d. xD (Simplify your answer. Type an exact answer, using radicals as needed. Type an expression using s as the variable. Use integers or fractions for any numbers in the expression.) Equilateral triangle e.x=] and y = (Simplify your answers. Type exact answers, using radicals as needed.) 2. f.x= and y = 10 (Bimplify your answers. Type exact answers. us ng racicals as needed.) 15
d. xD (Simplify your answer. Type an exact answer, using radicals as needed. Type an expression using s as the variable. Use integers or fractions for any numbers in the expression.) Equilateral triangle e.x=] and y = (Simplify your answers. Type exact answers, using radicals as needed.) 2. f.x= and y = 10 (Bimplify your answers. Type exact answers. us ng racicals as needed.) 15
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![### Geometric Problem Solving with Radicals
#### Problem d:
Solve for \( x \):
\[ x = \boxed{\phantom{0}} \]
(Simplify your answer. Type an exact answer, using radicals as needed. Type an expression using \( s \) as the variable. Use integers or fractions for any numbers in the expression.)
**Diagram:**
The diagram shows an equilateral triangle with a side length \( s \). The height \( x \) forms a right-angled triangle with \( \frac{s}{2} \) (half the base of the equilateral triangle) as one of the legs.
#### Problem e:
Solve for \( x \) and \( y \):
\[ x = \boxed{\phantom{0}}, \quad y = \boxed{\phantom{0}} \]
(Simplify your answers. Type exact answers, using radicals as needed.)
**Diagram:**
A cube with side length 2. The diagonal inside the cube is marked as \( y \) while another line from one corner to the middle of the opposite face is marked as \( x \).
#### Problem f:
Solve for \( x \) and \( y \):
\[ x = \boxed{\phantom{0}}, \quad y = \boxed{\phantom{0}} \]
(Simplify your answers. Type exact answers, using radicals as needed.)
**Diagram:**
A rectangular cuboid with dimensions 7 units, 10 units, and 15 units. The internal diagonals are marked as \( x \) and \( y \). The line \( y \) is the space diagonal of the cuboid, and \( x \) is a diagonal along one of the faces formed by 10 and 7 units.
---
These problems require you to find the lengths of various diagonal lines in geometrical shapes by using properties of triangles, specifically the Pythagorean theorem, and simplifying the answers using radicals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6506383-1f6c-4925-93a1-d439ea45d460%2F244ff87b-807c-4b33-8d47-4fc41c1f38db%2Fmsqa54c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometric Problem Solving with Radicals
#### Problem d:
Solve for \( x \):
\[ x = \boxed{\phantom{0}} \]
(Simplify your answer. Type an exact answer, using radicals as needed. Type an expression using \( s \) as the variable. Use integers or fractions for any numbers in the expression.)
**Diagram:**
The diagram shows an equilateral triangle with a side length \( s \). The height \( x \) forms a right-angled triangle with \( \frac{s}{2} \) (half the base of the equilateral triangle) as one of the legs.
#### Problem e:
Solve for \( x \) and \( y \):
\[ x = \boxed{\phantom{0}}, \quad y = \boxed{\phantom{0}} \]
(Simplify your answers. Type exact answers, using radicals as needed.)
**Diagram:**
A cube with side length 2. The diagonal inside the cube is marked as \( y \) while another line from one corner to the middle of the opposite face is marked as \( x \).
#### Problem f:
Solve for \( x \) and \( y \):
\[ x = \boxed{\phantom{0}}, \quad y = \boxed{\phantom{0}} \]
(Simplify your answers. Type exact answers, using radicals as needed.)
**Diagram:**
A rectangular cuboid with dimensions 7 units, 10 units, and 15 units. The internal diagonals are marked as \( x \) and \( y \). The line \( y \) is the space diagonal of the cuboid, and \( x \) is a diagonal along one of the faces formed by 10 and 7 units.
---
These problems require you to find the lengths of various diagonal lines in geometrical shapes by using properties of triangles, specifically the Pythagorean theorem, and simplifying the answers using radicals.
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