An equilateral triangle with side lengths of 10 units is translated 4 units to the right. What is the length of one side of the triangle
after translation, in units?

The linked answer is wrong because that integral gives you the net displacement of the object, not the total distance.

To get the distance, you have to integrate the speed (as opposed to velocity), which involves integrating the absolute value of the velocity function.

[tex]\mathrm{distance} = \displaystyle\int_1^5 |\sin(t)| \,\mathrm dt[/tex]

By definition of absolute value,

[tex]|\sin(t)|=\begin{cases}\sin(t)&\text{for }\sin(t)\ge0\\-\sin(t)&\text{for }\sin(t)<0\end{cases}[/tex]

Over this particular integration interval,

• sin(t ) ≥ 0 for 1 ≤ t < π, and

• sin(t ) < 0 for π < t ≤ 5

so you end up splitting the integral at t = π as

[tex]\mathrm{distance} = \displaystyle\int_1^\pi \sin(t)\,\mathrm dt + \int_\pi^5 (-\sin(t))\,\mathrm dt[/tex]

Now compute the distance:

[tex]\mathrm{distance} = -\cos(t)\bigg|_1^\pi + \cos(t)\bigg|_\pi^5[/tex]

[tex]\mathrm{distance} = -(\cos(\pi) - \cos(1)) + (\cos(5) - \cos(\pi))[/tex]

[tex]\mathrm{distance} = -2\cos(\pi) + \cos(1) + \cos(5) \approx 2.82[/tex]

making B the correct answer.

Answer:

Step-by-step explanation:

Interest amount is:

Answer:

Step-by-step explanation:

i

I agree with Alice because you do not know how much money Jill and Jack had before they went shopping. If they had the same amount of money Jill would have spent more because 40 percent is greater than 1/3.

Step-by-step explanation:

Thank me later

Answer:

The mathematical expression is 107*x

Step-by-step explanation:

Since we already know that 107x equals to 107*x, we knew that the expression would be 107*x.

Hopefully this helped (• ▽ •)

Answer:

45b - 10a

Step-by-step explanation:

Answer:

5(9a-2b)

Step-by-step explanation:

This is a polynomial and you have to factor it.

GCF of 45a and 10b is 5

5(9a-2b)

Branliest would be Appreciated

Answer:

The  constant of proportionality k = 12

Hence, option A is true.

Step-by-step explanation:

We know that when 'y' varies directly with 'x', we get

y ∝ x

y = kx

Where 'k' is called the constant of proportionality.

In our case,

The given equation is

y = 12x

comparing with the equation y = kx, we can say

k = 12 which is the constant of proportionality.

Therefore, we conclude that:

The  constant of proportionality k = 12

Hence, option A is true.

Answer:

sqrt7/4

Step-by-step explanation:

sin is opposite/hypotenuse which means sqrt63/12 then sqrt63=3sqrt 7 and simplifies get (sqrt7)/4 Done!

Answer:

No i do not agree

Step-by-step explanation:

the tip is 15$ im pretty sure

Answer:

That depend on how much you spend on electricity, and how much other spending you do.

For example: If your electric bill is 100 dollars, and it increases 30 percent to 130, that’s 30 extra dollars. If your electric bill is only 50 dollars, it will increase to 65, that’s an extra 15.

What percentage that increase is of your current spending will vary according to how much you spend. If you only spend 30 dollars, then you’ll need to cut all of it, or half of it to offset the increases I mentioned above. That’s a 100 percent or 50 percent reduction.

If you spend 1000 dollars, you’ll only need to cut spending by 3 percent to get that 30 dollars, or 1.5 percent to get the 15 dollars.

It all depends on your specific values, you can’t say “For every xx percent your electric bill increases, you need to cut spending by yy percent.”

for the consumption of X unit let u spends Y

for X - Y cost

for increased 30% means 13X/10 - 13Y/10 cost

extra money is 13Y/10 - Y = 3Y/10

note: hope this helps :)

thus (3Y/10)/ (13Y/10) *100 % = 300 / 13 = 23.07%.

