A triangle, where the two angles are 30° and 90°, what are the remaining angles

Answer:

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

We are given the following and are trying to find the second derivative at x = 2:

[tex]\displaystyle f(2) = 2[/tex]

[tex]\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}[/tex]

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

[tex]\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}[/tex]

When we differentiate this, we must follow the Chain Rule:                             [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big][/tex]

Use the Basic Power Rule:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')[/tex]

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big][/tex]

Simplifying it, we have:

[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big][/tex]

We can rewrite the 2nd derivative using exponential rules:

[tex]\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}[/tex]

To evaluate the 2nd derivative at x = 2, simply substitute in x = 2 and the value f(2) = 2 into it:

[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}[/tex]

When we evaluate this using order of operations, we should obtain our answer:

[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Given:

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

To find:

The surface area and the volume of the sphere.

Solution:

Volume of a sphere:

[tex]V=\dfrac{4}{3}\pi r^3[/tex]              ...(i)

Surface area of a sphere:

[tex]A=4\pi r^2[/tex]                      ...(ii)

Where, r is the radius of the sphere.

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

[tex]V=\dfrac{28}{3}\times A[/tex]

[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]

Multiply both sides by 3.

[tex]4\pi r^3=112\pi r^2[/tex]

[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]

[tex]r=28[/tex]

Using (i), the volume of the sphere is:

[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]

[tex]V\approx 91989[/tex]

Using (ii), the surface area of the sphere is:

[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]

[tex]A=9856[/tex]

Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.

Answer:

the answer = um ok

Step-by-step explanation:

Step-by-step explanation:

time = 2 hours

distance travelled(d) = 124 miles

so

speed = d/t

=  124/2

= 62 miles per hour

Therefore, the speed of car is 62 miles per hour.

Answer:

 - 5/3

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -1 -9)/(4 - -2)

   = (-1-9)/(4+2)

  = -10/6

  - 5/3

Answer:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 1 - 9}{4 - - 2} \\ \frac{ - 10}{6} \\ = - \frac{5}{3} \\ thank \: you[/tex]

Answer:

y = 6x-7

Step-by-step explanation:

product of 6 and x

6x

7 less than the product of 6 and x

6x-7

y = 6x-7

Answer:

13.3650978628

Step-by-step explanation:

Angle A=180-(Angle B+C)=180-117=63

Here,

b=BC, p=AC & AB=12

Using the relation of cos,

cosx=b/h

cos27=BC/15

15cos27=BC

Using a calculator,

BC=13.3650978628

Answer:

k=-1/2

Step-by-step explanation:

u have to change line 4x + ky=11 to this form:

y=11/k-4x/k

then, if 2 lines are parallel, their slopes have to equal

so: 8=-4/k -> k=-1/2

Answer:

don't know

Step-by-step explanation:

Answer:

true

hope it helps

PLEASE MARK BRAINLIEST

Answer:

r=7, Center:(4,8)

Step-by-step explanation:

( x - h )^2 + ( y - k )^2 = r^2 is the general formula for circle where radius is square root of r^2 and the center is (h,k).

Answer:

53

Step-by-step explanation:

The value of x in the given figure is 127 degrees.

Given that;

The lines m and n are parallel lines.

Now by definition of vertically opposite angle,

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other.

Hence from the figure we get;

Angle x and 127 degrees are vertically opposite angles.

Hence we get;

x = 127°

To learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ3

Answer:

answer B:

[tex]x= \dfrac{\pi}{2}\ or\ \dfrac{\pi}{6}\ or\ x=\dfrac{5\pi}{6}[/tex]

Step-by-step explanation:

[tex]2cos^2 x + 3sin x=3\\\\\Longrightarrow\ 2*(1-sin^2 x)+3sin x -3=0\\\\\Longrightarrow\ 2-2sin^2 x+3 sin x -3=0\\\\\Longrightarrow\ -2sin^2 x+3 sin x -1=0\\\\\Longrightarrow\ 2sin^2 x-3 sin x +1=0\\\\\Delta=3^2-4*2*1=1\\\\sin\ x=\dfrac{3-1}{4} \ or\ sin\ x=\dfrac{3+1}{4}\\\\sin\ x=\dfrac{1}{2} \ or\ sin\ x=1\\\\\Longrightarrow\ x= \dfrac{\pi}{6}\ or\ x= \dfrac{5\pi}{6}\ or\ x=\dfrac{\pi}{2} \\[/tex]

Answer:

So if x= 1 , y= -20 , z = -5 , we just have to replace those values on the equation

[tex]\frac{\sqrt{yz}}{(z-x)^{2} + y } =[/tex]  [tex]\frac{\sqrt{(-20) * (-5)}}{(-5-1)^{2} + (-20) } =[/tex]  [tex]\frac{\sqrt{100}}{(-6)^{2} -20 }[/tex]  [tex]= \frac{10}{16} =\frac{5}{8}[/tex]

