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katen-ka-za [31]
2 years ago
9

Find the sine function that is represented in the graph.

Mathematics
1 answer:
meriva2 years ago
6 0

Answer:

Choice D). f(x)=20\sin(4x) is correct.

Step-by-step explanation:

Given function graph is sinusoidal so let's compare with formula f(x)=A\sin(Bx-C)+D

We know that amplitude is the height from the center line to the peak (or to the trough). From graph we can see that height from the center line to the peak is 20

So amplitude A=20

In that formula, period is given by \frac{2\pi}{B}

From graph we see that period is \frac{\pi}{2}

So both must be equal

\frac{2\pi}{B}=\frac{\pi}{2}

\frac{2}{B}=\frac{1}{2}

cross multiplying them gives

B=4

Clearly there is no shift so C and D are 0

Now plug these values into formula f(x)=A\sin(Bx-C)+D

f(x)=20\sin(4x-0)+0

f(x)=20\sin(4x)

Hence choice D is correct.

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The most popular mathematician in the world is throwing aparty for all of his friends. As a way to kick things off, they decidet
ratelena [41]

Answer:

The no. of possible handshakes takes place are 45.

Step-by-step explanation:

Given : There are 10 people in the party .

To Find: Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?

Solution:

We are given that there are 10 people in the party

No. of people involved in one handshake = 2

To find the no. of possible handshakes between 10 people we will use combination over here

Formula : ^nC_r=\frac{n!}{r!(n-r)!}

n = 10

r= 2

Substitute the values in the formula

^{10}C_{2}=\frac{10!}{2!(10-2)!}

^{10}C_{2}=\frac{10!}{2!(8)!}

^{10}C_{2}=\frac{10 \times 9 \times 8!}{2!(8)!}

^{10}C_{2}=\frac{10 \times 9 }{2 \times 1}

^{10}C_{2}=45

No. of possible handshakes are 45

Hence The no. of possible handshakes takes place are 45.

4 0
2 years ago
WILL BE BRANLIEST!!!
stiks02 [169]

Answer:

See explanation

Step-by-step explanation:

A. Solution set is in the attachment (dark green shading in the middle)

B. Yes, 2(5) + 3(1) ≤ 15; 13 is less than or equal to 15

5 + 1 > 3, 6 is greater than 3

C. (4, 2) means that he buys 4 sandwiches and 2 hot lunches

8 0
2 years ago
Read 2 more answers
A bucket that has a mass of 30 kg when filled with sand needs to be lifted to the top of a 30 meter tall building. You have a ro
Rom4ik [11]

Answer:

765 J

Step-by-step explanation:

We are given;

Mass of bucket = 30 kg

Mass of rope = 0.3 kg/m

height of building= 30 meter

Now,

work done lifting the bucket (sand and rope) to the building = work done in lifting the rope + work done in lifting the sand

Or W = W1 + W2

Work done in lifting the rope is given as,

W1 = Force x displacement

W1 = (30,0)∫(0.2x .dx)

Integrating, we have;

W1 = [0.2x²/2] at boundary of 30 and 0

W1 = 0.1(30²)

W1 = 90 J

work done in lifting the sand is given as;

W2 = (30,0)∫(F .dx)

F = mx + c

Where, c = 30 - 15 = 15

m = (30 - 15)/(30 - 0)

m = 15/30 = 0.5

So,

F = 0.5x + 15

Thus,

W2 = (30,0)∫(0.5x + 15 .dx)

Integrating, we have;

W2 = (0.5x²/2) + 15x at boundary of 30 and 0

So,

W2 = (0.5 × 30²)/2) + 15(30)

W2 = 225 + 450

W2 = 675 J

Therefore,

work done lifting the bucket (sand and rope) to the top of the building,

W = 90 + 675

W = 765 J

5 0
2 years ago
A grocery sold 5kg of wheat flour at Rs30 per kg and gained 20%. If he had sold it at Rs27 per kg, what would be his gain or los
maria [59]

Answer:

His gain percent would have been 8%

Step-by-step explanation:

The key to answering this question is to first calculate the price at which the wheat flour was bought.

Mathematically;

% profit = (selling price-cost price)/cost price * 100%

Let the cost price be $x

Thus;

% profit = (30-x)/x * 100

20 = 100(30-x)/x

20x = 3000-100x

100x + 20x = 3000

120x = 3000

x = 3000/120

x = Rs 25

So let’s assume he sold at Rs 27

His profit would have been 27-25 = 2

His gain or loss percentage would’ve been;

2/25 * 100/1 = 200/25 = 8% (gain, since selling price is greater than the cost price)

3 0
2 years ago
Three straight lines intersect at $O$, and ray $\overrightarrow{OD}$ divides $\angle COE$ into two angles of equal measure. The
riadik2000 [5.3K]

Answer:

12

Step-by-step explanation:

m xxq

8 0
2 years ago
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