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Ivanshal [37]
3 years ago
9

Answer The Following Questions ?

Mathematics
1 answer:
IgorC [24]3 years ago
5 0

Answer:it is in fact a

Step-by-step explanation:

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show that the sum of the x- and y- intercepts of any tangent line to the curve sqrt(x) sqrt(y) = sqrt(c) is equal to c.
expeople1 [14]
The answer is <span>√x + √y = √c </span>
<span>=> 1/(2√x) + 1/(2√y) dy/dx = 0 </span>
<span>=> dy/dx = - √y/√x </span>

<span>Let (x', y') be any point on the curve </span>
<span>=> equation of the tangent at that point is </span>
<span>y - y' = - (√y'/√x') (x - x') </span>

<span>x-intercept of this tangent is obtained by plugging y = 0 </span>
<span>=> 0 - y' = - (√y'/√x') (x - x') </span>
<span>=> x = √(x'y') + x' </span>

<span>y-intercept of the tangent is obtained by plugging x = 0 </span>
<span>=> y - y' = - (√y'/√x') (0 - x') </span>
<span>=> y = y' + √(x'y') </span>

<span>Sum of the x and y intercepts </span>
<span>= √(x'y') + x' + y' + √(x'y') </span>
<span>= (√x' + √y')^2 </span>
<span>= (√c)^2 (because (x', y') is on the curve => √x' + √y' = √c) </span>
<span>= c.  hope this helps :D</span>
5 0
3 years ago
Two horses are ready to return to their barn after a long workout session at the track. The horses are at coordinates H(1,10) an
lana [24]
Distance between points \left(x_1,y_1\right) and \left( x_2,y_2 \right) is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Distance from H to B:

[tex]d=\sqrt{(10-(-3))^2+(1-(-9))^2}=\sqrt{169+100}=\sqrt{269}d=\sqrt{(1-(-3))^2+(10-(-9))^2}=\sqrt{16+361}=\sqrt{376}[/tex] units.

Distance from Z to B:

d=\sqrt{(10-(-3))^2+(1-(-9))^2}=\sqrt{169+100}=\sqrt{269} units.

Horse Z is closer to the barn.

(The conversion to meters is not required; the question does not ask for actual distances, so "units" is OK.)
6 0
3 years ago
Multiply 35×40 what equals
Vinil7 [7]
When you multiply 35 x 40 = 1400

:)
3 0
3 years ago
PLS HELP ASAP I NEED RN ILY
frutty [35]

Answer:

A Hope this helps

Step-by-step explanation:

4 0
2 years ago
Find the slope and the y-intercept in this equation: 3y+6=-2x
Dmitry [639]
Hello,

To solve this problem, you should first put in it slope intercept form.

Here are the steps:

3y + 6 = -2x   Add 6 to both sides
3y = -2x - 6    Divide both sides by 3
y = (-2/3)x - 2

The you can see that the slope is (-2/3) and the y-intercept is (0, -2).

I hope this helps,
MrEQ
7 0
3 years ago
Read 2 more answers
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