Determine the domain of the function.

A group of 3 children and 2 adults pay a total of $120 to take a karate class. A group of 5 children and 1 adult take the same k

sleet_krkn [62]

Answer:

215

Step-by-step explanation:

8 0

2 years ago

Work out the area of abcd.<br><br> please ensure you give workings out too.

ipn [44]

Answer:

$\displaystyle A_{\text{Total}}\approx45.0861\approx45.1$

Step-by-step explanation:

We can use the trigonometric formula for the area of a triangle:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle <em>between</em> the two side lengths.

As demonstrated by the line, ABCD is the sum of the areas of two triangles: a right triangle ABD and a scalene triangle CDB.

We will determine the area of each triangle individually and then sum their values.

Right Triangle ABD:

We can use the above area formula if we know the angle between two sides.

Looking at our triangle, we know that ∠ADB is 55 DB is 10.

So, if we can find AD, we can apply the formula.

Notice that AD is the adjacent side to ∠ADB. Also, DB is the hypotenuse.

Since this is a right triangle, we can utilize the trig ratios.

In this case, we will use cosine. Remember that cosine is the ratio of the adjacent side to the hypotenuse.

Therefore:

$\displaystyle \cos(55)=\frac{AD}{10}$

Solve for AD:

$AD=10\cos(55)$

Now, we can use the formula. We have:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Substituting AD for a, 10 for b, and 55 for C, we get:

$\displaystyle A=\frac{1}{2}(10\cos(55))(10)\sin(55)$

Simplify. Therefore, the area of the right triangle is:

$A=50\cos(55)\sin(55)$

We will not evaluate this, as we do not want inaccuracies in our final answer.

Scalene Triangle CDB:

We will use the same tactic as above.

We see that if we can determine CD, we can use our area formula.

First, we can determine ∠C. Since the interior angles sum to 180 in a triangle, this means that:

$\begin{aligned}m \angle C+44+38&=180 \\m\angle C+82&=180 \\ m\angle C&=98\end{aligned}$

Notice that we know the angle opposite to CD.

And, ∠C is opposite to BD, which measures 10.

Therefore, we can use the Law of Sines to determine CD:

$\displaystyle \frac{\sin(A)}{a}=\frac{\sin(B)}{b}$

Where A and B are the angles opposite to its respective sides.

So, we can substitute 98 for A, 10 for a, 38 for B, and CD for b. Therefore:

$\displaystyle \frac{\sin(98)}{10}=\frac{\sin(38)}{CD}$

Solve for CD. Cross-multiply:

$CD\sin(98)=10\sin(38)$

Divide both sides by sin(98). Hence:

$\displaystyle CD=\frac{10\sin(38)}{\sin(98)}$

Therefore, we can now use our area formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

We will substitute 10 for a, CD for b, and 44 for C. Hence:

$\displaystyle A=\frac{1}{2}(10)(\frac{10\sin(38)}{\sin(98)})\sin(44)$

Simplify. So, the area of the scalene triangle is:

$\displaystyle A=\frac{50\sin(38)\sin(44)}{\sin(98)}$

Therefore, our total area will be given by:

$\displaystyle A_{\text{Total}}=50\cos(55)\sin(55)+\frac{50\sin(38)\sin(44)}{\sin(98)}$

Approximate. Use a calculator. Thus:

$\displaystyle A_{\text{Total}}\approx45.0861\approx45.1$

8 0

3 years ago

What 9+1 please answer

Lunna [17]

Answer:

10

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

a ladder that is 20 feet long is leaning against the side of a building if the angle formed between the ladder and the ground is

Mademuasel [1]

Answer:

Step-by-step explanation:

Take 20( cosine of 75 degrees)

the answer is 5 ft

8 0

3 years ago

Read 2 more answers

How to find the area of irregular figures

Cloud [144]

Instead, break down the shape into rectangles. Next, calculate the area of both rectangles and add them together. The area of the first rectangle is 72 square centimeters and the area of the second rectangle is 50 square centimeters. Together there are 72 + 50 = 122 square centimeters.

That is how u find a irregular figure..hope this help u

3 0

3 years ago