Question

In the construction of a bridge, the support cables form specific angles to each other. The angle between two vectors representing the tensile force in two cables can influence the load distribution of the structure. Data: U=(3,4,0) V=(1,2,2) The scalar product is used to calculate the cosine of the angle θ between two vectors, according to the formula: Where: Alternatives for question 2 43°, cos(43°)=0.731 60°, cos?(60°)=0.5 45°, cos?(45°)=0.707 30°, cos?(30°)=0.866

189

likes

946 views

Answer to a math question In the construction of a bridge, the support cables form specific angles to each other. The angle between two vectors representing the tensile force in two cables can influence the load distribution of the structure. Data: U=(3,4,0) V=(1,2,2) The scalar product is used to calculate the cosine of the angle θ between two vectors, according to the formula: Where: Alternatives for question 2 43°, cos(43°)=0.731 60°, cos?(60°)=0.5 45°, cos?(45°)=0.707 30°, cos?(30°)=0.866

$Expert avatar$

Hermann

4.6

120 Answers

\begin{align*}\cos(\theta) &= \frac{U \cdot V}{||U|| \cdot ||V||} \\U \cdot V &= 3 \cdot 1 + 4 \cdot 2 + 0 \cdot 2 = 3 + 8 + 0 = 11 \\||U|| &= \sqrt{3^2 + 4^2 + 0^2} = \sqrt{9 + 16 + 0} = \sqrt{25} = 5 \\||V|| &= \sqrt{1^2 + 2^2 + 2^2} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3 \\\cos(\theta) &= \frac{11}{5 \cdot 3} = \frac{11}{15} \approx 0,733\end{align*}

\leftarrow \text{The closest given value to } 0.733 \text{ is } \cos(43^\circ) \text{, while the correct answer's angle should be } \theta = 45^\circ.

\boxed{45^\circ}

Frequently asked questions (FAQs)

What is the probability of rolling a sum of 7 when rolling two fair six-sided dice?

What is the limit of (2x^3 - 4x^2 + 3) / (5x - 2) as x approaches 2?

Conversion question: Convert 45 degrees to radians.

New questions in Mathematics

a runner wants to build endurance by running 9 mph for 20 min. How far will the runner travel in that time period?

find the value of the tangent if it is known that the cos@= 1 2 and the sine is negative. must perform procedures.

5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] ÷ (2/-5)} . 8/15

A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.

If f(x) = 3x 2, what is the value of x so that f(x) = 11?

A mutual fund manager has a $350 million portfolio with a beta of 1.10. The risk-free rate is 3.5%, and the market risk premium is 6.00%. The manager expects to receive an additional $150 million which she plans to invest in several different stocks. After investing the additional funds, she wants to reduce the portfolio’s risk level so that once the additional funds are invested the portfolio’s required return will be 9.20%. What must the average beta of the new stocks added to the portfolio be (not the new portfolio’s beta) to achieve the desired required rate of return?