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3 years ago

If a = 2m-n and b = -m +n , find the magnitude of c = 3a + 2b where m and n are two vectors inclined at 60°.

Mathematics

1 answer:

kati45 [8]3 years ago

7 0

Answer:a^2 +b^2 =c^2.

Step-by-step explanation:

square of magnitude of first vector + square of magnitude of second vector + twice the dot product of the two vectors whose sum's magnitude is to be found.

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All rectangles are parallelograms.<br> True<br> False

navik [9.2K]

Answer:

false

Step-by-step explanation:

Not all parallelograms are rectangles, only some of them are.

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3 years ago

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Pavlova-9 [17]

Answer:

The answer is D

Step-by-step explanation:

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3 years ago

Find the numbers b such that the average value of f(x) = 7 + 10x − 9x2 on the interval [0, b] is equal to 8.

barxatty [35]

Answer:

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

Step-by-step explanation:

The mean value of function within a given interval is given by the following integral:

$\bar f = \frac{1}{b-a}\cdot \int\limits^b_a {f(x)} \, dx$

If $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ , $a = 0$ , $b = b$ and $\bar f = 8$ , then:

$\frac{1}{b}\cdot \int\limits^b_0 {7+10\cdot x -9\cdot x^{2}} \, dx = 8$

$\frac{7}{b}\int\limits^b_0 \, dx + \frac{10}{b} \int\limits^b_0 {x}\, dx - \frac{9}{b} \int\limits^b_0 {x^{2}}\, dx = 8$

$\left(\frac{7}{b} \right)\cdot b + \left(\frac{10}{b} \right)\cdot \left(\frac{b^{2}}{2} \right)-\left(\frac{9}{b} \right)\cdot \left(\frac{b^{3}}{3} \right) = 8$

$7 + 5\cdot b - 3\cdot b^{2} = 8$

$3\cdot b^{2}-5\cdot b +1 = 0$

The roots of this polynomial are determined by the Quadratic Formula:

$b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

7 0

3 years ago

The image of the point (-6, -2) under a translation is (-4,2). Find the coordinates of the image of the point (-3, 4) under the

QveST [7]

ANSWER

(-1, 8)

EXPLANATION

First we have to find the rule for this translation.

The image of the x-coordinate of the given point is 2 untis more than the point, so the rule for the horizontal translation is to add 2.

The image of the y-coordinate of the given point is 4 units more than the point, so the rule for the vertical translation is to add 4:

$(x,y)\rightarrow(x+2,y+4)$

Therefore, the image of point (-3, 4) under the same translation is:

$(-3,4)\rightarrow(-3+2,4+4)=(-1,8)$

4 0

1 year ago

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) =x2 to the number of x-intercepts in

Natalija [7]

Important: Please use " ^ " to indicate exponentiation:

<span>"f(x) =x^2 to the number of x-intercepts in the graph of g(x) = x^2 +2."

Notes: the graph of f(x) = x^2 is a vertical parabola that opens up. It has its vertex at (0,0). This is the only point at which f(x)=x^2 has a horiz. intercept.

g(x) = x^2 + 2 has a graph that looks the same as that of f(x) = x^2, EXCEPT that the whole graph is moved 2 units UP. This new graph never touches or intersects the x-axis. Therefore, g(x) has NO horiz. intercepts (no x-int.).

</span>

7 0

3 years ago