(1)Identify the surface whose equation is r = 2cosθ by converting first to rectangular coordinates...(2)Identify the surface whose equation is r = 3sinθ by converting first to rectangular coordinates...(3)Find an equation of the plane that passes through the point (6, 0, −2) and contains the line x−4/−2 = y−3/5 = z−7/4...(4)Find an equation of the plane that passes through the point (−1,2,3) and contains the line x+1/2 = y+2/3 = z-3/-1...(5)Find a) the scalar projection of a onto b b) the vector projection of a onto b given = 〈2, −1,3〉 and = 〈1,2,2〉...(6)Find a) the scalar projection of a onto b b) the vector projection of a onto b given = 〈2,1,4〉 and = 〈3,0,1〉...(7)Find symmetric equations for the line of intersection of the planes x + 2 y + 3z = 1 and x − y + z = 1...(8)Find symmetric equations for the line of intersection of the planes x + y + z = 1 and x + 2y + 2z = 1...(9)Write inequalities to describe the region consisting of all points between, but not on, the spheres of radius 3 and 5 centered at the origin....(10)Write inequalities to describe the solid upper hemisphere of the sphere of radius 2 centered at the origin....(11)Find the distance between the point (4,1, −2) and the line x = 1 +t , y = 3 2−t , z = 4 3−t...(12)Find the distance between the point (0,1,3) and the line x = 2t , y = 6 2−t , z = 3 + t...(13)Find a vector equation for the line through the point (0,14, −10) and parallel to the line x=−1+2t, y=6-3t, z=3+9t<span>...</span>
Answer:
The rectangle is 5 inches long by 19 inches wide.
Step-by-step explanation:
Let's start by listing what we know:
- The perimeter of a rectangle is 48 inches.
- The width of the rectangle is 4 inches more than 3 times the length of the rectangle.
Let's represent the width with "w" and length with "l", and make a system of equations based on what we know.
Now, let's solve the system of equations using substitution:
The length of the rectangle is 5 inches.
Now, let's use this to solve for the width.
The width of the rectangle is 19 inches.
Let's check our work:
The results match, so our answer is correct.
The rectangle is 5 inches long by 19 inches wide.
Do you rationalists the denominator by subtracting by 2
The answer: " x = 5 " .
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Explanation:
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Given: " x = √(15 <span>− 2x) " ; Solve for "x" ;
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"Square" each side of the equation:
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</span> → (x)² = [√(15 − 2x) ] ² ;
→ x = 15 − 2x ;
Now, add "2x" to each side of the equation:
→ x + 2x = 15 − 2x + 2x ;
→ 3x = 15 ;
Now, divide each side of the equation by "3" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 3x / 3 = 15 / 3 ;
→ " x = 5 " .
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When you graph both equations, the solutions are all points found in the shaded region of where the graphs overlap. Solutions are also found on y <span>≥ -2x-2 because it has a greater than or equal to sign and the line is solid.
The red line is y > x - 5
The blue line is y </span><span>≥ -2x-2</span>