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erik [133]
3 years ago
5

Solve 4 cos2x-3 = 0 for all real values of x.

Mathematics
1 answer:
vichka [17]3 years ago
3 0

4 cos² x - 3 = 0

4 cos² x = 3

cos² x = 3/4

cos x = ±(√3)/2

Fixing the squared cosine doesn't discriminate among quadrants.  There's one in every quadrant

cos x = ± cos(π/6)

Let's do plus first.  In general, cos x = cos a has solutions x = ±a + 2πk integer k

cos x = cos(π/6)

x = ±π/6 + 2πk

Minus next.

cos x = -cos(π/6)

cos x = cos(π - π/6)

cos x = cos(5π/6)

x = ±5π/6 + 2πk

We'll write all our solutions as

x = { -5π/6, -π/6, π/6, 5π/6 } + 2πk integer k

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jamie borrowed $31,000 to put towards a down payment for a home. Jamie plans to repay the loan in 7 years. The bank offered a 4.
erastova [34]

Answer:

56,691.00 which would be 21 payments at 4.1 % compounded quarterly.

84 months in 7 years

÷ 4

= 21

21

×4.1 =

26,691 +

31,000 =

56,691

7 0
3 years ago
Find the coordinates of the point 7/10 of the way from A to B
OverLord2011 [107]

Answer:

  (6.8, 1.3)

Step-by-step explanation:

<u>Given</u>:

  A(-3, -5), B(11, 4)

<u>Find</u>:

  P such that AP/AB = 7/10

<u>Solution</u>:

Using the desired relation, we have ...

  (P -A)/(B -A) = 7/10

  10(P -A) = 7(B -A) . . . . . multiply by 10(B-A)

  10P = 7B +3A . . . . . . . . add 10A to both sides

  10P = 7(11, 4) +3(-3, -5) = (77 -9, 28 -15) = (68, 13)

  P = (68, 13)/10 = (6.8, 1.3)

The point 7/10 of the way from A to B is (6.8, 1.3).

7 0
3 years ago
Is this statement true or false? You calculate a finance charge by subtracting the cost of the purchase from the total payment,​
zalisa [80]

Answer:

True

Step-by-step explanation:

Brainliest?

7 0
3 years ago
Read 2 more answers
suppose A and B are complementary angles, m a =(3x+5) and m b= (2x-15). Solve for x and then find m a and m b
vlada-n [284]
2 angles are complementary if the sum of their measures is 90°.

For example  if m(P) = 41°  and m(Q)=49°, then P and Q are complementary.


Thus A and B are complementary means that m(A)=m(B)=90°:

(3x+5°) + (2x-15°) =90°

5x-10°=90°

5x=100°

x=20°



Thus 

m(A)=3x+5°=3* 20°+5°=60°+5°=65°

m(B)=2x-15°=2*20°-15°=40°-15°=25°
8 0
3 years ago
the surface area of the rectangular prism is given by formula S=2 (ab+bh+ah) find the value of h when a = 10, b=6 and s=440
lorasvet [3.4K]

Answer:

10

Step-by-step explanation:

440=2(60+6x+10x)

220=60+16x

160=16x

x=10

h=10

8 0
2 years ago
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