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Levart [38]
3 years ago
7

Write an equation for the given function given the period, phase shift, and vertical shift.

Mathematics
1 answer:
lbvjy [14]3 years ago
4 0

ANSWER

y = \cot(x  -  \frac{\pi}{3} )  + 2

EXPLANATION

The cotangent function that is fully transformed is of the form

y =a  \cot(bx + c)  + d

where 'a' is the amplitude.

\frac{\pi}{b}  = \pi

is the period.

This implies that b=1

The phase shift is

\frac{c}{b}  =  -  \frac{\pi}{3}

Substitute b=1 to get;

c  =  -  \frac{\pi}{3}

and d=2 is the vertical shift.

We choose a=1 to get the required function as

y = \cot(x  -  \frac{\pi}{3} )  + 2

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Mrac [35]

Answer:

B. m ∠ 1 = 90° and m ∠ 2 = 90°

Step-by-step explanation:

For most situations, the conjecture would probably be true, but there is one exception that makes this statement false.

When two right angles are supplementary, none of them is acute.

For an angle to be acute it needs to be lesser than 90°, and for a pair of angles to be supplementary they should add up to exactly 180°.

With a pair of right angles (90° each), their sum adds up to 180° but neither of them are acute.

Therefore, the answer is B. m ∠ 1 = 90° and m ∠ 2 = 90°

4 0
3 years ago
Find the volume of a pyramid with a square base where the area of the base is 8.3 m 2 and the height of the pyramid is 9.8 m
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245.56

Step-by-step explanation:

7 0
3 years ago
You need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture. How much
ozzi

Answer:

A. 605 mL of the 35% solution

B. 55 mL of the 95% solution

Step-by-step explanation:

It is given that, you need 660 mL of a 40% alcohol solution. On hand, you have 35% alcohol mixture. You also have a 95% alcohol mixture.

Let x and y be the amount of 35% alcohol solution and 95% alcohol solution (in mL) respectively.

So,

Amount equation: x+y=660        ...(1)

Alcohol equation : 0.35x+0.95y=0.40(660)\Rightarrow 0.35x+0.95y=264     ...(2)

On solving (1) and (2), we get

0.35(660-y)+0.95y=264

231-0.35y+0.95y=264

0.6y=264-231

y=\dfrac{33}{0.6}

y=55

Now, substitute y=55 in (1).

x+55=660  

x=660-55  

x=605  

Therefore, we need 605 mL of the 35% solution  and 55 mL of the 95% solution.

4 0
3 years ago
A manufacturer of televisions subjects the equipment to a comprehensive testing process for all essential functions before the t
Scorpion4ik [409]

Answer:

The probability is   P(X \le 9) =0.9138

Step-by-step explanation:

From the question we are told that

   The probability of the television passing the test is  p = 0.95

    The sample size is  n  =  10

Generally the comprehensive testing process for all essential functions  follows a binomial distribution  

i.e  

         X  \~ \ \ \  B(n , p)

and the probability distribution function for binomial  distribution is  

      P(X = x) =  ^{n}C_x *  p^x *  (1- p)^{n-x}

Here C stands for combination hence we are going to be making use of the combination function in our calculators      

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=>  P(X \le 9) = [^{10}C_9 *  (0.95)^9 *  (1- 0.95)^{10-9}]+ [^{10}C_{10} *  {0.95}^{10} *  (1- 0.95)^{10-10}]

=> P(X \le 9) = [10 *  0.6302  * 0.05 ]+ [1 *0.5987 * 1 ]

=> P(X \le 9) =0.9138

8 0
3 years ago
Letter code into<br> the answer<br> box. All CAPS,<br> no spaces.
nlexa [21]

Answer:

Try CEGI

Step-by-step explanation:

if it's wrong im sorry-

6 0
3 years ago
Read 2 more answers
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