Using spherical polar coordinates r, 8, 4 to find CM of a uniform solid hemisphere of radius R, whose flat face lies in the xy plane with its center at the origin. The element of volume is in spherical polars of dV = r² dr sine de dip.
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A: It is given that, a→=2.8i^+5.7j^-8.1k^ b→=-4.9i^+4.4j^+3.8k^ c→=1.8i^+2.8j^+4.6k^ and, r→=a→-b→+c→…
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- Help with this problemTwo 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-axisPlz C and D.
- The functions ¢1(x) and ø2(x) are normalized: d φ( (α) φι(α) dx 0(x) 62(x) = 1 = 1 -00 -00 and are mutually orthogonal dx oi(x) $2(x) dx 4i(x) $1(x) = 0 . Is the function b_(x) = ¢1(x) – $2(x) normalized? If not, determine its normalization constant and write the formula for the normalized y_ (x). Is the function +(x) = ¢1(x) + ¢2(x) %3D orthogonal to _(x)?Vector 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→ ?T The total surface area, A, of the cylinder can be expressed as A = (a) Find the value of k. (b) Find the value of that makes the total surface area a minimum
- (1) A metallic sphere has a density p and a radius r. (a) Using dimensional analysis, derive a formula for the mass of the sphere. (b) Using dimensional analysis, derive a dependence of the sphere radius if its mass and density are known.Enplain the equation Fz-VU.A dart gun contains a spring of spring constant k = 16 N/m which is used to shoot a dart of mass m. The dart leaves the gun at a speed of v = 3.1 m/s after the spring is compressed 1 cm. what is the darts speed when it hits the floor (vf in m/s) if it is fired horizontally at a height of h = 2 m what angle in degree does the darts final velocity make with the horizontal?
- A high tech company uses a satellite to measure the size of features on the surface of the earth. They use this technology to measure a particular rectangular field and find it's length to be 444 ± 1.8 in meters and it's width to be 198 ± 1.63 in meters. They plan to report the perimeter (sum of two lengths and two widths) of the field as P± SP in units of yards. (1 meter = 1.094 yards) What is SP?A rectangle expands and contracts with time t (in seconds). Its area is given by A= 4 + sin t square meters. At t = 3.14 (pi), the following is observed. (1) the width of the rectangle expands at the rate of 0.1 meters per second. (2) The width of the rectangle is 1 meter long How fast is the height of the rectangle changing at t = 3.14 (pi)?1.3 Determines the value of m so that the vectors ū = [-2,6,4] and v = [m,9,6] are: A) collinear B) orthogonal