Simplify the expressions. (a) −(25 + 12) (b) −7 − (6 − 3)
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Simplify the expressions.
(b)
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- The x and y coordinates of point P are (-8.50 m, -7.00 m). What is the polar angle of point P?Two points in the xy plane have Cartesian coordinates (1.50, -3.50) m and (-6.50, 6.50) m. (a) Determine the distance between these points. m (b) Determine their polar coordinates. (1.50, -3.50) (1.50, -3.50) 0 = (-6.50, 6.50) T= (-6.50, 6.50) 0 = m counterclockwise from the +x-axis m counterclockwise from the +x-axisGiven that A + B = x₁Î + Y₁Ĵ and Ö Ē = x₂Î + y₂), what is ? A ® B = ²/² ( x ₁ + x₂) ₁ + 1/{ (Y₁ +92)ĵ B Î D B = ½ (×₁ − ×₂) Î + ½ (Y₁ −³₂)Î E B = ½¼½ (X₁ − ×₂)Î + ½ (Y₁ + Y2 )Ĵ ³ = ½ (X₁ + X₂) Î + ½ (Y₁ −Y₂)ĵ B = ½ (³₁ −³₂)ĵ
- 2 Use the determinant of a matrix to find the area of the triangle whose vertices are (6, 1), (8,5), and (3, 1). ▸ Area = W S Enter an integer or decimal number [more..] Calculator Check Answer X 36 3 20 F3 E $ 4 D 이 C F4 R F % 5 F5 V T MacBook Air A 6 G F6 Y B & 7 H AK F7 C * 00 8 N DII FB - ( 9 F9 K M O V F10 XVector B→B→ has magnitude 7.30 and direction 14.0° below the +x-axis. Vector C→C→ has x-component Cx = −2.00 and y-component Cy = −6.70. f. What angle does the resultant vector C→+B→C→+B→ make with the +x-axis in clockwise direction? A positive angle is counterclockwise from the +x-axis. answer in degrees g. What is the magnitude of C→−B→C→-B→ ? h. What angle does the vector C→−B→C→-B→ make with the +x-axis in counterclockwise direction? A positive angle is counterclockwise from the +x-axis. i. What is the x-component of C→−B→C→-B→ ? j. What is the y-component of C→−B→C→-B→ ?The figure shows three vectors. Vector A→ has a length of 35.0, vector B→ has a length of 69.0, and vector C→ has a length of 21.0. Solve the given equations. A→∙B→= ? B→∙(A→+C→)= ?
- The figure shows three vectors. Vector A→ has a length of 31.0, vector B→ has a length of 67.0, and vector C→ has a length of 22.0. Find each magnitude and direction. |A→×B→|= ? direction: ? |C→×B→|= ?1. Vector A is along the x-axis and vector B makes an angle with the z-axis. The magnitude of A - B is (a) A - B cos 0 (b) A - B sin 0 (c) √A²-B² (d) (A - B sin 0)2 + B² cos²0) (e) (A - B cos 0)² + B² sin² 0)6. Given vectors Ã= 2â, + 4ây + 10â, and B = -5âp + âo – 3âz, find (a) Ã+ B at P(0, –2,5) , with o = 90° (b) ÷Ē (c) Ã× B (d) The angle between A and B at P (e) The scalar component of A along B at P
- Consider vectors a = (3, −12) b = (−1, 4)and c = 0. Determine the non-zero scalars ? and ? such that c = ? a + ? b.(6%) Problem 5: Consider the following vectors: A = 4.6i + 1.4j+ 3.4k В = -6. 5i + 7.1j + 10.2k 25% Part (a) What is the x-component of the vector V = 3(A × 2B)? Vx= sin() cos() tan() 7 8 9 НOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 cosh() tanh() cotanh() + END Degrees Radians Vd BACKSPACE DEL CLEAR Feedback Submit Hint I I give up! Hints: 2 for a 0% deduction. Hints remaining: 0 Feedback: 3% deduction per feedback. -This is a cross-product, so the answer will be a vector. In this part, we just want the x-component of the vector. Keep in mind that scalars like "2" and "3" distribute 3.Note: Please provide a simple and step-by-step solution.