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3 years ago

12

(See diagram) The gradient of the line joining the origin to the point A is 1/2. The distance between A and the origin is sqrt 2

205. What are the coordinates of A?

1 answer:

GuDViN [60]3 years ago

3 0

Answer:

(42, 21) or (–42, –21)

Step-by-step explanation:

let A(x, y), A on line 2y = x

distance

x² + y² = 2205

(2y)² + y² = 2205

y² = 441

y = ±21

x = ±42

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How do find volume of the triangular pyramid, I’m so confused I need the formula as well ASAP,!!,, please thanks so much

lidiya [134]

Answer:

5100

Step-by-step explanation:

20 x 17 x 15 = 5100. hope this helps you!!!

also formula is 1/2 x b x h x l

6 0

2 years ago

Read 2 more answers

Show the work please

Kay [80]

Answer:

1) (x + 3)(3x + 2)

2) x= +/-root6 - 1 by 5

Step-by-step explanation:

3x^2 + 11x + 6 = 0 (mid-term break)

using mid-term break

3x^2 + 9x + 2x + 6 = 0

factor out 3x from first pair and +2 from the second pair

3x(x + 3) + 2(x + 3)

factor out x+3

(x + 3)(3x + 2)

5x^2 + 2x = 1 (completing squares)

rearrange the equation

5x^2 + 2x - 1 = 0

divide both sides by 5 to cancel out the 5 of first term

5x^2/5 + 2x/5 - 1/5 = 0/5

x^2 + 2x/5 - 1/5 = 0

rearranging the equation to gain a+b=c form

x^2 + 2x/5 = 1/5

adding (1/5)^2 on both sides

x^2 + 2x/5 + (1/5)^2 = 1/5 + (1/5)^2

(x + 1/5)^2 = 1/5 + 1/25

(x + 1/5)^2 = 5 + 1 by 25

(x + 1/5)^2 = 6/25

taking square root on both sides

root(x + 1/5)^2 = +/- root(6/25)

x + 1/5 = +/- root6 /5

shifting 1/5 on the other side

x = +/- root6 /5 - 1/5

x = +/- root6 - 1 by 5

x = + root6 - 1 by 5 or x= - root6 - 1 by 5

4 0

3 years ago

the minute hand of a clock is 5 inches long. what is the area of the circle, in square inches, created in a hand sweep in an hou

ira [324]

Solve the area of the whole circle since in an hour, the minute hand covers the whole clock
assuming that the minute hand reaches all the way out to the edge of the clock

the minute hand is the radius
area=pi times r^2
r=5
5^2=25
area=pi times 25
area=25pi

aprox pi=3.14
25 times 2.14=78.5

area=78.5 in^2

6 0

3 years ago

Please Help!!<br><br>Use Euler’s formula to write in exponential form.

LekaFEV [45]

Answer:

C, $4e^{i(7\pi/4)}$

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

$e^{ix}=\cos{x}+i\sin{x}$

Given the complex number $2\sqrt{2}-2i\sqrt{2}$ , we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.

One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression $2(\sqrt{2}-i\sqrt{2})$

Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression $4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right)$ , and <em>now </em>we have something to work with.

Looking back at Euler's formula $e^{ix}=\cos{x}+i\sin{x}$ , we can map our expression inside the parentheses to the one on the right side of the formula, giving us $\cos{x}=\frac{\sqrt2}{2}$ and $\sin{x}=-\frac{\sqrt2}{2}$ , or equivalently:

$\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x$

At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so $x=\frac{7\pi}{4}$ , and we can finally replace our expression in parentheses with its exponential equivalent:

$4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}$

Which is c on the multiple choice section.

4 0

3 years ago

|x+1|<4 please and thank youuuu

user100 [1]

Answer:

-5,3

Step-by-step explanation:

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3 years ago