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2 years ago

Find the slope of the curve y=2/x at x=a.

Mathematics

1 answer:

Degger [83]2 years ago

6 0

Answer:

We are given:- y=2/x
We need to find the slope of the curve at x=a.

Step-by-step explanation:

Solution,

We use the slope formula, setting x=a :

$\displaystyle{{{{ \lim_{h \to0}}}} \frac{ \frac{2}{x + h} - \frac{2}{x} }{h} = \lim_{h \to0} \frac{ \frac{2}{a + h} - \frac{2}{a} }{h} }$

$\displaystyle{ \lim_{h \to0} \frac{ \frac{2a - 2(a + h)}{a(a + h)} }{h} = \displaystyle{ \lim_{h \to0} \frac{2a - 2(a + h)}{ha(a + h)} }}$

$\displaystyle{ \lim_{h \to0} \frac{2a - 2a - 2h}{ha(a + h)} = \displaystyle{ \lim_{h \to0} \frac{ - 2h}{ha(a + h)} }}$

$\displaystyle{ \lim_{h \to0} \frac{ - 2}{a(a + h)} = - \frac{ 2}{ {a}^{2} } }$

Therefore, The slope of the curve y=2/x at x=a is -2/a^2.

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If sinA=√3-1/2√2,then prove that cos2A=√3/2 prove that

Ivan

Answer:

$\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}$

Step-by-step explanation:

Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .

Given :-

• $\sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}$

To Prove :-

• $\sf\implies cos2A =\dfrac{\sqrt3}{2}$

Proof :-

We know that ,

$\sf\implies cos2A = 1 - 2sin^2A$

Therefore , here substituting the value of sinA , we have ,

$\sf\implies cos2A = 1 - 2\bigg( \dfrac{\sqrt3-1}{2\sqrt2}\bigg)^2$

Simplify the whole square ,

$\sf\implies cos2A = 1 -2\times \dfrac{ 3 +1-2\sqrt3}{8}$

Add the numbers in numerator ,

$\sf\implies cos2A = 1-2\times \dfrac{4-2\sqrt3}{8}$

Multiply it by 2 ,

$\sf\implies cos2A = 1 - \dfrac{ 4-2\sqrt3}{4}$

Take out 2 common from the numerator ,

$\sf\implies cos2A = 1-\dfrac{2(2-\sqrt3)}{4}$

Simplify ,

$\sf\implies cos2A = 1 -\dfrac{ 2-\sqrt3}{2}$

Subtract the numbers ,

$\sf\implies cos2A = \dfrac{ 2-2+\sqrt3}{2}$

Simplify,

$\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} }$

Hence Proved !

8 0

3 years ago

-4/9 * -5/8 I really want to know the answer home work is due and I need a explanation

lilavasa [31]

-4/9 times -5/8 you can cross cancel the 4 and 8 so it makes the problem -1/9 times -5/2 which equals -5/18

4 0

3 years ago

An ice cream shop sells cones at the volume of 94.2 cubic meters they want to double the volume of the cones without changing th

marin [14]

The volume of a cone is $V=\pi r^2\frac{h}3$ where r = radius and h = height. If the cone has a volume of 94.2 cm³ (I assume you didn't mean m³ because that would be ridiculously huge) and a height of 10 cm, we can plug these values into the formula to find the radius. Don't do any rounding.

$94.2 = \pi r^2\frac{10}3 \\ 282.6 = \pi r^2 *10 \\ 28.26 = \pi r^2 \\ 8.99543738355 = r^2 \\ 2.99923946752=r$

Now we know that's going to be the radius of our new cone as well since we're keeping the diameter the same. The volume is going to be double 94.2 which is 188.4. Let's solve for the height.

$188.4 = \pi (2.99923946752)^2\frac{h}3 \\ 188.4 = \pi(8.99543738355)\frac{h}3 \\ 188.4 = 28.26\frac{h}3 \\ 565.2 = 28.26h \\\\ \boxed{h = 20, r\approx 3}$

5 0

3 years ago

A watermelon seed is 0.4 cm long how far ould a line of 114 seeds strech in meters

Alexeev081 [22]

it would be 0.456 meters.

6 0

2 years ago

The price of a $250 item after successive discounts of 20% and 30% is?

Ivan

Answer:

The price of item after successive discounts are 20% and 30% is $140.

Step-by-step explanation:

The marked price of item is $250.

Two successive discounts are 20% and 30%.

Price of item after discounts of 20% is

$250-\frac{20}{100}(250)=250-50=200$

New price of item after first discount is $200.

Price of item after second discount, i.e., 30% is

$200-\frac{30}{100}(200)=200-60=140$

Therefore, the price of item after successive discounts are 20% and 30% is $140.

3 0

3 years ago

Find the slope of the curve y=2/x at x=a.​

Find the slope of the curve y=2/x at x=a.