The value pi/4 is a solution for the equation 3 sqrt 2 cos theta+2=-1

Answers

Answer 1

Answer:

Answer:

FALSE

Step-by-step explanation:

$3\sqrt2\cos\theta+2=-1\n\n\text{Method 1}\n\n\text{Put}\ \theta=(\pi)/(4)\ \text{to the equation and check the equality:}\n\n\cos(\pi)/(4)=(\sqrt2)/(2)\n\nL_s=3\sqrt2\cos(\pi)/(4)+2=3\sqrt2\left((\sqrt2)/(2)\right)+2=((3\sqrt2)(\sqrt2))/(2)+2\n\n=((3)(2))/(2)+2=3+2=5\n\nR_s=-1\n\nL_s\neq R_s\n\n\boxed{FALSE}$

$\text{Method 2}\n\n\text{Solve the equation:}\n\n3\sqrt2\cos\theta+2=-1\qquad\text{subtract 2 from both sides}\n\n3\sqrt2\cos\theta=-3\qquad\text{divide both sides by}\ 3\sqrt2\n\n\cos\theta=-(3)/(3\sqrt2)\n\n\cos\theta=-(1)/(\sqrt2)\cdot(\sqrt2)/(\sqrt2)\n\n\cos\theta=-(\sqrt2)/(2)\to\theta=(3\pi)/(4)+2k\pi\ \vee\ \theta=-(3\pi)/(4)+2k\pi\ \text{for}\ k\in\mathbb{Z}\n\n\text{It's not equal to}\ (\pi)/(4)\ \text{for any value of }\ k.$

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PLEASE HELP ME!!!! 50 points! Given the points C(-1, -3) and D(5, 6), find the coordinates of the point E on directed line segment CD that partitions CD into the ratio 2 to 1.

A. (1, 0)

B. (3, 3)

C. (-3, 3)

D. (2, 1.5)

Answers

Answer:

B. (3,3)

Step-by-step explanation:

In order to find the coordinates of point E that partitions the line segment CD into a ratio of 2:1, we can use the following formula for finding the coordinates of a point that divides a line segment in a given ratio:

For a line segment with endpoints A(x1, y1) and B(x2, y2), and a division ratio of m:n, the coordinates of the point E(x, y) that divides the line segment in this ratio are given by:

$\sf x =( (m* x_2 + n* x_1) )/((m + n))$

$\sf y =( (m* y_2 + n* y_1) )/((m + n))$

In this case, we want to divide the line segment CD into a ratio of 2:1, so m = 2 and n = 1.

Wehave the coordinates of C(-1, -3) and D(5, 6).

Using the formula:

$\begin{aligned} x &\sf =( (2* 5 + 1* (-1)))/( (2 + 1)) \n\n &\sf = (10-1)/(3)\n\n &\sf = (9)/(3)\n\n &\sf = 3 \end{aligned}$

and

$\begin{aligned} y &\sf =( (2* 6 + 1* (-3)) )/( (2 + 1)) \n\n &\sf = (12-3)/(3) \n\n &\sf = (9)/(3)\n\n &\sf = 3 \end{aligned}$

So, the coordinates of point E that partitions the line segment CD into a ratio of 2:1 are E(3, 3).

So, the answer is B. (3,3)

Answer:

Step-by-step explanation:

bc yes

Simplify and identify the domain -4/4x+8 times 5(x+3)x^2-9

Answers

Hello,

R\{-2} all reals excepted -2
====================

The width of a rectangle is 61 centimeters more than the length. The perimeter is 406 centimeters. Find the length and the width.

Answers

$Step \; 1: \; Assign \; Variables \; for \; the \; unknown \; that \; we \; need \; to \; find$

$Let \; x \; be \; length \; of \; the \; rectangle$

$Step \; 2: \; Set \; up \; equation \; based \; on \; information \;\n given \; about \; the \; rectangle$

$Statement \; 1: Width \; of \; a \; rectangle \; \nis \; 61cm \; more \; than \; the \; length\n\nWidth \; = \; 61+x\n\nStatement \; 2: \; The \; perimeter \; is \; 406cm\n\nPerimeter=2(Length+Width)\nPerimeter =2(x+61+x)\n\nSo \; the \; mathematical \; equation \; would \; be \n 2(x+61+x)=406$

$Step \; 3: \; Solve \; the \; equation \; by \n undoing \; whatever \; is \; done \; x.\n\n2(x+61+x)=406\nGroup \; and \; Combine \; like \; terms \; inside \; the \; parenthesis\n\n2(2x+61)=406\nDistribute \; 2 \; in \; the \; left \; side \; of \; the \; equation\n\n4x+122=406\nSubtract \; 122 \; on \; both \; sides\n\n4x+122-122=406-122\nSimplify \; on \; both \; sides\n\n4x=284\nDivide \; on \; both \; sides\n\n(4x)/(4)=(284)/(4)\nSimplify \; fractions \; on \; both \; sides\n\nx=71$

$Conclusion:\nLength=x=71cm\nSubstituting \; 71 \; for \; x \; and \; find \; Width \; value.\nWidth=61+x=71+61=132cm\n\nLength \; is \; 71 cm \; and \; Width \; is 132cm$

Final answer:

The length of the rectangle is 71 centimeters and the width is 132 centimeters.

Explanation:

To find the length and width of the rectangle, we can set up a system of equations. Let's denote the length of the rectangle as L and the width as W. We know that W = L + 61. The formula for the perimeter of a rectangle is P = 2L + 2W. Plugging in the given values, we have 406 = 2L + 2(L + 61). Simplifying this equation, we get 406 = 4L + 122. Subtracting 122 from both sides, we obtain 284 = 4L. Dividing both sides by 4, we get L = 71. Finally, substituting the value of L into the equation W = L + 61, we find W = 71 + 61 = 132. Therefore, the length of the rectangle measures 71 centimeters and the width measures 132 centimeters.

Learn more about Rectangle dimensions here:

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Justin weighs 15 pounds less than Greg weighs. Half of Greg’s weight is 75 pounds less than Justin’s weight. How much does each of them weigh? Greg weighs 200 pounds, and Justin weighs 185 pounds. Greg weighs 190 pounds, and Justin weighs 175 pounds. Greg weighs 180 pounds, and Justin weighs 165 pounds. Greg weighs 170 pounds, and Justin weighs 155 pounds.

Answers

J=G-15
(G/2)=J-75

Substitute
(G/2)=G-15-75
G/2 =G-90
G-G/2= 90
G/2=90
G=180

J=G-15=180-15=165

Greg weighs 180 pounds, and Justin weighs 165 pounds.

Answer:

180 and 165

Find x of this shape.