Answer:

Answer:

Step-by-step explanation:

Given,

[tex] {x}^{8} = {( {2}^{2} )}^{4} [/tex]

Since,

[tex] { ({a}^{x} )}^{y} = {a}^{xy} [/tex]

Then,

[tex] = > {x}^{8} = {2}^{2 \times 4} [/tex]

[tex] = > {x}^{8} = {2}^{8} [/tex]

(Since the exponents are same so the bases will be also same)

Therefore,

=> x = 2

As per condition,

[tex] {x}^{2} [/tex]

(Putting value of x = 2)

[tex] ={2}^{2} [/tex]

= 4 (Ans)

Answer:

50.6

Step-by-step explanation:

The perimeter of the circle is 12.56 because we take 1/2 of 8 (the length of the short side of the rectangle) and multiply that by pie (or 3.14). Now that we know that the perimeter of the circle is 12.56 we add that to 8 (short side of the rectangle) and we add that to 15 twice (which is 30)

Answer:

or,

3/4×2/3=6/8

or, 3/4×3/3=9/12

Answer:

Step-by-step explanation:

1/3×2/8=2/24

1/2×5/12=5/42

5/6×3/4=15/24

Hope it is helpful to you

Answer:

7/3 = 7 ÷  7 ÷ 3/7 (i think)

Step-by-step explanation:

check mathpapa.com

https://www.mathpapa.com/algebra-calculator.html

Answer: C

Step-by-step explanation:

intersection of f(x) and g(x) is x=-3

f(-3)=g(-3)

Answer C

Answer:

The answer is f(-3)=g(-3)

Step-by-step explanation: just took the test hope it helps❤️

Answer:

18

Girl  = g

Boy = b

1g 1b  1g 2b  1g 3b

2g 1b  2g 2b  2g 3b

3g 1b  3g 2b  3g 3b

4g 1b   4g 2b  4g 3b

5g 1b   5g 2b  5g 3b

6g 1b   6g 2b  6g 3b

---------------------------------------

Another way you can do this,

6 × 3 = 18

In the end there will be 18 selections.

Well, all we have to do is add, so:

6 + (-47) =

6 - 47 =

-41

Answer:

(-41)

Step-by-step explanation:

Subtract and write big numbers sign.

47 - 6= (-41)

Answer:

98

Step-by-step explanation:

The value of the expression below when x=3 and y=8 is 98.

Step-by-step explanation:

do like the picture I sent

__________

Step-by-step explanation:

Q = { 1/31 < x < 1/22 }

Q = { 1/30, 1/29, 1/28, 1/27, 1/26, 1/25, 1/24, 1/23 }

#mathisfun

Answer:

(5x+6)(2x+5)-(2x+4)(x+8) simplified is 8x^2+17x-2

Step-by-step explanation:

Answer:

13x²+16x+28

Step-by-step explanation:

S=(5x+6)×(3x+2)=15x²+28x+12

2x+5-x-3=x-2

5x+6-3x+2=2x+8

(x-2)×(2x-8)=2x²-12x+16

15x²+28x+12-2x²-12x+16=13x²+16x+28

Answer:

3x ^ 2 + 12x-36 = 0

3(x²+ 4x-12)=0

3(x²-2x+6x-12)=0

3[x(x-2)+6(x-2)]=0

3(x-2)(x+6)=0

⇒[tex]\left \{ {{x-2=0} \atop {x+6=0}} \right.[/tex]⇔[tex]\left \{ {{x=2} \atop {x=-6}} \right.[/tex]

We know that our bag has n white tiles and 5 black tiles.

So, the total number of tiles in the bag is n + 5.

We know that a tile is drawn at random and is replaced, then a second tile is drawn.

a) We want to find the probability that the first tile is white.

Because all the tiles have the same probability of being randomly drawn, the probability of drawing a white tile is just the quotient between the number of white tiles and the total number of tiles in the bag.

[tex]P = n/(n + 5)[/tex]

And for the second draw, we do not have any restrictions, so the probability is the above one.

[tex]P = n/(n + 5)[/tex]

b) Now we want both tiles to be white.

For the first one we already know the probability, which is:

[tex]P = n/(n + 5)[/tex]

And because the tile is replaced, the probability of drawing a white tile again is exactly the same:

[tex]Q =n/(n + 5)[/tex]

The joint probability (the probability of both of these outcomes to happen together) is the product of the individual probabilities.

Probability = [tex]P*Q = (n/(n + 5))^2[/tex]

If you want to read more about probability, you can read:

https://brainly.com/question/24256398

Answer:

A. Scalene & E. Right

Step-by-step explanation:

The triangle is a scalene-right triangle. It is a right triangle because it has a 90 degree/right angle. It is a scalene triangle because all 3 sides have different lengths.