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3 years ago

Simplify square root of five times the quantity six minus four square root of three.

Mathematics

1 answer:

NemiM [27]3 years ago

5 0

6√5 - 4√3-

i took the test but sorry if its wrong

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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

The Perimeter of a rectangle is 194 cm. The length of the rectangle is three centimeters less than four times the size of width.

Rus_ich [418]

Given that:
Perimeter=194 cm
Width=w
Length, L= 4w-3
Formula for perimeter of rectangle:
P=2(L+W)
Put values
194=2(4w-3+w)
194=2(5w-3)
Divide both sides by 2.
97=5w-3
Add 3 to both sides
100=5w
w=20

So length= 4 (20) -3 = 80-3 =77 cm
and width= 20 cm

Answer: Length=77 cm and width=20 cm

6 0

3 years ago

Find the equation of the line. A line that is perpendicular to the graph of 3x +2y =6 and contains the point (6,-3)

aniked [119]

9514 1404 393

Answer:

2x -3y = 21

Step-by-step explanation:

The perpendicular line will have an equation with the x- and y-coefficients swapped and one of them negated. The constant will be the value that makes the equation true at the given point.

3x +2y = 6 . . . . . given equation

2x -3y = c . . . . . . coefficients swapped, one negated

2(6) -3(-3) = c = 21 . . . . . the value of c for the given point

The desired equation is ...

2x -3y = 21

6 0

3 years ago

Which of the following is the solution of 5e^2x-4=11

Alex_Xolod [135]

Add 4
.. 5e^(2x) = 15
Divide by 5
.. e^(2x) = 3
Take the natural log
.. 2x = ln(3)
Divide by 2
.. x = ln(3)/2 . . . . . . . . . corresponds to the 3rd selection

8 0

4 years ago

Read 2 more answers

Simplify the expression.

podryga [215]

Answer:

12(−12m+38)

Step-by-step explanation:

12(−12m+38)

7 0

3 years ago