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1 year ago

F(x)=x² +6 Find an equation for the tangent line to the graph of f(x) = x² +6 at (5,31). y=

Mathematics

1 answer:

olganol [36]1 year ago

8 0

Answer:

y = x^2 + 6 given equation

y = m x + b equation of straight line required

dy/dx = 2 x tangent to given curve

dy/dx = slope = 2 * 5 = 10

Thus our line must be of the form

y = 10 x + b

31 = 10 * 5 + b at the point required

b = 31 - 50 = -19

Then our final equation becomes

y = 10 x - 19

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Triangle ABC is an oblique triangle. If angle A equals 57°, angle B equals 73°, and AB equals 24 in, what is the length of AC?

natulia [17]

Step-by-step explanation:

$\huge{\underbrace{\overbrace{\mathfrak{\pink{Answer:}}}}}$

Angle C must = [180 - 73 - 57 ] = [180 - 130] = 50°

And using rhw Law if Sines, we have.....

AB/sin C = AC/sin B → 24/sin(50) = AC/sin(73) → AC = 24*sin(73)/sin(50) = about 29.96 in

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3 years ago

Well, I have to write 20 words, so... I think this is enough.

Varvara68 [4.7K]

<h3>Answer: Choice D</h3><h3>m = n</h3><h3>b = sqrt(pi)*a</h3>

=====================================================

Explanation:

Each circle has a radius of 'a'. So r = a.

The area of each circle is pi*r^2 = pi*a^2

The area of each square with side length b is b^2

The two stacks have the same volume only when the circle area is equal to the square area, so whenever pi*a^2 = b^2 is true.

Solving for b leads to b = sqrt(pi*a^2) = sqrt(pi)*a

The stacks must also be the same height for the volumes to be the same, so m = n as well.

6 0

3 years ago

A bandleader randomly select's two students out of 100 bandmembers if you and your brother are both bandmembers what is the prob

kherson [118]

<span>There are 100 * 99 = 9900 different ways to choose two students out of 100 bandmembers. You and our brother are 2 of that ways: you being selected first and you being selected second. Therefore the probability that you two are selected is 2 / 9900 = 0,000202. You can also think as the probability of you being selected among 100 bandmembers, which is 1/100, times the probability of your brother being selected among 99 members, which is 1/99 => (1/100) * (1/99) = 1/ (100*99) = 1 / 9900; plus the same for your brother being selected first and you second => [1/9900] * 2 = 2/9900, which is the same calculated above.</span>

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3 years ago

The radius of the large sphere is double the radius of the small sphere. How many times is the volume of the large sphere than t

kobusy [5.1K]

The volume of a sphere is $\cfrac{4}{3}\ \pi r^3$

So, if the small sphere has radius $r$ and the largest sphere has radius $2r$ , their volumes are

$V_1 = \cfrac{4}{3}\ \pi r^3,\quad V_2 = \cfrac{4}{3}\ \pi (2r)^3 = \cfrac{4}{3}\ \pi 8r^3$

So, their ratio is

$\cfrac{V_2}{V_1} = \cfrac{\frac{4}{3}\ \pi 8r^3}{\frac{4}{3}\ \pi r^3} = 8$

7 0

3 years ago

Read 2 more answers

[10 points] A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimens

MissTica

Answer:

6 inches square by 3 inches high

Step-by-step explanation:

For a given surface area, the volume of an open-top box is maximized when it has the shape of half a cube. If the area were than of the whole cube, it would be 216 in² = 6×36 in².

That is, the bottom is 6 inches square, and the sides are 3 inches high.

_____

Let x and h represent the base edge length and box height, respectively. Then we have ...

x² +4xh = 108 . . . . box surface area

Solving for height, we get ...

h = (108 -x²)/(4x) = 27/x -x/4

The volume is the product of base area and height, so is ...

V = x²h = x²(27/x -x/4) = 27x -x³/4

We want to maximize the volume, so we want to set its derivative to zero.

dV/dx = 0 = 27 -(3/4)x²

x² = (4/3)(27) = 36

x = 6

h = 108/x² = 3

The box is 6 inches square and 3 inches high.

_____

<em>Comment on maximum volume, minimum area</em>

In the general case of<em> an open-top box</em>, the volume is maximized when the cost of the bottom and the cost of each pair of opposite sides is the same. Here, the "cost" is simply the area, so the area of the bottom is 1/3 the total area, 36 in².

If the box has a <em>closed top</em>, then each pair of opposite sides will have the same cost for a maximum-volume box. If costs are uniform, the box is a cube.

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3 years ago