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4 years ago

For the function y=-1+6cos(2pi/7(x-5)) what is the minimum value?

Mathematics

1 answer:

s344n2d4d5 [400]4 years ago

7 0

Answer:

The minimum value of y is -7

Step-by-step explanation:

Given: $y=-1+6\cos(\dfrac{2\pi}{7}(x-5))$

We are given a cosine function.

We need to find minimum value of function.

$y=-1+6\cos(\dfrac{2\pi}{7}(x-5))$

Here y is depends on cosine function.

y is minimum when cosine is minimum because y is directly proportional to cosine function.

Minimum value of cos x is -1

Therefore, For minium value of y

$\cos(\dfrac{2\pi}{7}(x-5))=-1$

Minimum value of y

$y=-1+6(-1)$

$y=-7$

Hence, The minimum value of y is -7

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Find the missing sides.

love history [14]

Answer:

Part 3)

$x=6\ units$

$y=3\ units$

Part 4) $x=18\sqrt{2}\ units$

Step-by-step explanation:

Part 3)

Find the value of x

In the right triangle of the figure we know that

The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse

$cos(30\°)=\frac{3\sqrt{3}}{x}$

and remember that

$cos(30\°)=\frac{\sqrt{3}}{2}$

substitute

$\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}$

Simplify

$x=(2*3)=6\ units$

Find the value of y

In the right triangle of the figure we know that

The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse

$sin(30\°)=\frac{y}{x}$

and remember that

$sin(30\°)=\frac{1}{2}$

substitute

$\frac{1}{2}=\frac{y}{6}$

$y=6/2=3\ units$

Part 4) Find the value of x

Applying the Pythagoras Theorem

$x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units$

Simplify

$x=18\sqrt{2}\ units$

6 0

3 years ago

What does it find the GCF of each set of numbers using prime at factorizstion

lozanna [386]

You use the factor tree.
10
5 2 then you have 2 prime numbers and you have to multiply them together

3 0

3 years ago

Shayla is having a picnic and wants to buy enough hamburgers so that each guest can have one. If she is planning on having 52 gu

yKpoI14uk [10]

Answer:

6 ≤ x ≤ 7

Step-by-step explanation:

Dividing 52 by 8 gives you a decimal between 6 and 7. Since you can only but hamburgers in packages of 8, the inequality is 6 ≤ x ≤7 with x being the number of hamburger bags.

8 0

3 years ago

What is the best first step to solve the inequality 5x - 32 2? O Add 3 to both sides of the equation. Subtract 3 from both sides

lukranit [14]

Answer:

<h3>A. Add 3 to both sides of the equation</h3>

Step-by-step explanation:

The inequality equation is not well written Let's say the equation is given as:

5x - 3 > 2

<em>The best first step in solving this equation is by removing - 3 from the left hand side of the equation since all we want to do is make x the subject of the formula:</em>

To remove the -3, <u>we will have to add 3 to both sides of the inequality </u>as shown:

5x - 3 + 3> 2 +3

5x + 0 > 5

5x > 5

To get x, we will then divide both sides by 5

5x/5 > 5/5

x > 1

hence the best first step according to the explanation above is to Add 3 to both sides of the equation. Option A is correct

3 0

3 years ago

If a number x is chosen at random from the numbers -2,-1, 0, 1,2.what is the probability that x2<2.

Katyanochek1 [597]

Answer:

Do you mean 2x<2 or

X <2 or do you mean x²<2

Step-by-step explanation:

If your question is X²<2

Then

Total outcomes=5

Possible outcomes=3(-1,0,1)

Probability of x²<2=3/5

If your question means probability of2x<2

Then

Total outcomes=5

Possible outcomes=3 (-2,-1,0)

Probability of 2x<2=3/5

If your question means x< 2

Then

Total outcomes=5

Possible outcomes=4 (-2,-1,0,1)

Probability of x <2 =4/5

If I have not answered your question

then you can comment and ask me if you have any doubts

Hope this helps

8 0

4 years ago