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luda_lava [24]
2 years ago
11

If θ is an angle in standard position and its terminal side passes through the point (-7,-5), find the exact value of cot ⁡ θ co

tθ in simplest radical form.
Mathematics
1 answer:
tresset_1 [31]2 years ago
4 0

Plot the point (-7, -5). We are in quadrant 3.

We also know that tan θ = opp/adj.

Cot θ = adj/opp.

Let us use a^2 + b^2 = r^2 to show you how to find r, the radius aka hypotenuse.

Look: (-7)^2 + (-5)^2 = r^2

If you should ever need to find r, do this:

(-7)^2 + (-5)^2 = r^2

(49) + 25) = r^2

74 = r^2

Take the square root on both sides of the equation to find r.

sqrt{74} = sqrt{r^2}

sqrt{74} = r

It is ok to simplify the sqrt{74} but not needed.

We now have the three sides of the triangle that is form in quadrant 3.

We can now read cot θ from the triangle itself.

So, cot θ = adj/opp = (-7)/(-5) or 7/5.

No need to find r but I simply wanted to show you how it's done in case you are given a question where r must be found.

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Julie will build a rectangular pen for her dog against a barn. A wall from the barn will form one side of the pen. She has 32 m
MAXImum [283]

Answer:

<h3> The width (side perpedicular to the barn):  <u>x = 8 m</u></h3><h3>      The lenght (side parallel to the barn):  <u>y = 16 m</u> </h3>

Step-by-step explanation:

x  - the width of the barn

She has 32 m of fencing so for the lenght remain (32-2x) m of fencing:

y = 32 - 2x

Area of the fencing:  A = x•y

A(x) = x•(32 - 2x)

A(x) = -2x² + 32x             ←  quadratic function

The maximum value of quadratic function occurs at:  x=-\frac b{2a}

a = -2,  b = 32

x=-\frac b{2a}=-\frac{32}{2\cdot(-2)}=-(-8)=8

32-2x = 32 - 2•8 = 16

4 0
3 years ago
I dont know which two chose
pshichka [43]
- Points J, K, and Q are collinear
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7 0
3 years ago
Which point is a solution to the system of inequalities below?
vodomira [7]

The ordered pair which is a solution to the given inequality is: C. (2, 1).

<h3>What is an inequality?</h3>

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

  • Less than (<).
  • Greater than (>).
  • Less than or equal to (≤).
  • Greater than or equal to (≥).

Next, we would test the ordered pair with the given inequality to determine a solution as follows:

For ordered pair (4, 4), we have:

3x + 2y < 15

3(4) + 2(4) < 15

12 + 8 < 15

20 < 15 (False).

For ordered pair (3, 3), we have:

3x + 2y < 15

3(3) + 2(3) < 15

9 + 6 < 15

15 < 15 (False).

7x - 4y > 9

7(3) - 4(3) > 9

21 - 12 > 9

9 > 9 (False)

For ordered pair (2, 1), we have:

3x + 2y < 15

3(2) + 2(1) < 15

6 + 2 < 15

8 < 15 (True).

7x - 4y > 9

7(2) - 4(1) > 9

14 - 4 > 9

10 > 9 (True)

For ordered pair (1, 0), we have:

3x + 2y < 15

3(1) + 2(0) < 15

3 + 0 < 15

3 < 15 (True).

7x - 4y > 9

7(1) - 4(0) > 9

7 - 4 > 9

3 > 9 (False)

Read more on inequality here: brainly.com/question/27166555

#SPJ1

7 0
1 year ago
A store brought 9 cases of light bulbs in May and 8 cases in June. There are 48 light bulbs in a case. How many light bulbs did
UkoKoshka [18]
So the store bought 9 cases of lightbulbs and in a case, there are 48.
9 * 48 = the number of lightbulbs in the nine cases. 432 is the number of light bulbs in the 9 cases they bought in May. So then let's move on to the cases they bought in June. Do the same thing 8 * 48 is 384. So then add the two amounts together and then you will get 816 which will be your answer. I hope this helps!
5 0
3 years ago
Read 2 more answers
Heeeeeeeeeeeelpppppppp
KonstantinChe [14]

Answer:

$59.85

is your answer

8 0
3 years ago
Read 2 more answers
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