What is a reasonable estimate for the problem?

Mathematics

2 answers:

Vaselesa [24]3 years ago

7 0

Estimate means to round your number for an easier answer -100/4= -25, approx -25

Alexeev081 [22]3 years ago

3 0

The answer is c. -25!

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Vector question. Let v=<-2,1> u=<3,-5> , find:

lyudmila [28]

Answer:

1. ) $\vec {v}.\vec{u}= -11$

2.) The angle between v and u is 147.52°.

Step-by-step explanation:

Given:

$\vec {v}= ( -2 , 1 )\\\vec {u}= ( 3 , -5 )$

To Find:

1. $\vec {v}.\vec{u}= ?$

2. $\theta = ?$

Solution:

$\vec {v}.\vec{u}$ is scalar product given as,

$\vec {v}.\vec{u}=|\vec {v}||\vec {u}|\cos \theta$

$|\vec {v}|=|(-2, 1)|=\sqrt{(-2)^{2} +1^{2}}=\sqrt{5}\\|\vec {u}|=|(3, 5)|=\sqrt{(3)^{2} +(-5)^{2}}=\sqrt{34}$

$\vec {v}.\vec{u}=(-2i +j).(3i-5j)\\$

Here only i.i = j.j =1 and i.j = j.i = 0

∴ $\vec {v}.\vec{u}=(-2\times 3 +1\times -5)\\\vec {v}.\vec{u}=-6-5=-11 \\$

Now, Substituting the above values we get

$-11=\sqrt{5}\times \sqrt{34}\cos \theta\\ \cos \theta=\frac{-11}{\sqrt{170}} \\ \cos \theta =-0.84366\\\therefore \theta =cos^{-1}(-0.84366)\\\therefore \theta =147.52\°$

As it is negative mean $\theta$ is in Second Quadrant Because Cosine is negative in Second Quadrant.

1. ) $\vec {v}.\vec{u}= -11$

2.) The angle between v and u is 147.52°.

5 0

3 years ago

PLEASEE HELP ME IM VERY CONFUSED ON THIS!!!

Anastasy [175]

SIDE LENGTH OF TRIANGLE: 2.14 inches
SIDE LENGTH OF HEXAGON: 6 inches

To solve this problem, we know that the shapes have equal sides as it states “equilateral triangle”. A triangle has 3 sides and a hexagon has 6 sides. We are told the perimeters are the same so you can set their perimeters equal to each other to solve for x. You would get this : 3(1.4x + 2) = 6(0.5x +2)
With basic algebra you would get x= 5
Then you substitute that value into the length sides of the triangle and hexagon. For the triangle you would approx get 2.14 inches and for the hexagon 6 inches