All categories

1 year ago

Figure 4 shows part of the curve with equation

Mathematics

1 answer:

swat321 year ago

7 0

The values of a and b are 2 and π/5, respectively

<h3>How to determine the values of a and b?</h3>

The graph of the complete question is added as an attachment

The equation of the graph is given as:

y = sin(ax - b)

From the graph, we have the following points:

(π/10, 0), (3π/5, 0) and (11π/10, 0)

Substitute the above points in y = sin(ax - b)

sin(a(π/10) - b) = 0 and sin(a(3π/5) - b) = 0

Take the arc sin of both sides

a(π/10) - b = 0

a(3π/5) - b = π

Subtract the equations to eliminate b

a(π/10) - a(3π/5) = -π

Divide through by π

a(1/10) - a(3/5) = -1

Express fractions as decimals

0.1a - 0.6a = -1

Evaluate the difference

-0.5a = -1

Divide by -0.5

a = 2

Substitute a = 2 in a(3π/5) - b = π

2 * (3π/5) - b = π

Evaluate the product

6π/5 - b = π

This gives

b = 6π/5 - π

Evaluate the difference

b = π/5

Hence, the values of a and b are 2 and π/5, respectively

You might be interested in

The students in a class were each asked to name their favorite meal of the day. Which table could be represented by percentage b

sineoko [7]

Answer:

Step-by-step explanation:

I say G because when you look at the bar, the maximum is 100% and G is 20 in total. Therefore, the maximums are the same types and both can be divided by 10.

7 0

3 years ago

Read 2 more answers

Pls anwers pls friend fast pls

Natalija [7]

Answer:

(b) (a) (d) (a) (c)

Step-by-step explanation:

(i) The probability of an even card is 1/2 because the number of even cards and odd cards are the same so there is a 50% of getting an even card. (b)

(ii) Since the card is replaced, there is still a card for all numbers between 1-20. There are 8 prime numbers and 20 cards so the probability of getting a prime number is 8/20 or 4/10 or 2/5. (a)

(iii) The card was not replaced so there are only 19 cards and there are only 5 numbers that are multiples of 3 and greater than 4. The probability must be 5/19. (d)

(iv) A sure event means that it will happen 100%. So P(A) = 1 since the number one represents 100%. (a)

(v) All cards have replaced and there is only one number that is a multiple of 3 and 5 which is 15. 1 card out of 20 is a desired outcome so 1/20 is the probability. (c)

7 0

3 years ago

Will make you brainliest!!! If correct!!

Virty [35]

Answer:

Step-by-step explanation:

y = - $\frac{1}{4}$ x + 3 ( equation of line t )

y - (- 2) = - $\frac{1}{4}$ [ x - (- 2)] ⇒ y = - $\frac{1}{4}$ x - $\frac{5}{2}$ ( equation of line u )

5 0

3 years ago

Explain how to write 50,000 in exponent form

viktelen [127]

My answer is that
5×10^4

7 0

4 years ago

Freddie is at chess practice waiting on his opponent's next move. He notices that the 4-inch-long minute hand is rotating around

Alex777 [14]

One complete revolution of the minute hand sweeps a central angle of 360° which is equivalent to 60 minutes.
That is, the minute hand creates
(360°/(60 min) = 6 degrees/min.

From 3:35 to 3:55 is 20 minutes.
It sweeps a central angle of
(20 min)*(6 deg/min) = 120°

Because 360° = 2π radians,
120° = (120/360)*2π = (2π)/3 radians

Answer:
$\frac{2 \pi }{3} \,radians$
In decimals, this is 2.1 radians (nearest tenth)

Part 2:
Because the minute hand is 4 inches long, the length of the arc swept is
(4 in)*(2π/3 radians) = 8π/3 inches

Answer:
$\frac{8 \pi }{3} \,inches$
In decimals, this is 8.4 inches (nearest tenth).

7 0

3 years ago