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3 years ago

Mrs. Parker cut a watermelon into fourths. She gave 1 piece to her 3 children to share equally. How much will each child eat?

Mathematics

1 answer:

beks73 [17]3 years ago

6 0

Answer: ¹/₁₂ watermelon

Step-by-step explanation:

Mrs. Parker had a watermelon which she cut into fourths and then gave one of those pieces to her children.

This means that she gave them 1/4 of a watermelon.

There are 3 children and they are to share this piece equally:

= 1/4 ÷ 3

= 1/4 * 1/3

= 1/12

<em>Each child will get 1/12 of the water melon. </em>

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Find cot and cos <br> If sec = -3 and sin 0 > 0

Natali5045456 [20]

Answer:

Second answer

Step-by-step explanation:

We are given $\displaystyle \large{\sec \theta = -3}$ and $\displaystyle \large{\sin \theta > 0}$ . What we have to find are $\displaystyle \large{\cot \theta}$ and $\displaystyle \large{\cos \theta}$ .

First, convert $\displaystyle \large{\sec \theta}$ to $\displaystyle \large{\frac{1}{\cos \theta}}$ via trigonometric identity. That gives us a new equation in form of $\displaystyle \large{\cos \theta}$ :

$\displaystyle \large{\frac{1}{\cos \theta} = -3}$

Multiply $\displaystyle \large{\cos \theta}$ both sides to get rid of the denominator.

$\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}$

Then divide both sides by -3 to get $\displaystyle \large{\cos \theta}$ .

Hence, $\displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}$

__________________________________________________________

Next, to find $\displaystyle \large{\cot \theta}$ , convert it to $\displaystyle \large{\frac{1}{\tan \theta}}$ via trigonometric identity. Then we have to convert $\displaystyle \large{\tan \theta}$ to $\displaystyle \large{\frac{\sin \theta}{\cos \theta}}$ via another trigonometric identity. That gives us:

$\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}$

It seems that we do not know what $\displaystyle \large{\sin \theta}$ is but we can find it by using the identity $\displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}$ for $\displaystyle \large{\sin \theta > 0}$ .

From $\displaystyle \large{\cos \theta = -\frac{1}{3}}$ then $\displaystyle \large{\cos ^2 \theta = \frac{1}{9}}$ .

Therefore:

$\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}$

Then use the surd property to evaluate the square root.

Hence, $\displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}$

Now that we know what $\displaystyle \large{\sin \theta}$ is. We can evaluate $\displaystyle \large{\frac{\cos \theta}{\sin \theta}}$ which is another form or identity of $\displaystyle \large{\cot \theta}$ .

From the boxed values of $\displaystyle \large{\cos \theta}$ and $\displaystyle \large{\sin \theta}$ :-

$\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}$

Then rationalize the value by multiplying both numerator and denominator with the denominator.

$\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}$

Hence, $\displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}$

Therefore, the second choice is the answer.

__________________________________________________________

Summary

Trigonometric Identity

$\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}$

Surd Property

$\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}$

Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.

5 0

2 years ago

Please please please help!! i’ll mark the brainliest and give 15 points!!!!

Korolek [52]

9514 1404 393

Answer:

-108

Step-by-step explanation:

About the easiest way to do this for small values of n is to compute each of the terms using the given recurrence relation.

$a_1=4\\\\a_2=-3a_1=-3(4)=-12\\\\a_3=-3a_2=-3(-12)=36\\\\a_4=-3a_3=-3(36)=-108\\\\\boxed{a_4=-108}$

_____

<em>Alternate solution</em>

You recognize that the recurrence relation describes a geometric sequence with a first term of 4 and a common ratio of -3. The n-th term of a geometric sequence is ...

$a_n=a_1\cdot r^{n-1} \qquad\text{for first term $a_1$ and common ratio $r$}$

Then the 4th term will be ...

$a_4=4\cdot(-3)^{4-1}=4\cdot(-27)=-108$

3 0

3 years ago

· Expand and simplify (x - 2)(x + 7)

lisov135 [29]

Answer:

Expand:

x^2+7x-2x-14

Answer:

x^2+5x-14

Step-by-step explanation:

3 0

3 years ago

Determine a, given that A = 63°, C = 49°, and c = 3. Round answers to the nearest whole number. Do not use a decimal point or ex

GREYUIT [131]

The value of a given that A = 63°, C = 49°, and c = 3 is 4 units

<h3>How to determine the value of a?</h3>

The given parameters are:

A = 63°, C = 49°, and c = 3

Using the law of sines, we have:

a/sin(A) = c/sin(C)

So, we have:

a/sin(63) = 3/sin(49)

Multiply both sides by sin(63)

a = sin(63) * 3/sin(49)

Evaluate the product

a = 4

Hence, the value of a is 4 units