Which lines or line segments or rays must be drawn or con- structed in a triangle to locate its a) orthocenter? b) centroid?

Q: O FIND THE レ-く,2,3> VOLUME oF TAE PARALLELEPIPED VECTURS WITH V = <4,10,87 w = <1,0,17 and AS ADJA…

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Q: Which figure below cannot be tessellated? O Star O Kite O Rhombus O Trapezoid

A: We have to cheek the

Q: If the plane shown below is perpendicular to the altitude of the cylinder, what is the perimeter of…

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Q: Find the volume of the parallelepiped whose adjacent axes PQ, PR and PS where P (1,-2, 2), Q (1, -1,…

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Q: Exercise 5. Let AABC be a triangle, let D be the point on the (extended) line AB such that DC 1 AB,…

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Q: Exercise : Campute the area enclosed by the lines y=x+1, x =2 and the x - and y-aces, li) geometry…

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Q: 2(a) Explain centroid of a triangle and rectangle with sketch.

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Q: 7. If the net was folded into a box, which sides represent the lateral surfaces? a f C e d

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Q: In the strip of rectangles shown below, a certain rigid motion applied to the leftmost rectangle…

A: The given pattern has vertical reflection symmetry since it would have two mirror images if we draw…

Q: Draw an obtuse triangle and, by construction, find the centroid of the triangle. (HINT: Begin by…

A: To get an obtuse triangle, draw a triangle with one of its interior angle should be greater than…

Q: Use Exercise 22 to find the centroid of the triangle with vertices (0,0), (a, 0) and (a, b) where…

A: To find the centroid we add the x coordinates and the y coordinates respectively and then divide by…

Q: Every triangle has a balancing point, called the centroid. O True O False

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Q: The figure shows a parallelepiped spanned by vectors a,b and c Which of the following formulas…

A: The formula to calculate the volume is given by, Volume=area of base⋅height             =∥b×c∥ ∥a∥…

Q: Which figure below cannot be tessellated? O Rhombus O Star O Kite O Trapezoid

A: Tessellation Tessellation or Tiling is a pattern which is created using identical shapes. These…

Q: Derive the frenet frame, curvature and torison o the binormal indicatrix of hypocycloid?

A: We need to Derive the fernet frame, curvature and torsion o the binormal indicatrix of hypocycloid.

Q: Prove that the midsegment of a trapezoid is parallel to the bases and its length is the average of…

A: To prove that the mid-segment of a trapezoid is parallel to its base, first consider a trapezoid…

Q: Consider the parallelepiped with adjacent edges u = 3i + 2j + k v = i + j + 2k w = i + 3j + 3k (a)…

A: Let us consider the parallelepiped with adjacent edgesu = 3i + 2j + kv = i + j + 2kw = i + 3j + 3k…

Q: 7. Let ABCD be a trapezoid which is inscribed with a circle of center O. Calculate the measure of…

A: Given  let ABCD be a trapezoid which is inscribed with a circle of center O

Q: A space has the line element, ds? = v*du? +u*dv² . Determine whether this space is flat or curved.

A: It is given that the line element ds2=v2du2+u2dv2. it is required to determine that whether this…

Q: Find the volume of the parallelepiped (box) determined by u, v, and w. u V i+ 3j 4i - j+4k 2i + 4k

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Q: Which figure below cannot be tessellated? O Rhombus O Trapezoid O Regular pentagon O Kite

A: Tessellated shapes are those which can be arranged in such a way that there is no space between…

Q: What cross-section cannot be formed by intersecting a plane with a right cylinder? Campbol OM…

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Q: Consider the parallelepiped with adjacent edges Find the volume. V = i 137 u = 8i + 7j + k v = i + j…

A: Directly use the formula for the volume of parallelepiped.

Q: 16. In a rhombus ABCD, AC = 24 cm and BD 10 cm. Calculate the perimeter of the rhombus. %3D %3D

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Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

Q: A cube with a cylinder cut from Its center is cut along the plane shown below. Which of the…

A: When the cube with a cylinder cut from its center is cut along the plane as shown in the figure,

Q: A hemisphere is cut along the plane shown below. Which of the following is the cross-section of this…

A: a hemi sphere is cut along the plane shown in question.

Q: Show that the volume of a parallelepiped with sides A, B and C is given by A · (B × C)

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Q: Draw the solid of revolution obtained by rotating the given plane region about line L. Which figure…

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Q: Give the definition of a rhombus and prove that the area of a rhombus is half the product of the…

A: A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus,…

Q: Find a formula for the distance from the point P(x, y, z) to the a. xy-plane . b. yz-plane c.…

A: a) xy plane is given by z=0 We have to find distance of (x,y,z) from z=0

Q: 20. A uniform wire is bent into the form of a triangle with sides a, b, Prove that the distances of…

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Q: Must the centroid of an isosceles triangle lie on the altitude to the base?

A: The centroid of an isosceles triangle lie on the altitude.

Q: Find the volume of the parallelepiped spanned by u = (1, 0, 4), v = (1, 2, 1) and w = (-4, 2, 9) in…

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Q: 16. What is the area of a rhombus whose diagonals have lengths d, = 12 inches and d, 14 inches? Show…

A: Given diagonals of rhombus d1 and d2 are  12 inches and 14 inches respectively.

Q: Consider the parallelepiped with adjacent edges Find the volume. V = i 102 u = 8i + 7j + k v = i + j…

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Q: HW #1I Geometay O Find the mamber of sides of a nogulan foligon lach of whose interioi is contaim…

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Q: Determine the coordinates of the centroid of the shaded area. 25 y 70 I 50 25 60 60 50. 175…

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Q: Identify the center shown below as a centroid, an incenter or a circumcenter.

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Q: Find the volume of the box (parallelepiped) that is determined by u = i + 2j - k, v = -2i + 3k, and…

A: Solution:-  The given vector is  u→=i+2j-kv→=-2i+0j+3kw→=0i+7j-4k

Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Using washer method

Q: Locate the centroid of the plane area shown if a 25 in. 20 in. r = 15 in. 30 in.

A: Area of Rectangle equals to : Arectangle=20+3025                =1250in2 Area of semi circle equals…

Q: What solid is formed when a right triangle is rotated around a line containing one of its legs? cone…

A: Shape problem....

Q: Assume the pattern of congruent squares shown in the figure continues forever. Write rules for rigid…

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Q: 1) What is drawn on a flat surface bounded by straight or curved lines? 2) What is a closed plane…

A: Topic :- Geometry

Q: 3. Quadrilateral QR ST is a dilation of quadršateral ORST, with the origin as the center of…

A: Take any point from quadrilateral QRST take S S (-2 , 10 ) S ' ( -1 , 5 )

Q: Which figure below cannot be tessellated? O Rhombus O Trapezoid O Heptagon O Square

A: Tessellation is a special pattern of shapes that fits together with no overlap or gaps.

Q: Derive the frenet frame, curvature and torison of the binormal indicatrix of hypocycloid?

A: We need to Derive the fernet frame, curvature and torsion o the binormal indicatrix of hypocycloid.

Q: What is the area of the rhombus as shown below?

A: Given that: A rhombus as shown.