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3 years ago

What is the common difference in the following arithmetic sequence?

Mathematics

2 answers:

Tasya [4]3 years ago

8 0

Can’t see the image upload it again

Novosadov [1.4K]3 years ago

7 0

Answer:

There's nothing there.

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PLEASE HELP ME If 0 < z ≤ 90 and sin(9z − 1) = cos(6z + 1), what is the value of z? z = 3 z = 4 z = 5 z = 6

Burka [1]

Answer:

z = 6

Step-by-step explanation:

We know that ...

sin(x) = cos(90 -x)

Substituting (9z-1) for x, this is ...

sin(9z -1) = cos(90 -(9z -1))

But we also are given ...

sin(9z -1) = cos(6z +1)

Equating the arguments of the cosine function, we have ...

90 -(9z -1) = 6z +1

90 = 15z . . . . . . . . . add (9z-1) to both sides

6 = z . . . . . . . . . . . . divide by 15

_____

<em>Comment on the graph</em>

The attached graph shows 5 solutions in the domain of interest. These come from the fact that the relation we used is actually ...

sin(x) = cos(90 +360k -x) . . . . . for any integer k

Then the above equation becomes ...

90 +360k = 15z

6 +24k = z . . . . . . . . . for any integer k

The sine and cosine functions also enjoy the relation ...

sin(x) = cos(x -90)

sin(9z -1) = cos(9z -1 -90) = cos(6z +1)

3z = 92 . . . . . equating arguments of cos( ) and adding 91-6z

z = 30 2/3

6 0

3 years ago

Given that f(x)= x^2-3/2 find f^-1(x)

Scilla [17]

Answer:

$\bold{f(x)=-\frac{1}{2}}$

Step-by-step explanation:

$f(x)= x^2-\frac{3}{2}$ replace x with -1

$f(x)= -1^2-\frac{3}{2}$ solve exponents

-1² = -1 × -1 = 1

$f(x)= 1-\frac{3}{2}$ subtract

$\bold{f(x)=-\frac{1}{2}}$

7 0

2 years ago

What are prime numbers

Tasya [4]

Answer:

2, 3, 5, 7 and 11 are the first few prime numbers.

Step-by-step explanation:

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.

6 0

3 years ago

Read 2 more answers

Factorize completely <br> 2x^2+4x-6

rodikova [14]

Answer:

Solution given;

2x²+4x-6

2x²+6x-2x-6

2x(x+3)-2(x+3)

(x+3)(2x-2)

is your answer

6 0

3 years ago

Read 2 more answers

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol ( mu μ, p, sigma σ) for

ella [17]

Answer:

Null hypothesis: $H_0:\; \mu = 48\; ^\circ\rm F$ .

Alternative hypothesis: $H_1:\; \mu \ne 48\; \rm ^\circ F$ .

Step-by-step explanation:

In hypothesis testing, the alternative hypothesis $H_1$ represents the claim that is being tested. According to the claim in this question, the true (population) mean $\mu$ is "incorrect," or not equal to (" $\ne$ ") the proposed value of $48\; \rm ^\circ F$ . Hence, the alternative hypothesis for this question would be $H_0:\; \mu \ne 48\; \rm ^\circ F$ .

On the other hand, the null hypothesis represents what happens when that claim is disproved; it should always use the equal sign (" $=$ ".) In this question, that's the same as saying that the (population) mean $\mu$ is indeed equal to $48\; \rm ^\circ F$ . Hence, the null hypothesis for this question would be: $H_1:\; \mu = 48\; \rm ^\circ F$ .

5 0

3 years ago