increase= 0.9% / 4.5% x 100%

Percentage increase=20%

Therefore If shareholders in an electronics company were informed that the company's market share increased from 4.5% to 5.4%, a rise of 0.9 percentage points. The percent increase in sales that this represent is: 20%.

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