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2 years ago

List three numbers that are less then 66,100

Mathematics

2 answers:

Blizzard [7]2 years ago

6 0

Answer:

1, 2, 3

Step-by-step explanation:

1, 2 and 3 are all less that 66,100

9966 [12]2 years ago

4 0

Answer:

Step-by-step explanation:

65,000

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I need to solve the equation please help me

lesantik [10]

Answer:

$\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}$

Step-by-step explanation:

We are given the equation:

$4\sin^2(x)+6\sin(x)+2=0$

First, we can divide everything by 2:

$2\sin^2(x)+3\sin(x)+1=0$

Notice that we have an equation in quadratic form. Namely, if we make a substitution where u = sin(x), we acquire:

$2u^2+3u+1=0$

Solve for u. Factor:

$(2u+1)(u+1)=0$

Zero Product Property:

$2u+1=0\text{ or } u+1=0$

Solving for both cases:

$\displaystyle u=-\frac{1}{2}\text{ or } u=-1$

And by substitution:

$\displaystyle \sin(x)=-\frac{1}{2}\text{ or } \sin(x)=-1$

For the first case, recall that sin(x) is -1/2 for every 7π/6 and every 11π/6. Hence, for the first case, our solutions are:

$\displaystyle x=\frac{7\pi}{6}+2n\pi \text{ and } x=\frac{11\pi}{6}+2n\pi, n\in\mathbb{Z}$

Where n is an integer.

For the second case, sin(x) is -1 for every 3π/2. Thus:

$\displaystyle x=\frac{3\pi}{2}+2n\pi$

All together, our solutions are:

$\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}$

4 0

2 years ago

A given line has the equation 10x + 2y = −2.

sergij07 [2.7K]

Firstly, let's convert 10x + 2y = -2 to slope-intercept form (y = mx + b):

10x + 2y = -2
2y = -10x - 2
y = -5x - 2/5

The slope is -5. Parallel lines have the same slope; the question provides the y-int (12), so our equation is:

y = -5x + 12

Hope this helps.

5 0

2 years ago

Read 2 more answers

A rectangle has a length of 45 inches less than 4 times its width. if the area of the rectangle is 3325 square inches, find the

Maru [420]

The length of the rectangle is based on its width, so let's call width w and put the length in terms of the width. We are told that the width is 45 less than 4 times the width, so the length is 4w - 45. Area is found by multiplying length times width and we are given the area as 3325. So we will set up length times width and solve for w, which we will then use to solve for l. 3325 = (4w - 45)(w). Multiplying out we have $3325=4w^2-45w$ . Move the constant over by subtraction and then we will have a quadratic that can be factored to solve for w. $4w^2-45w-3325=0$ . We would put that through the quadratic formula to solve for w. When we do that we get that w = 35 and w = -23.75. The 2 things in math that will never EVER be negative is time and distance/length, so -23.75 is out. That means that the width is 35. The length is 4(35) - 45 which is 95. The dimensions of your rectangle are length is 95 and width is 35. There you go!