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2 years ago

Find the equation of the tangent to the curve

Mathematics

1 answer:

12345 [234]2 years ago

4 0

9514 1404 393

Answer:

y = -x/16 +1

Step-by-step explanation:

The slope is at any point x is ...

y' = -4/x^2

so, at x=8, the slope is ...

m = -4/8^2 = -4/64 = -1/16

The point-slope form of the equation of the line is ...

y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

Then the line with slope -1/16 through point (8, 1/2) is ...

y - 1/2 = -1/16(x -8)

y = -1/16x +1/2 + 1/2 . . . . . eliminate parentheses, add 1/2

y = -1/16x +1 . . . . . equation of the tangent line

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A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a hieght of 3 inches. The cone has a radiu

arlik [135]

The height of the cone is inches, if the cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

Step-by-step explanation:

The given is,

A cylinder and a cone have the same volume

Cylinder has a radius 2 inches and height of 3 inches.

Cone has a radius of 3 inches

Step:1

For Cylinder'

Formula to calculate the volume of cylinder is,

$V = \pi r^{2} h$ ..................................................(1)

where,

r - 2 inches

h - 3 inches

From the equation (1)

= $\pi$ × $2^{2}$ × 3

= 37.70

V = 37.70 cubic inches

Step:2

For cone,

Formula to calculate the volume of cone is,

$V = \pi r^{2} \frac{h}{3}$ ..................................................(2)

From the statement,

cylinder and a cone have the same volume

$V_{cylinder}$ = $V_{cone}$

37.70 = $\pi$ × $3^{2}$ × $\frac{h}{3}$

37.70 = 9.42478 × h

Height of the cone, h = 4 inches

Result:

Thus the height of the cone is 4 inches, if a cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

4 0

2 years ago

The following steps show how the right side of

hodyreva [135]

Answer:

Its A.

Step-by-step explanation:

I just finsihed that question.

7 0

3 years ago

Read 2 more answers

To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level) b = 800 meters fro

Nady [450]

Answer: The height of the mountain is 1,331.4 meters (approximately)

Step-by-step explanation: From the information given, the students were standing at point b which is 800 meters from the base of the mountain and the angle of elevation from that point is 59°. Assuming that the ground is level, we can derive a right angled triangle from this set of details and hence we have triangle ABC, where angle β is the reference angle, (59 degrees), BC is the distance from the students to the base of the mountain (800 meters) and the line AC is the height of the mountain.

The line AC is the opposite, since angle B is the reference angle, therefore we shall use the trigonometric ratio as follows;

Tan β = opposite/adjacent

Tan 59 = AC/800

Tan 59 x 800 = AC

1.6643 x 800 = AC

1331.44 = AC

AC ≈ 1331.4

Therefore the height of the mountain is approximately 1,331.4 meters

6 0

3 years ago

Read 2 more answers

Question 1,2, and 3 how do i factor those? Can you show the work and explain how?

DiKsa [7]

1: $3n^{2}+9n+6$

notice that each part is divisible by 3

$3n^{2}$ ÷ 3 = $n^{2}$

9n ÷ 3 = 3n

6 ÷ 3 = 2

so it becomes $3(n^{2} +3n+2)$

3n can be rewritten as 2n+n

-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)

which would get you

$3(n^{2} +2n+n+2)$

Now that it's rewritten, you can factor out n + 2 from the equation.

the answer is

3(n+2)(n+1)

And you can check that by multiplying (n+2)(n+1) which is $n^{2} +2n+n+2$ and then each of those by 3, which is $3n^{2} +6n+3n+6$ or $3n^{2}+9n+6$ , our origional equation

2: $28+x^{2} -11x$

So I rewrote this as $x^{2} -11x+28$ (it's the same thing, just reordered using the commutative property)

now -11x can be rewritten as -4x-7x

(remember, the two numbers should multiply to equal 28, which is our constant.)

$x^{2} -4x-7x+28$

now we can factor out x from the first expression and -7 from the second

$x(x-4)-7(x-4)$

and lastly you factor out x-4,

which would give you

(x-4)(x-7)

Make sure to check your work and make sure it multiplies to $x^{2} -11x+28$

3: $9x^{2} -12x+4$

The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12

So if you rewrite 9 as $3^{2}$ and 4 as $2^{2}$ , the equation becomes

$3^{2} x^{2} -12x+2^{2}$