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3 years ago

For 0° ≤ x < 360°, what are the solutions to sin(StartFraction x Over 2 EndFraction) + cos(x) – 1 = 0 ?

Mathematics

1 answer:

nataly862011 [7]3 years ago

6 0

Answer:

{60°,300°}

Step-by-step explanation:

edge 2020

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What is the following product? (4x square root 5x^2 + 2^2 square root 6)^2

tangare [24]

The product is $104 x^{4}+16 \sqrt{30} x^{4}$

Explanation:

The given expression is $\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}$

We need to determine the product of the given expression.

First, we shall simplify the given expression.

Thus, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x \sqrt{5} x+2 x^{2} \sqrt{6}\right)^2$

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)^2$

Expanding the expression, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)$

Now, we shall apply FOIL, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}\right)^{2}+2 ( 2 x^{2} \sqrt{6})(4 x^{2} \sqrt{5})+\left(2 x^{2} \sqrt{6}\right)^{2}$

Simplifying the terms, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=16 \cdot 5 x^{4}+16 \sqrt{30} x^{4}+4 \cdot 6 x^{4}$

Multiplying, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=80 x^{4}+16 \sqrt{30} x^{4}+24 x^{4}$

Adding the like terms, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=104 x^{4}+16 \sqrt{30} x^{4}$

Thus, the product of the given expression is $104 x^{4}+16 \sqrt{30} x^{4}$

7 0

3 years ago

Which of the following statements shows the distributive property?

Papessa [141]

Answer:

$\displaystyle 5(4 - 2) = 20 - 10$

This is a genuine statement of you look real closely at it.

I am joyous to assist you anytime.

6 0

4 years ago

13. A sprinkler system can shoot water at a distance of 15 yards. It is set up to rotate

egoroff_w [7]

Answer:

about two feet

Step-by-step explanation:

4 0

4 years ago

Divide 7/15 by 3/5 A. 7/9 B. 75/21 C. 21/75 D. 7/25

hodyreva [135]

7/15 ÷ 3/5 =
= 7/15 * 5/3 =
= 7/3 * 1/3 = (after simplifying)
= 7/9

Correct answer: A

Just keep in mind that dividing one fraction by another fraction is as much as multiplying the same fraction by an inverse of the second one.

4 0

3 years ago

Read 2 more answers

a sequence of numbers is given by 25,30,35..............,300. find the number of terms in the sequence

Lorico [155]

Answer:

Step-by-step explanation:

clearly, the sequence is built by adding 5 for every new term.

so, an = an-1 + 5

a1 = 25 (the starting value)

a2 = a1 + 5 = 25 + 5 = 30

a3 = a2 + 5 = a1 + 5 + 5 = a1 + 2×5 = 25 + 10 = 35

...

an = an-1 + 5 = a1 + (n-1)×5

now, we know, the last term is 300.

when we determine for which n we get an = 300, we know that n is the number of terms in the sequence.

so,

300 = a1 + (n-1)×5 = 25 + 5n - 5 = 20 + 5n

280 = 5n

n = 56

a56 = 300

so, we have 56 terms in this sequence

6 0

3 years ago

Read 2 more answers