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kogti [31]
3 years ago
9

Which of the following trigonometric inequalities has no solution over the interval 0 ≤ x ≤ 2pi radians?

Mathematics
1 answer:
valentinak56 [21]3 years ago
6 0

Answer:

A .cos(x)<1

Step-by-step explanation:

According to the first inequality

cos(x)<1

x < arccos 1

x<0

This therefore does not have a solution within the range 0 ≤ x ≤ 2pi

x cannot be leas than 0. According to the range not value, 0≤x which is equivalent to x≥0. Thus means otvis either x = 0 or x> 0.

For the second option

.cos(x/2)<1

x/2< arccos1

x/2<0

x<0

This inequality also has solution within the range 0 ≤ x ≤ 2pi since 0 falls within the range of values.

For the inequality csc(x)<1

1/sin(x) < 1

1< sin(x)

sinx>1

x>arcsin1

x>90°

x>π/2

This inequality also has solution within the range 0 ≤ x ≤ 2pi since π/2 falls within the range of values

For the inequality csc(x/2)<1

1/sin(x/2) < 1

1< sin(x/2)

sin(x/2)> 1

x/2 > arcsin1

X/2 > 90°

x>180°

x>π

This value of x also has a solution within the range.

Therefore option A is the only inequality that does not have a solution with the range.

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27^4–9^5 3^9 is divisible by 25
hichkok12 [17]

Answer:

  no

Step-by-step explanation:

If you mean

  27^4 - 9^5·3^9 = -1161730026

it has no factors of 5, so cannot be divisible by 25.

__

If you mean ...

  (27^4 -9^5)/3^9 = ((3^3)^4 -(3^2)^5)/3^9 = 3^10(3^2 -1)/3^9 = 3(9-1) = 24

it is not divisible by 25, either.

6 0
3 years ago
you are riding a bicycle which has tires with a 25-inch diameter at a steady 15-miles per hour, what is the angular velocity of
motikmotik

Answer:

The angular velocity is 6.72 π radians per second

Step-by-step explanation:

The formula of the angular velocity is ω = \frac{v}{r} , where v is the linear velocity and r is the radius of the circle

The unit of the angular velocity is radians per second

∵ The diameter of the tire is 25 inches

∵ The linear velocity is 15 miles per hour

- We must change the mile to inch and the hour to seconds

∵ 1 mile = 63360 inches

∵ 1 hour = 3600 second

∴ 15 miles/hour = 15 ×  \frac{63360}{3600}

∴ 15 miles/hour = 264 inches per second

Now let us find the angular velocity

∵ ω = \frac{v}{r}

∵ v = 264 in./sec.

∵ d = 25 in.

- The radius is one-half the diameter

∴ r = \frac{1}{2} × 25 = 12.5 in.

- Substitute the values of v and r in the formula above to find ω

∴ ω = \frac{264}{12.5}

∴ ω =  21.12 rad./sec.

- Divide it by π to give the answer in terms of π

∴ ω = 6.72 π radians per second

The angular velocity is 6.72 π radians per second

3 0
3 years ago
After a 12% increase the cost of a new cooker is £190.40
Svetllana [295]

Answer:

1

X+.12*x=190.40

X(1+.12)=190.40

X=190.40/1.12=170

2a

X+x+25=100

2x=75

X=37.5%

Men=.375*270=101

2b

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2 years ago
Figure abcd is a parallelogram what are the measures of b and c
Over [174]

what is the question

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3 years ago
Mrs. Kitchell has graded 12 out of 48 papers so far. What percent of the papers has Mrs. Kitchell graded so far?
ioda
1/4 of the work so 25%!
7 0
2 years ago
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