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pshichka [43]
3 years ago
9

Doe anyone know this? At least someone have to

Mathematics
1 answer:
Paul [167]3 years ago
4 0

Answer:

While I will not give you an answer, I will tell you how to find it. Don't get scared! I promise it's not complicated. You basically only need to do subtraction.

Concept Explanation:

Okay, so let's start off by defining "complement" and "supplement":

"Complement" - <em><u>complementary angles</u></em>: two angles whose sum equals 90°

"Supplement" - <u><em>supplementary angles</em></u>: two angles whose sum equals 180°

So, this question is asking you what the <u>other angle</u> is. Based on whether they ask you for the <em>complement</em> or <em>supplement</em>, you only need to subtract the first angle they give you from 90° (if it's asking for the complement) or 180° (if it's asking you for the supplement).

Here are some examples if you're still confused!

--------------------------------------------------------------------------------------------------------------

- What is the complement of a 32° angle?

↓

Since they're asking for the <u>complement</u>, we will subtract 32° (the angle they give us) from 90° (because it's a <u>complement</u>)

↓

90 - 32 = 58

↓

So our answer is: <u>58°</u>

--------------------------------------------------------------------------------------------------------------

Now let's do a supplement one.

--------------------------------------------------------------------------------------------------------------

- What is the supplement of an 84° angle?

↓

Because they're asking for the <u>supplement</u>, we will subtract 84° (the angle they give us) from 180° (because it's a <u>supplement</u>)

↓

180 - 84 = 96

↓

Then our answer will be: <u>96°</u>

--------------------------------------------------------------------------------------------------------------

That's all! It's just some subtraction once you know what the vocabulary means. Please comment if you have any other questions.

If you want me to check your answers once you try your problem, I can do that as well!

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For the graphed function f(x) = (4)x − 1 + 2, calculate the average rate of change from x = 1 to x = 2.
lorasvet [3.4K]

Average rate of the function: 3

Step-by-step explanation:

The function in this problem is

f(x)=4^{x-1}+2

The average rate of change of a function over an interval (x_1,x_2) is given by

r=\frac{f(x_2)-f(x_1)}{x_2-x_1}

where

f(x_1),f(x_2) are the values of the function calculated in x_1,x_2 respectively

For the function in this problem we have:

x_1=1, so

f(x_1)=f(1)=4^{1-1}+2=4^0+2=1+2=3

x_2=2, so

f(x_2)=f(2)=4^{2-1}+2=4^1+2=4+2=6

So, the average rate of change is

r=\frac{6-3}{2-1}=\frac{3}{1}=3

Learn more about rate of change:

brainly.com/question/4152194

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#LearnwithBrainly

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3 years ago
point b on the ground is 5 cm from point E at the entrance to Ollie's house. He is 1.8 m tall and is standing at Point D, below
enot [183]

Point B on the ground is 5 cm from point E at the entrance to Ollie's house.

Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

The complete question is as follows:

Ollie has installed security lights on the side of his house that is activated by a  sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.

The objective of this information is:

  • To find angle CAB and;
  • Find the distance Ollie is from the entrance to his house when he first activates the sensor.

The diagrammatic representation of the information given is shown in the image attached below.

Using  cosine rule to determine angle CAB, we have:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}= \dfrac{CA}{Sin \hat {ABC}}}

Here:

\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}}

\mathbf{\dfrac{4.5}{Sin \hat {15^0}} = \dfrac{6}{Sin \hat {CAB}}}

\mathbf{Sin \hat {CAB} = \dfrac{Sin 15 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = \dfrac{0.2588 \times 6}{4.5}}

\mathbf{Sin \hat {CAB} = 0.3451}

∠CAB = Sin⁻¹ (0.3451)

∠CAB = 20.19⁰

From the diagram attached;

  • assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;          

Then, we can say:

∠CBD = ∠GBF

∠GBF = (CAB + ACB)      

(because the exterior angles of a Δ is the sum of the two interior angles.

∠GBF = 15° + 20.19°

∠GBF = 35.19°

Using the trigonometric function for the tangent of an angle.

\mathbf{Tan \theta = \dfrac{GF}{BF}}

\mathbf{Tan \ 35.19  = \dfrac{1.8 \ m }{BF}}

\mathbf{BF  = \dfrac{1.8 \ m }{Tan \ 35.19}}

\mathbf{BF  = \dfrac{1.8 \ m }{0.7052}}

BF = 2.55 m

Finally, the distance of Ollie║FE║ from the entrance of his bouse is:

= 5 - 2.55 m

= 2.45 m

Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

Learn more about exterior angles here:

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