The length of a rectangle is 1 yd more than twice the width, and the area of the rectangle is 45 yd2 . Find the dimensions of the rectangle. Length : Width :

Answer:

[tex]\displaystyle x=\left\{\arcsin\left(\frac{-1+\sqrt{3}}{2}\right), \pi-\arcsin\left(\frac{-1+\sqrt{3}}{2}\right)\right\}[/tex]

Or their approximations:

[tex]x\approx \left\{0.375, 2.767\right\}[/tex]

Step-by-step explanation:

We are given:

[tex]\cos(2x)=2\sin(x)[/tex]

And we want to find the solution in [0, 2π).

Recall the double-angle identities for cosine:

[tex]\begin{aligned} \cos(2x)&=\cos^2(x)-\sin^2(x) \\&=2\cos^2(x)-1\\&=1-2\sin^2(x)\end{aligned}[/tex]

We will use the third version. Hence:

[tex]1-2\sin^2(x)=2\sin(x)[/tex]

Move all terms to one side:

[tex]-2\sin^2(x)-2\sin(x)+1=0[/tex]

This is now in quadratic form. For simplicity, let u = sin(x):

[tex]-2u^2-2u+1=0[/tex]

Solve for u. Simplify:

[tex]2u^2+2u-1=0[/tex]

By the quadratic formula:

[tex]\displaystyle u=\frac{-(2)\pm\sqrt{(2)^2-4(2)(-1)}}{2(2)}}[/tex]

Evaluate:

[tex]\displaystyle u=\frac{-1+\sqrt{3}}{2}\approx 0.366\text{ and } u=\frac{-1-\sqrt{3}}{2}\approx-1.366[/tex]

Note that the second solution is > -1. Hence, we will disregard it. (The range of sine is only -1 ≤ y ≤ 1.)

Back-substitute:

[tex]\displaystyle \sin(x)=\frac{-1+\sqrt{3}}{2}[/tex]

Since it is approximately 0.366, it will occur twice (once in QI and again in QII. This is because sine is positive only in those two quadrants). Using a calculator:

[tex]\displaystyle x_1=\arcsin\left(\frac{-1+\sqrt{3}}{2}\right)\approx0.375[/tex]

Using reference angles, the other solution is:

[tex]\displaystyle x_2=\pi -x_1=\pi -\arcsin\left(\frac{-1+\sqrt{3}}{2}\right) \approx2.767[/tex]

Answer:36cm

Step-by-step explanation:The area of a circle is pi times the radius squared (A = π r²

a) Diameter is 12cm

; (b) radius is 6cm

; and (c) area is 36πcm2.

Explanation:If r is the radius of a circle, then its circumference is 2πr

and area is πr2.

As circumference is given to be 12π, we have 2πr=12π

or r=12π2π=6cm.

As such radius is 6cm

and diameter being double of radius, diameter is 2×6=12cm.

and area is π×62=36 cm2

.

Answer:

(-2)(4)

Step-by-step explanation:

(-2)(4) because we made four ”steps” of the lenght of two on the left

Answer:

1. x is inversely proportional to y

x=k/y

k is the constant of proportionality

x =60/y

2. x=60/y

x=60/12

x=5

Answer: Equivalent equations are equations with identical solutions. You can find them by simply simplifying an equation.

EXAMPLE:

1 + 2 + 3 = 5x

An equivalent equation would be 3 + 3 = 5x

Answer:

check in my page someone will answer it for me

Step-by-step explanation:

then you get your answer

Answer:

should look like this a bit

Step-by-step explanation:

heres another pov

Answer:

i believe its 24+12

Step-by-step explanation:

Answer:

I'm pretty sure it's a

Step-by-step explanation:

step by step

Answer:

D

Step-by-step explanation:

Answer:

Your answer is approxamantly 68%

Step-by-step explanation:

a is the answer i took the test

Answer:

x = 2

Step-by-step explanation:

The four sides of a rhombus are equal.  Thus, 10x + 6 = 4x + 18.

Solve this equation for x:

6x = 12

So, finally, x = 2

Answer:

16

Step-by-step explanation:

because to get what you need add 27 and 28 and you get 55 then subtract 71 by 55 to get 16

71-(27+28)

Answer:

Grace sold 16 tickets.

Step-by-step explanation:

We have a total of 71 tickets sold between 3 people. Blake sold 27 tickets and Chang sold 28 tickets. Adding those sold by Blake and those sold by Chang, gives us: 27 + 28 = 55, if that amount is subtracted from the total sales that are 71 tickets, the result would be: 71 - 55 = 16, which would be the tickets sold by Grace.

Answer:

2/3

Step-by-step explanation:

please mark this answer as brainliest

Answer:

[tex] \frac{4}{6} \\ = \frac{2}{3} \\ = 0.66[/tex]

Answer:

y=3/4x +7

Step-by-step explanation:

The equation for slope-intercept is y=mx+b, where m is the slope and b is the intercept.

To find b, we can plug in the x,y, and given slope.

[tex]4 = \frac{3}{4} ( - 4) + b \\ 4 = - 3 + b \\ b = 7[/tex]

so now we can write b and m in the original equation.

which gives us, y =3/4x +7

Answer:

4

Step-by-step explanation:

You have positive number and it is bigger that negative so your result will be positive too:

7-3=4

Answer:

xy-2x+3y-6

(xy-2x) (3y-6)

x(y-2) 3(y-2)

(x+3) (y-2)

hope this answer helps you.....

Answer:

I think it is 1.5

Step-by-step explanation:

I'm not that sure sorry :(

Volume of human eyeball is 3 times more than volume of dog's eye .

Given,

Human eyeball diameter = 2.5 cm

Dog eyeball diameter = 1.75 cm

Now,

Firstly calculate the volume of humans eye,

Volume of sphere = 4/3 πr³

r = radius of eyeball

r = d/2

r = 2.5/2

r = 1.25 cm

Volume = 2.60π cm³

Now calculate the volume of dogs eye,

V = 4/3 πr³

r = d/2

r = 1.75/2

r = 0.875 cm

V = 0.893π

Thus from the calculation volume of human eye is more by approximately 3 times .

Know more about volume of sphere,

https://brainly.com/question/21623450

#SPJ4

Answer:

15?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

B(1) = 2

Step-by-step explanation:

Function B(x), according to the graph, which point has an x-value of 1? Point (1, 2). So the solution is 2.

Answer:

(13/2,-5/2)

Step-by-step explanation:

I hope this helps

Answer:

The triangle is scalene triangle because its all sides are different

So, you can go with it and

Request :- if you are helped with my answer pls tag me brianliest I really want it.......

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Answer:

64.345

Step-by-step explanation:

1 gal=3.785

multiply 3.785 x 17

Answer:

The system of equations that can be used to find the number of each type sold is given as:

x + y = 17 ...... Equation 1

76x + 141y = 1460....... Equation 2

Step-by-step explanation:

Let

x represent the number of polyester-fill bags sold

y represent the number of down-fill bags sold.

In one week the store sold 17 sleeping bags

x + y = 17 ...... Equation 1

x = 17 - y

At Raging River Sports, polyester-fill sleeping bags sell for $76. Down-fill sleeping bags sell for $141. In one week the store sold 17 sleeping bags for $1,460.

Hence:

$76 × x + $141 × y = $1460

76x + 141y = 1460....... Equation 2

Therefore, the system of equations that can be used to find the number of each type sold is given as:

x + y = 17 ...... Equation 1

76x + 141y = 1460....... Equation 2

Answer:

Mean = 11

Median = 12

Mode = 14

Step-by-step explanation:

I hope this helped!