Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the CCW direction. Vanessa stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail. Imagine an angle with its vertex at the center of the circular ski trail that subtends Vanessa's path.


How many radians has the angle swept out since Vanessa started skiing?

Answer:

[tex] (200*1.4) *10^4[/tex]

And we got:

[tex] 280 x10^4[/tex]

And if we move the decimal point two units to the left we got:

[tex] 2.8 x10^6[/tex]

Step-by-step explanation:

We know that each elefeant weight about [tex]1.4 x10^4[/tex]

And we have a total of 200 elephants so then we can find the total weights for the elephants with this formula:

[tex] 200 *1.4*10^4[/tex]

Using the properties of multiplication we can do this:

[tex] (200*1.4) *10^4[/tex]

And we got:

[tex] 280 x10^4[/tex]

And if we move the decimal point two units to the left we got:

[tex] 2.8 x10^6[/tex]

Step-by-step explanation:

When the problem says 3f(x), it means that you are multiplying f(x) by 3. The same goes for 2g(x).

[tex]3(2x^2+8x-4)= 6x^2+24x-12[/tex]

[tex]2(5x+6) = 10x+12[/tex]

Now, we subtract f(x) from g(x) after being multiplied.

[tex](6x^2+24x-12)-(10x+12)[/tex]

[tex]6x^2+14x-24[/tex]

Answer:

34.63

Step-by-step explanation:

A=a2+2aa2

4+h2=32+2·3·32

4+42≈34.63201

Answer:

Volume of the pyramid =  927.72 m² (Approx)

Step-by-step explanation:

Given:

Length of base = 16.6 m

Height of the pyramid = 10.1 m

Find:

Volume of the pyramid = ?

Computation:

Area of the square base = Side²

Area of the square base = (16.6)²

Area of the square base = 275.56 m²

[tex]Volume\ of\ the\ pyramid = \frac{1}{3}(Area\ of\ base)(Height)\\\\Volume\ of\ the\ pyramid = \frac{1}{3}(275.56)(10.1)\\\\Volume\ of\ the\ pyramid = 927.7186[/tex]

Volume of the pyramid =  927.72 m² (Approx)

Answer:

Both are correct

Step-by-step explanation:

3. ×3. 9

5. ×3. 15

3. ×5. 15

5. ×5. 25

Answer:

As shown in picture, if MC is median of triangle ABC, M is midpoint of AB.

Denote the coordinate of A, B and M are (Ax, Ay), (Bx, By) and (Mx, My) respectively.

The formula relating coordinate of A, B and M is:

Ax + Bx = 2Mx

Ay + By = 2My

In detail,

-1 + Bx = 2 x 4 => -1 + Bx = 8 => Bx = 9

11 + By = 2 x 11 = > 11 + By = 22 => By = 11

=> Option D is correct

Hope this helps!

:)

Step-by-step explanation:

7/ 12 is equivalent to - 7/-12

Answer: the answer is 19

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Answer:

2 B + p h

Step-by-step explanation:

The Surface Area = 2 B + p h

B is the area of the triangular base of prism

p perimeter of the base and

h the height of the prism

Answer:SA=(1/2)(5)(12)+(1/2)(5)(12)+(5)(2)+(12)(2)(13)(2)

Ans C

Step-by-step explanation:

Edgy

Answer:

n = 3/5

Step-by-step explanation:

We are given the ratio 6 : 10.

We see that we want to get a number n to 1 ratio; n : 1

In order to get one, we must divide 10 by 10, and so we would divide the entire ratio by 10 and simplify:

6/10 : 10/10

3/5 : 1 or 0.6 : 1

Answer:

17.2

Step-by-step explanation:

3x=12+y

x=12+y/3

[tex]8( \frac{12 + y}{3}) \div 2y[/tex]

[tex] \frac{96 + 8y}{3} \times \frac{1}{2y} [/tex]

[tex] \frac{96 + 8y}{6y} [/tex]

(y is divided by y so it no longer exists)

[tex] \frac{96 + 8}{6} [/tex]

[tex] \frac{104}{6} [/tex]

[tex]17.2[/tex]

Answer:

30

Step-by-step explanation:

55 rounded to the nearest ten is 60

60/2=30

Answer:

30

Step-by-step explanation:

55 is closer to 60 than 40. And you divide 60 by 2 you get  30.

Exact value

Decimal form

0.47712125

Answer:

[tex]log_{81} 3 = \frac{1}{4}[/tex]

Step-by-step explanation:

[tex]Let \; log_{81} 3 = x \\\therefore 3 = {81}^x ..(by\: changing\: in \: exponential\: form)\\\therefore 3^1 = {3}^{4x}\\\therefore 1 = 4x.\\(\because bases \: are \: equal,\: hence \: exponents\: will\: also\: be \: equal)\\\therefore x = \frac{1}{4}\\\\\huge\purple{\boxed{\therefore log_{81} 3 = \frac{1}{4}}}[/tex]

Answer:

12ft

Step-by-step explanation:

house A = 2*house B

24 = 2*b

24/2 = 12

Answer:

house B is 12 because 24 divided by two is 12

Find the given attachments

Answer:

Yes, they differ across the two delivery styles of the previous course.

Step-by-step explanation:

So, we are given the following data or information or parameters from the question above;

Flipped(group) => 166(n) 2.45(l) 1.09(s).

Traditional(group) => 129(n) 1.59(l) 1.20(s).

Therefore, the hypothesis is given below as; Jo : b1 = b2, Jx : b1 ≠ b2.

Recall that we are given; 166 = (n1), 2.45 = (l1), 1.09 = (s1) and 129 = (n2) , 1.59 = (l2), 1.20 = (s2).

Therefore, we will be using the following mathematical representation or formula to solve this question;

s = √(s1^2/ n1 + s2^2/n2).

When we slot it the values accordingly and solve for s, we will have a value of;

s = 0.1354.

Thus , for our t*, we can calculate that by using the formula below:

t*= l1 - l2/ s.= (2.45 - 1.59)/ 0.1354= 6.35.

Thus: p value = 2P(V> 6.35) = 2.1 × 10^-10.

Since we are given that a=0.01, thus, p value is less than 0.01 we can reject Jo.

Answer:

  -3/2

Step-by-step explanation:

8n/6 = -2 . . . the quotient of 8 times a number and 6 is -2

n = -12/8 = -3/2 . . . . multiply by 6/8

The number is -3/2.

Answer:

3

Step-by-step explanation:

A(0, -3); O(0,0)

AO=√[(0-0)²+(0+3)²]=√3²=3

Answer:

64

Step-by-step explanation:

[tex] {8}^{2} = 8 \times 8 = 64[/tex]

Answer:

The answer is 1,787.75 square inches

Step-by-step explanation:

Answer:

1,787.75

Step-by-step explanation:

Answer:

b both pairs of opposite sides are parallel

Answer:

B or the second choice from the top

Step-by-step explanation:

The definition of a parallelogram, in my own words, is a quadrilateral with two pairs of opposite parallel sides (hence the name). Therefore, the second choice from the top is correct. Hope this helps!

Answer:

1000m

STEP BY STEP EXPLANATION: 300m+300m+200m+200m

=600m+400m

=1000m

The perimeter of the field is 1000m

Since the field is 300m long and 200m wide.

We know that the perimeter of the rectangle is

= 2(length + width)

= 2(300 + 200)

= 2(500)

= 1000m

Therefore we can conclude that The perimeter of the field is 1000m

Learn more about perimeter here: https://brainly.com/question/17211131

Answer:

88

Step-by-step explanation:

Sum of angles in a quadrilateral= 360 degrees

<OCA=90degrees [ tangent perpendicular to the circle.

<OBA= 90degrees =tangent perpendicular

to the circle

<OCA + <OBA +92 + <OAB= 360

90 + 90 + 92 + <OAB = 360

272 + < OAB = 360

<0AB= 360- 272 =88 degrees

Answer: 88

Step-by-step explanation: Khan Academy

Answer:

8 cartons

Step-by-step explanation:

1000milliliter = 1 liter

Hence 2 liters of mango juice = 2000 millilitres.

Therefore, no of cartons = 2000/250 = 8 cartons

Answer:

  B.  129.7°

Step-by-step explanation:

The law of sines tells you ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin((c/a)sin(A)) = arcsin(117/57·sin(22°)) = 50.3°

The value shown is the result of using the arcsin function, but we know that the supplement of this angle has the same sine value. Then, we could have ...

  C = 180° -50.3° = 129.7°

The figure shows C as an obtuse angle, so we choose this latter value as the appropriate answer to this question.

  C = 129.7° . . . . . matches choice B

_____

Comment on the answer

We note that choice C (50.3°) matches the result of straightforward use of the law of sines. This triangle actually has two solutions for angle C, as we have noted above. Often, figures are "not to scale," so the appearance of angle C as an obtuse angle cannot always be taken at face value. Here, because both choices for angle C are offered, we use the appearance of the figure to help decide the right one.

Answer:

254.34

Step-by-step explanation:

area = [tex]\pi r^{2}[/tex]

area B = 3.14 x [tex](\frac{18}{2})^{2}[/tex] = 254.34

Answer:

.13

Step-by-step explanation:

We need to find the areas of the regions

Area of the shaded region

A =pi r^2

  pi (5)^2

 25pi

The area of the total region

A = pi r^2

A = pi 14^2

  = 196 pi

P(shaded) = shaded/ total

                 = 25 pi/196 pi

                     25/196

                   .12755102

To the nearest hundredth

                   .13

Answer:

0.13

Step-by-step explanation:

Total area:

Pi × 14²

3.14 × 196

615.44

Shaded area:

3.14 × 5²

78.5

Probability: 78.5/615.44

0.12755102

Answer:

It's 1 inch higher than the limit

Step-by-step explanation:

Answer:

1 1/2

Step-by-step explanation:

Answer:

[tex]y = 4(x^{2} + 8x + 15) = 4x^{2} + 32x + 60[/tex]

Step-by-step explanation:

A parabola has the following format:

[tex]y = f(x) = ax^{2} + bx + c[/tex]

If a is positive, it's minium value is:

[tex]y_{M} = -\frac{\bigtriangleup}{4a}[/tex]

In which

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

Factoring:

[tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], in which [tex]x_{1} and x_{2}[/tex] are the intercepts.

In this question:

[tex]x_{1} = -5, x_{2} = -3[/tex]

So

[tex]a(x - x_{1})*(x - x_{2}) = a*(x - (-5))*(x - (-3)) = a*(x+5)*(x+3) = a*(x^{2} + 8x + 15)[/tex]

Suppose a = 1, we have:

[tex]x^{2} + 8x + 15[/tex]

[tex]\bigtriangleup = 8^{2} - 4*1*15 = 4[/tex]

The minimum value will be:

[tex]y_{M} = -\frac{4}{4} = -1[/tex]

We want this minimum value to be -4, which is 4 times the current minimum value, so we need to multiply a by 4. Then

[tex]a = 4[/tex]

And the parabola is:

[tex]y = 4(x^{2} + 8x + 15) = 4x^{2} + 32x + 60[/tex]