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3 years ago

Use the cosine sum and difference identities to find the exact value. COS(5pi/12)

2 answers:

8 0

5π/12 = (5 · 180°) : 12 = 75°
cos 75° = cos ( 45° + 30° )= cos 45° cos 30° - sin 45° sin 30° =
=√2/2 * √3/2 - √2/2 * 1/2 = $\frac{ \sqrt{6} }{4} - \frac{ \sqrt{2} }{4}= \frac{ \sqrt{6} - \sqrt{2} }{4}$
=(2.4495 - 1.4142): 4 = 0.258825

Nina [5.8K]3 years ago

5 0

Square root of 2(square root of 3-1)/4. Honestly apex is trying to mess you up lol

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200 σ j=1 2j( j 3) describe the steps to evaluate the summation. what is the sum?

ziro4ka [17]

The sum of the equation is = 5494000.

<h3>What does summation mean in math?</h3>

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

<h3>Briefing:</h3>

Distribute 2j to (j+3).

Rewrite the summation as the sum of two individual summations.

Evaluate each summation using properties or formulas from the lesson.

The lower index is 1, so any properties can be used.

The sum is 5,494,000.

<h3>Calculation according to the statement:</h3>

$\sum_{j=1}^{200} 2 j(j+3)$

simplifying them we get:

$\sum_{j=1}^{200} 2 j^{2}+6 j$

Split the summation into smaller summations that fit the summation rules.

$\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j$

$\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}$

The formula for the summation of a polynomial with degree 2

is:

$\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}$

Substitute the values into the formula and make sure to multiply by the front term.

$(2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$$

we get: 5373400

Evaluating same as above : $6 \sum_{j=1}^{200} j$

we get: 120600

Add the results of the summations.

5373400 + 120600

= 5494000

The sum of the equation is = 5494000.

To know more about summations visit:

brainly.com/question/16679150

#SPJ4

6 0

2 years ago

+8+-9+-2 on a number line

Zarrin [17]

Hi there! I can help you! 8 + (-9) + (-2). When adding negative integers, you have to subtract. 8 - 9 is -1 and -1 - 2 is -3. You would have to start at 8 and go to the left 11 times to land on -3. The sum to the problem is -3.

3 0

3 years ago

I’m currently working on my quadrilaterals unit (specifically with trapezoids & kites) and I need major help on a lot of the

allochka39001 [22]

Answer: 29.2

Step-by-step explanation:

The lengths of the two longer legs are both $\sqrt{8^2 + 4^2}=\sqrt{80}$

The lengths of the two shorter legs are both $\sqrt{4^2+4^{2}}=\sqrt{32}$

So $P=2\sqrt{80}+2\sqrt{32} \approx 29.2$

5 0

2 years ago

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Simplify this expression, and leave your answer in scientific notation: 4 x 10^6/2 x 10^8

Anna007 [38]

Answer:

Step-by-step explanation:

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3 years ago

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How are addition properties and subtraction rules helpful when solving problems

snow_lady [41]

For the sum we have the following properties:
The properties are commutative, asosiative, distributive and neutral element.

Commutative property: When two numbers are added, the result is the same regardless of the order of the addends.

Associative property: When three or more numbers are added, the result is the same regardless of the order in which the addends are added.

Neutral element: The sum of any number and zero is equal to the original number.

Distributive property: The sum of two numbers multiplied by a third number is equal to the sum of each summand multiplied by the third number.<span><span>

</span><span>For subtraction we have:

</span><span> The arithmetic operation of the subtraction (subtraction) is indicated by the minus sign (-) and is the opposite, or inverse, operation of the addition. </span><span>That is, it is an arithmetic operation that serves to find the difference between two numbers.
</span><span>
In subtraction A - B = D
</span><span>A is the minuendo
</span><span>B is the substraendo
</span><span>D is the difference

</span><span>Answer:
</span><span>The properties of addition and subtraction serve to rewrite and simplify calculations.</span></span>

8 0

3 years ago

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