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8090 [49]
2 years ago
11

The vector ab has a magnitude of 20 units and is parallel to the vector 4i + 3j. find ab.

Mathematics
1 answer:
stepladder [879]2 years ago
7 0

The vector ab has a magnitude of 20 units and is parallel to the

vector 4i + 3j. Hence, The vector AB is 16i + 12j.

<h3>How to find the vector?</h3>

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

Given;

The vector ab has a magnitude of 20 units and is parallel to the

vector 4i + 3j.

magnitude

\sqrt{4^2 + 3^2} \\\\\sqrt{16 + 9} \\\\= 5

Unit vector in direction of resultant = (4i + 3j) / 5

Vector of magnitude 20 unit in direction of the resultant

= 20  x (4i + 3j) / 5

= 4 x (4i + 3j)

= 16i + 12j

Hence, The vector AB is 16i + 12j.

Learn more about vectors;

brainly.com/question/12500691

#SPJ1

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An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so the equa
Orlov [11]

it cant be a negative number or zero

 so now you are left with 0.5, 2 and 7.9

15.7 - 0.5 = 15.2 ( 15.2/2 = 7.6)  this is possible

15.7 - 2 = 13.7 ( 13.7/2 = 6.85) this is possible

15.7 - 7.9 = 7.8 ( 7.8/2 = 3.9) (7.9/2 = 3.95) since the sides would be shorter than half the base this is not possible to form a triangle


so b can be either 0.5 or 2



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4 0
3 years ago
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The perimeter of a rectangle equals one and a half times its area. Express the length of the rectangle in terms of the width (us
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Answer:

Step-by-step explanation:

let x and y be length and width of rectangle.

Perimeter=2(x+y)

area=xy

2(x+y)=1/2 xy

4(x+y)=xy

4x+4y=xy

x y-4y=4 x

y(x-4)=4 x

y=\frac{4x}{x-4}

4 0
3 years ago
Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 1
belka [17]

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

            F(x) = \int\limits^a_b {f(x)} \, dx

By using integration formula

\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c

Given  x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

 \int\limits^6_^-6} (x^{5}  + 8 x^{4}  + 2 x^{2}  + 5 x + 15) )dx

<em>On integration , we get</em>

=   (\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}

F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)

= (\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))

After simplification and cancellation we get

 =  \frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6

on calculation , we get

= \frac{124,416}{5} + \frac{864}{3} + 180

On L.C.M  15

= \frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}

= 25 351.2 units²

<u><em>Conclusion</em></u>:-

<em>The area of the region between the graph of the given function and the x-axis = 25,351 units²</em>

6 0
3 years ago
Why is the accounting cycle important?
ankoles [38]
Because without it the economy would fail :)
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Answer:

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You can search up "box plot" and go on images to see what i mean

(copy and pasted from your last post!)

Step-by-step explanation:

I can probably help on part 4 and send a sketch but I currently can't use my phone to send a pic and I am currently on my desktop :'(

I rlly hope you do well! Don't lose hope! <3

(also like ur pfp, i enjoyed the anime too ahehe)

7 0
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