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4 years ago

Perpendicular line equation for (0,2); 3y-x=0

1 answer:

7 0

3y-x=0
3y=x
y=1/3x (slope)

(0,2)
y=1/3x+2
Above is the given line.
The perpendicular line containing point (0,2) would be y=-3+2

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Light bulbs usually cost 2$. They are on sale for 0.50 of the regular price. What is the sale price? Is this a better price than

Vinil7 [7]

Answer:

The sale price is $1

$1 is not a better price since there is a cheaper price of $0.7

Step-by-step explanation:

Original price is $2

The price now is 0.5 × $2 = $1

If the sale price was 0.35 of the original price;

It would be 0.35 × $2 = $0.7

$1 is not a better price since there is a cheaper price of $0.7

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3 years ago

Find the equation of the line tangent to the graph of

garik1379 [7]

Answer:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

$\displaystyle y=\sin^{-1}\big(\frac{x}{5}\big)\text{ at } x=\frac{5}{2}$

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

$\displaystyle y^\prime=\frac{1}{\sqrt{1-(\frac{x}{5})^2}}\cdot\frac{1}{5}$

Simplify:

$\displaystyle y^\prime=\frac{1}{5\sqrt{1-\frac{x^2}{25}}}$

We can factor out the denominator within the square root:

$\displaystyle y^\prime =\frac{1}{5\sqrt{\frac{1}{25}\big(25-x^2)}}$

Simplify:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}$

So, we can find the slope of the tangent line at <em>x</em> = 5/2. By substitution:

$\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}$

Evaluate:

$\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\frac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}$

We will also need the point at <em>x</em> = 5/2. Using our original equation, we acquire that:

$\displaystyle y=\sin^{-1}(\frac{1}{2})=\frac{\pi}{6}$

So, a point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}(x-\frac{5}{2})$

Distribute:

$\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}$

Isolate. Hence, our equation is:

$\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}$

7 0

3 years ago

Which equation represents the line with slope 1/4 that passes through (-4, 8)?

RoseWind [281]

Answer

B DID THE TEST

Step-by-step explanation:

YOU WILL DO YOU GOOD LUCK

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3 years ago

Help! Please! Thanks

Illusion [34]

Answer:

C. 3 (t+2)

Step-by-step explanation:

First, for the top fraction, simplify it:

4(t^2-4)/8=4(t+2)(t-2)/8

Now, flip the denominator and multiply the top and bottom fractions:

4(t+2)(t-2)/8 * 6/t-2

You can cancel the (t-2) terms so you get:

4(t+2) *6/8

Reduce the 6/8 to 3/4 so you get:

4(t+2)*3/4

Now cancel the 4's:

3(t+2) Your answer is C.

4 0

3 years ago

What is the solution to the inequality below? x2 < 36

11Alexandr11 [23.1K]

B. x - 6 or x 6
because x = 6

6 0

3 years ago