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Debora [2.8K]
2 years ago
14

Part A: Given sine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).

Mathematics
1 answer:
aliya0001 [1]2 years ago
4 0

Answer:

  A.  {60°, 120°, 420°}

  B.  θ = 15π/4; sec(θ) = √2

Step-by-step explanation:

<h3>A.</h3>

The sine function is periodic with period 360°, and it is symmetrical about the line θ = 90°. The reference angle for the given value of sin(θ) is ...

  θ = arcsin(√3/2) = 60°

The next larger angle with the same sine is (2×90°) -60° = 120°. Any multiple of 360° added to either one of these angles will give an angle with the same sine. A possible set of 3 angles is ...

  {60°, 120°, 420°}

__

<h3>B.</h3>

One degree is π/180 radians, so the given angle in radians is ...

  θ = 675° = 675(π/180) radians = 15π/4 radians

This angle has the same trig function values as 7π4, a 4th-quadrant angle with a reference angle of π/4, or 45° The secant of that angle is

  sec(45°) = √2

The 4th-quadrant angle has the same sign, so ...

  sec(675°) = sec(15π/4) = √2

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^PLZ HELP, I NEED IT BY TODAY!!! (PART B and PART C only) PLZ THANKS
Lana71 [14]

<em><u>Part B (Taxi):</u></em>

12 miles = 0.5 miles + (115×0.1) miles

Rate: $2.40 + (115×0.20)

         = $25.40

Total cost (with tip): $25.40 + $2

                               = $27.40

20 miles = 0.5 miles + (195×0.1) miles

Rate: $2.40 + (195×0.20)

         = $41.40

Total cost (with tip): $41.40 + $2

                               = $43.40

50 miles = 0.5 miles + (495×0.1) miles

Rate: $2.40 + (495×0.20)

         = $101.40

Total cost (with tip): $101.40 + $2

                               = $103.40

<em><u>Part B (Uber):</u></em>

12 miles (rate) = $1 + ($1.05×12)

                        = $13.60

Total cost (with tip): $13.60 + $2

                               = $15.60

20 miles (rate) = $1 + ($1.05×20)

                         = $22

Total cost (with tip): $22 + $2

                               = $24

50 miles (rate) = $1 + ($1.05×50)

                        = $53.50

Total cost (with tip): $53.50 + $2

                               = $55.50

<em><u>Part C</u></em>

Uber is a better mode of transportation. This is because given the same distance travelled for both the taxi and the Uber, Uber has a lower cost compared to the taxi.

3 0
2 years ago
The area of a circle is 42.29m2.<br> Find the length of the diameter rounded to 1 DP.
Firdavs [7]

Step-by-step explanation:

area of a circle=πr²

=42.29m²

42.29m²=πr²

then find for r, multiply it by two to obtain the diameter of the circle

6 0
3 years ago
One half of a number added to two thirds of the number is 21. Find the number and show your work
Svet_ta [14]
The number would be 18.
Half of 18 = 9
Two thirds of 18 = 12
9 + 12 = 21
3 0
3 years ago
Professor Halen teaches a College Mathematics class. The scores on the midterm exam are normally distributed with a mean of 72.3
lbvjy [14]

Answer:

14.63% probability that a student scores between 82 and 90

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 72.3, \sigma = 8.9

What is the probability that a student scores between 82 and 90?

This is the pvalue of Z when X = 90 subtracted by the pvalue of Z when X = 82. So

X = 90

Z = \frac{X - \mu}{\sigma}

Z = \frac{90 - 73.9}{8.9}

Z = 1.81

Z = 1.81 has a pvalue of 0.9649

X = 82

Z = \frac{X - \mu}{\sigma}

Z = \frac{82 - 73.9}{8.9}

Z = 0.91

Z = 0.91 has a pvalue of 0.8186

0.9649 - 0.8186 = 0.1463

14.63% probability that a student scores between 82 and 90

3 0
3 years ago
I NEED HELP. PLEASE ANSWER QUICK. BRAINLIEST WILL BE GIVEN. THERE IS A BOT AUTO ANSWERING. PLEASE ANSWER ANYWAY
dimaraw [331]

Answer:

The answer is A

Step-by-step explanation:

The shape is a rhombus when plotted on a quardanent plane. The shape is similar to a diamond.

7 0
3 years ago
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