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3 years ago

15

An exhibition was open for one weekend only. On the Saturday, there were 360 visitors to the exhibition. There were 15% fewer vi

sitors on the Sunday than there were on Saturday. Work out how many visitors there were on the Sunday.

2 answers:

Papessa [141]3 years ago

8 0

Answer:306

Step-by-step explanation:

360×.15= 54

360-54= 306

Marysya12 [62]3 years ago

3 0

Answer:

306 Hope it helps :3

Step-by-step explanation:

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Answer:

I think the second option is the most appropriate option.

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2 years ago

Simplify the expression by combining like terms. -8x - 4x

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Can someone please explain how to do this!!!

DedPeter [7]

Hi there!

So we are given that:-

tan theta = 7/24 and is on the third Quadrant.

In the third Quadrant or Quadrant III, sine and cosine both are negative, which makes tangent positive.

Since we want to find the value of cos theta. cos must be less than 0 or in negative.

To find cos theta, we can either use the trigonometric identity or Pythagorean Theorem. Here, I will demonstrate two ways to find cos.

<u>U</u><u>s</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>I</u><u>d</u><u>e</u><u>n</u><u>t</u><u>i</u><u>t</u><u>y</u>

$\large \displaystyle{ {tan}^{2} \theta + 1 = {sec}^{2} \theta}$

Substitute tan theta = 7/24 in.

$\large \displaystyle{ {( \frac{7}{24}) }^{2} + 1 = {sec}^{2} \theta }$

Evaluate.

$\large \displaystyle{ \frac{49}{576} + 1 = {sec}^{2} \theta} \\ \large \displaystyle{ \frac{625}{576} = {sec}^{2} \theta}$

Reminder -:

$\large \displaystyle{ sec \theta = \frac{1}{cos \theta} }$

Hence,

$\large \displaystyle{ \frac{576}{625} = {cos}^{2} \theta} \\ \large \displaystyle{ \sqrt{ \frac{576}{625} } = cos \theta} \\ \large \displaystyle{ \frac{24}{25} = cos \theta}$

Because in QIII, cos<0. Hence,

$\large \displaystyle \boxed{ \blue{cos \theta = - \frac{24}{25} }}$

<u>U</u><u>s</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>P</u><u>y</u><u>t</u><u>h</u><u>a</u><u>g</u><u>o</u><u>r</u><u>e</u><u>a</u><u>n</u><u> </u><u>T</u><u>h</u><u>e</u><u>o</u><u>r</u><u>e</u><u>m</u>

$\large \displaystyle{ {a}^{2} + {b}^{2} = {c}^{2} }$

Define c as our hypotenuse while a or b can be adjacent or opposite.

Because tan theta = opposite/adjacent. Therefore:-

$\large \displaystyle{ {7}^{2} + {24}^{2} = {c}^{2} } \\ \large \displaystyle{49 + 576 = {c}^{2} } \\ \large \displaystyle{625 = {c}^{2} } \\ \large \displaystyle{25 = c}$

Thus, the hypotenuse side is 25. Using the cosine ratio:-

$\large \displaystyle{cos \theta = \frac{adjacent}{hypotenuse}}$

Therefore:-

$\large \displaystyle{cos \theta = \frac{24}{25} }$

Because cos<0 in Q3.

$\large \displaystyle \boxed{ \red{cos \theta = - \frac{24}{25} }}$

Hence, the value of cos theta is -24/25.

Let me know if you have any questions!

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