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2 years ago

Angles A and B are located in the first quadrant such that sinA= 7/25 and cosB = 5/13. Determine the exact value for cos (A-B).

Mathematics

1 answer:

fomenos2 years ago

8 0

Answer:

204/325

Step-by-step explanation:

You can work this a couple of ways. We expect you are probably expected to use trig identities.

cos(A) = √(1 -sin²(A)) = 24/25

sin(B) = √(1 -cos²(B)) = 12/13

cos(A -B) = cos(A)cos(B) +sin(A)sin(B) = (24/25)(5/13) +(7/25)(12/13)

= (24·5 +7·12)/325

cos(A -B) = 204/325

The other way to work this is using inverse trig functions. It is necessary to carry the full calculator precision if you want an exact answer.

cos(A -B) = cos(arcsin(7/25) -arccos(5/13)) = cos(16.2602° -67.3801°)

= cos(-51.1199°) ≈ 0.62769230 . . . . (last 6 digits repeating)

The denominators of 25 and 13 suggest that the desired fraction will have a denominator of 25·13 = 325, so we can multiply this value by 325 to see what we get.

325·cos(A-B) = 204

so, the exact value is ...

cos(A -B) = 204/325

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castortr0y [4]

Step-by-step explanation: To solve this absolute value inequality,

our goal is to get the absolute value by itself on one side of the inequality.

So start by adding 2 to both sides and we have 4|x + 5| ≤ 12.

Now divide both sides by 3 and we have |x + 5| ≤ 3.

Now the the absolute value is isolated, we can split this up.

The first inequality will look exactly like the one

we have right now except for the absolute value.

For the second one, we flip the sign and change the 3 to a negative.

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Solving each inequality from here, we have x ≤ -2 or x ≥ -8.

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2 years ago

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You bike 1 mile the first day of your training, 1.3 miles the second day, 1.9 miles the third day, and 3.1 miles the fourth d

JulsSmile [24]

Answer:

19.9 miles

Step-by-step explanation:

In this problem we have:

$d_1=1 mi$ is the distance travelled during the 1st day

$d_2=1.3 mi$ is the distance travelled during the 2nd day

$d_3=1.9 mi$ is the distance travelled during the 3rd day

$d_4=3.1 mi$ is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

$d_2-d_1=0.3\\d_3-d_2=2\cdot 0.3 = 0.6\\d_4-d_3=2\cdot 0.6 = 1.2$

Which can be rewritten using the general formula:

$d_{n+1}-d_n=2(d_n-d_{n-1})$

This means that

$d_{n+1}=d_n+2(d_n-d_{n-1})$

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

$d_1=1\\d_2=1.3\\d_3=1.9\\d_4=3.1\\d_5=3.1+2\cdot 1.2=5.5\\d_6=5.5+2\cdot 2.4=10.3\\d_7=10.3+2\cdot 4.8=19.9 mi$

So, the distance travelled on the 7th day is 19.9 miles.

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3 years ago

If the radius of mars is about 13.7% of neptune's radius, what is the radius of neptune?

Marianna [84]

The volumetric mean radius of Mars is about 3389.5 km. We know that it's 13.7% of Neptune's mean radius, so we can write it down as:

3389.5 = 13.7% of x (where x is Neptune's radius)
3389.5 = 13.7% x
3389.5 = 137/1000x / * 1000 (both sides)
3389500 = 137x / ÷ 137 (both sides)
x = 24740.87591240876
x ≈ 24740.88

Answer: The mean radius of Neptune is about 24740.88 km.

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3 years ago

Which expression is equivalent to 3xy + 10xy - 5x + 2x - 2yx? A) 15xy + 7x Eliminate B) 13xy - 7x - 2yx C) -8xy D) -3x + 11xy

Vedmedyk [2.9K]

3xy + 10xy - 5x + 2x - 2yx

Add 3xy to 10xy

13xy - 5x + 2x - 2yx

Add -5x to 2x

Final Answer: B.) 13xy -3x - 2yx

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2 years ago

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Vadim26 [7]

Answer:

3V/b = h

Step-by-step explanation:

Step 1: Write equation

V = 1/3bh

Step 2: Multiply both sides by 3

3V = bh

Step 3: Divide both sides by b

3V/b = h

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