Learning Materials
Features
Discover
Chapter 6: Problem 114
Use a sketch to find the exact value of \(\cos \left(\tan ^{-1} \frac{3}{4}\right)\) (Section 4.7, Example 7)
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
A force of 80 pounds on a rope is used to pull a box up a ramp inclined at \(10^{\circ}\) from the horizontal. The rope forms an angle of \(33^{\circ}\) with the horizontal. How much work is done pulling the box 25 feet along the ramp?
Let $$\mathbf{u}=-\mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \text { and } \quad \mathbf{w}=-5 \mathbf{j}$$ Find each specified scalar or vector. $$5 \mathbf{u} \cdot(3 \mathbf{v}-4 \mathbf{w})$$
A force of 6 pounds acts in the direction of \(40^{\circ}\) to the horizontal. The force moves an object along a straight line from the point (5,9) to the point \((8,20),\) with the distance measured in feet. Find the work done by the force.
Use the vectors $$\mathbf{u}=a_{1} \mathbf{i}+b_{1} \mathbf{j}, \quad \mathbf{v}=a_{2} \mathbf{i}+b_{2} \mathbf{j}, \quad \text { and } \quad \mathbf{w}=a_{3} \mathbf{i}+b_{3} \mathbf{j},$$ to prove the given property. $$\mathbf{u} \cdot(\mathbf{v}+\mathbf{w})=\mathbf{u} \cdot \mathbf{v}+\mathbf{u} \cdot \mathbf{w}$$
I'm working with a unit vector, so its dot product with itself must be 1
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine