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3 years ago

A cone where the angle of vertex is 2pi/3. Fill in the blanks found in the attachment.

Mathematics

1 answer:

Firdavs [7]3 years ago

4 0

As far as I understand, you've made two mistake which do not satisfy your task. Well, I seggest you adding b = 2pi/3 to the first gap instead of what you add in the previous effort. Then, to solve the next part, I would change f on <span>8/sqrt(3)*cospi
I bet that this answer will sort everything out. Regards!</span>

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50 POINTS!!

Charra [1.4K]

Answer:

$FH=73$

Step-by-step explanation:

We are given that a segment FH and G is the midpoint of FH.

FH= $14x-4$

$FG=5x+9$

We have to find the measure of FH.

When G is the midpoint of segment FH

Then , FG=GH

$FH=FG+GH$

Segment addition property

$14x-4=FG+FG$

Substitution property

$14x-4=2FG$

$14x-4=2(5x+9)$

$14x-4=10x+18$

$14x-10x=18+4$

$4x=22$

$x=\frac{22}{4}=5.5$

Substitute the values then we get

$FG=5(5.5)+9=36.5$

$FG=GH=36.5$

$FH=14(5.5)-4=73$

8 0

3 years ago

A particle moves along a straight line. The distance of the particle from the origin at time t is modeled by the equation below.

laiz [17]

Answer:

The value of t that will satisfy the equation is π/6 (which is 30 degrees)

Step-by-step explanation:

The function that models the movement of the particle is given as;

S(t) = 2 sin(t) + 3 cos (t)

Now we want to the value of t between 0 and pi/2 that satisfies the equation;

s(t) = (2+ 3√3)/2 = 1 + 3√3/2

What we do here is simply find that value of t that would ensure that;

2sin(t) + 3cos(t) = 1 + 3√3/2

Without any need for rigorous calculations, this value of t can be gotten by inspection.

From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2

We can make a substitution for it in this equation.

We obtain the following;

2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2

Do not forget however that we have a range. And the range in question is between 0 and π/2

Kindly that π/2 in degrees is 90 degrees

So our range of values here is between 0 and 90 degrees.

So to follow the notation in the question, the value within the range that will satisfy the equation is π/6

4 0

3 years ago

7. Consider the purchase of two cereal boxes.

AveGali [126]

Answer:

a) 0.25

b) 0.25

c) 0.0625

Step-by-step explanation:

The complete question is:

Do you remember when breakfast cereal companies placed prizes in boxes of cereal? Possibly you recall that when a certain prize or toy was particularly special to children, it increased their interest in trying to get that toy. How many boxes of cereal would a customer have to buy to get that toy? Companies used this strategy to sell their cereal.

One of these companies put one of the following toys in its cereal boxes: a block (B), a toy watch (W), a toy ring (R), and a toy airplane (A). A machine that placed the toy in the box was programmed to select a toy by drawing a random number of 1 to 4. If a 1 was selected, the block (or B) was placed in the box; if a 2 was selected, a watch (or W) was placed in the box; if a 3 was selected, a ring (or R) was placed in the box; and if a 4 was selected, an airplane (or A) was placed in the box. When this promotion was launched, young children were especially interested in getting the toy airplane.

What is the probability of getting an airplane in the first cereal box?

Since the machine randomly selects toys, each toy has the same probability of being obtained in a cereal box.

Then, the total outcomes are 4 and the probability of getting an airplane in the first cereal box is 0.25 (25%).

What is the probability of getting an airplane in the second cereal box?

Two independent events do not change the probability of occurrence of one event or another.

The probability of getting an airplane in the second cereal box is 0.25 (25%).

What is the probability of getting airplanes in both cereal boxes?

P(1°∩2°)= P(1°) × P(2°) = $\frac{1}{4} \times \frac{1}{4} =\frac{1}{16}$