Answer:  6.93641618497 You would have to round that to the nearest sum.

Answer:

numerator on top

denominator on bottom

Step-by-step explanation:

Answer:

13+34=47

Step-by-step explanation:

Let us call the number x

13+x=47

so we can assume

47-13=x

47=13=34

13+34=47

Answer:

0.5874

Step-by-step explanation:

Answer:

0.5874

Step-by-step explanation:

Getting 58.74 percent of a number is the same as multiplying the number 0.5874

Answer:

Step-by-step explanation:

The area of a trapezium is given as;

Area = [tex]\frac{1}{2}[/tex](a + b)h

where: a is the length of the upper side, b is the length of its base and h is its height.

This implies that; a = x - 4, b = x + 5, h = 2x and area = 351

Thus,

351 =  [tex]\frac{1}{2}[/tex]((x - 4) + (x + 50)) 2x

      = (x - 4 + x + 5) x

531 = (2x + 1) x

      = 2[tex]x^{2}[/tex] + x

So that;

2[tex]x^{2}[/tex] + x - 531 = 0

This gives a quadratic equation.

Answer:

112.5 divided by 15=7.5

112.5 divided by 15=7.5 equation is true answer.

Given option are:

15 divided by 112.5 = 7.5

15 ÷ 112.5 = 0.1333

This option is wrong.

15 divided by 112.5 = 75

15 ÷ 112.5 = 0.1333

This option is wrong.

112.5 divided by 15 = 7.5

112.5 ÷  15 = 7.5.

This option is right.

112.5 divided by 15 = 75.

112.5 ÷  15 = 7.5.

This option is wrong.

Therefore, the correct equation is 112.5 divided by 15=7.5

Learn more about divide here:

https://brainly.com/question/30038387

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Answer:

x<-3

Explanation:

Divide both sides by -2 to isolate x.

Since you have divided by a negative number and it changed the positive number to a negative one, you'll need to change the direction of the sign to now reflect that.

I hope that helped!

sana tama po

Answer:

11

Step-by-step explanation:

i hope this help:)s

Answer:

2 pound bags and have a remeinder of 1/10

Step-by-step explanation:

Answer:

She can fill 2 bags for her lunch and will have 1/10 pound left.

Step-by-step explanation:

It is easier if there is a common denominator, so I made the 2/5 into 4/10, so it is the same as 9/10 pound she bought.

4/10 is one bag, and if you double that, it is 8/10 pounds used. This is two bags of raisins for her lunch.

9/10 - 8/10 leaves 1/10 pound remaining, and not in a bag.

Answer:

D. [tex] 2\sqrt {133}[/tex]

Step-by-step explanation:

[tex] {x}^{2} = {18}^{2} + ( {12}^{2} + {8}^{2} ) \\ \\ {x}^{2} = 324 + (144 + 64) \\ \\ {x}^{2} = 324 + 204 \\ \\ {x}^{2} = 528 \\ \\ x = \sqrt{532} \\ \\ x = \sqrt{4\times 133} \\ \\ x = 2\sqrt {133}[/tex]

Answer:

2 miles.

Step-by-step explanation:

17.95 +17.95= 35.90

Answer:

The answer to the question provided is

1. y = 4x - 3.

2. y = -2x - 2.

Answer:

thank you sm!

Step-by-step explanation:

I hope you have a good day / night ^^

☁️☁️☁️☁️☁️☁️☁️☁️☁️☁️☁️☁️☁️☁️

Answer:

267 3/4 miles

just do 12 3/4*21

1.92307692308

Hope this helps! :D

Hi there!

For these two equations, we would be using PEMDAS...

[tex]3[/tex]·[tex]3=9-5=4[/tex]

[tex]5[/tex]·[tex]6=30+19=49[/tex]

Hope this helps!

Answer:

x = 3

Step-by-step explanation:

Measure of a triangle is 180° degree.

.·. 46 + 105 + 6x + 11 = 180

.·. 162+6x=180

.·. 6x=180-162

.·. 6x= 18

.·. x= 18/6

.·. x= 3