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BARSIC [14]
3 years ago
13

I need qestion number d) solution please help me​

Mathematics
1 answer:
natita [175]3 years ago
8 0

Answer:

It is an identity, the proof is in the explanation

Step-by-step explanation:

csc(A)-cot(A)=tan(A/2)

I'm going to start with right hand side

tan(A/2)=(1-cos(a))/(sin(a))                half angle identity

tan(A/2)=1/sin(a)-cos(a)/sin(a)         separate fraction

tan(A/2)=csc(a)-cot(a)                     reciprocal and quotient identities

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Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)
Lisa [10]

Answer:

f(x) = 4x^2 - 3x + 6

Step-by-step explanation:

Quadratic function is given as f(x) = ax^2 + bx + c

Let's find a, b and c:

Substituting (0, 6):

6 = a(0)^2 + b(0) + c

6 = 0 + 0 + c

c = 6

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

f(x) = ax^2 + bx + c

16 = a(2)^2 + b(2) + 6

16 = 4a + 2b + 6

16 - 6 = 4a + 2b + 6 - 6

10 = 4a + 2b

10 = 2(2a + b)

\frac{10}{2} = \frac{2(2a + b)}{2}

5 = 2a + b

2a + b = 5 => (Equation 1)

Substituting (3, 33), and c = 6

f(x) = ax^2 + bx + x

33 = a(3)^2 + b(3) + 6

33 = 9a + 3b + 6

33 - 6 = 9a + 3b + 6 - 6

27 = 9a + 3b

27 = 3(3a + b)

\frac{27}{3} = \frac{3(3a + b)}{3}

9 = 3a + b

3a + b = 9 => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

3a + b = 9

2a + b = 5

a = 4

Replace a with 4 in equation 2.

2a + b = 5

2(4) + b = 5

8 + b = 5

8 + b - 8 = 5 - 8

b = -3

The quadratic function that represents the given 3 points would be as follows:

f(x) = ax^2 + bx + c

f(x) = (4)x^2 + (-3)x + 6

f(x) = 4x^2 - 3x + 6

6 0
3 years ago
If 5 sips +4 gulps = 1 glass and 13 sips +7 gulps = 2 glasses, how many sips equal a gulp?
nataly862011 [7]

Answer:

3 sips equal a gulp

Step-by-step explanation:

we have

5sips+4gulps=1glass ----> equation A

13sips+7gulps=2glass

Divide by 2 both sides

6.5sips+3.5gulps=1glass ----> equation B

equate equation A and equation B

5sips+4gulps=6.5sips+3.5gulps

Group terms that contain the same variable

4gulps-3.5gulps=6.5sips-5sips

0.5gulps=1.5sips

gulps=(1.5/0.5)sips

gulps=3sips

therefore

3 sips equal a gulp

3 0
3 years ago
Suppose that an insect population’s density, in thousands per acre, during year n, can be modeled by the recursive formula: a1 =
vlabodo [156]

Answer:

The population alternates between increasing and decreasing

Step-by-step explanation:

<u><em>The options of the question are</em></u>

A) The population density decreases each year.

B) The population density increases each year.

C) The population density remains constant.

D) The population alternates between increasing and decreasing

we have

a_n=2.9(a_n_-_1)-0.2(a_n_-_1)^2

a_1=8

Find the value of a_2

For n=2

a_2=2.9(a_1)-0.2(a_1)^2

a_2=2.9(8)-0.2(8)^2=10.4

Find the value of a_3

For n=3

a_3=2.9(a_2)-0.2(a_2)^2

a_3=2.9(10.4)-0.2(10.4)^2=8.528

For n=4

a_4=2.9(a_3)-0.2(a_3)^2

a_4=2.9(8.528)-0.2(8.528)^2=10.1858

For n=5

a_5=2.9(a_4)-0.2(a_4)^2

a_5=2.9(10.1858)-0.2(10.1858)^2=8.7887

therefore

The population alternates between increasing and decreasing

7 0
3 years ago
Read 2 more answers
Pls help!!!!!!!!!!!!!!!!
Zolol [24]

Answer:

23 degrees

Step-by-step explanation:

62+95=157

180-157=23

7 0
2 years ago
Read 2 more answers
Sarah counted 16 dogs playing fetch out of 24 total dogs at the park. which fraction represents the ratio of dogs that were play
mamaluj [8]
It's 16:24
so the ratio is 2:3
6 0
2 years ago
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