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3 years ago

15% + 6% * 5 = Please answer the equation correctly

Mathematics

2 answers:

aleksley [76]3 years ago

5 0

Answer:

0.45

Step-by-step explanation:

All you do is simplify

PLZ MARK BRAINLIEST

Ksenya-84 [330]3 years ago

4 0

Remember:

-Brackets
-indices
-division
-multiplication
-addition
-subtraction

6 * 5 = 30

30 + 15 =45%

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2cos5xcos3x+sinx=cos8x

harkovskaia [24]

It looks like your equation (it's not an identity) is

2 cos(5x) cos(3x) + sin(x) = cos(8x)

Recall that

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==> 2 cos(x) cos(y) = cos(x + y) + cos(x - y)

so that

2 cos(5x) cos(3x) = cos(8x) + cos(2x)

Then the equation simplifies to

cos(8x) + cos(2x) + sin(x) = cos(8x)

cos(2x) + sin(x) = 0

Also recall that

cos(2x) = 1 - 2 sin²(x)

so the equation is quadratic in sin(x) and can be factorized:

1 - 2 sin²(x) + sin(x) = 0

2 sin²(x) - sin(x) - 1 = 0

(2 sin(x) + 1) (sin(x) - 1) = 0

Solve for x :

2 sin(x) + 1 = 0 or sin(x) - 1 = 0

sin(x) = -1/2 or sin(x) = 1

[x = arcsin(-1/2) + 2nπ or x = π - arcsin(-1/2) + 2nπ] or x = arcsin(1) + 2nπ

(where n is any integer)

x = -π/6 + 2nπ or x = -5π/6 + 2nπ or x = π/2 + 2nπ

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3 years ago

Pablo's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Pablo $5.50 per pound, and type

alexandr402 [8]

Answer:

We know blend A costs 5.50 and blend B costs 4.30. We know that Pablo made 153 pounds of coffee this month. Let's let A=amount of blend A used and B=amount of blend B used. Since he made 153lbs coffee, we know that

A+B=153.

But he spent 756.30. The total amount he spent on a blend of coffee is the price * amount used. So he spent 5.50*A on blend A and 4.30*B on B, so in total, he spent 5.50*A+4.30*B in coffee. But this must add to 756.30! So

5.5A+4.3B = 756.30

Now we have two equations:

A+B = 153

5.5A + 4.3B = 756.30

We need to solve for B. I hate decimals so let's get rid of them in the second equation by multiplying both sides of the equation by 100 (which simply moves the decimals on everything two to the right). So now we have

A+B = 153

550A + 430 B = 75630

Now let's multiply the first equation by 550 (so we can eventually get rid of pesky A). So multiply the left and right side of the first equation by 550, so we have

550A + 550B = 84150

550A + 430B = 75630

Now subtract the second equation from the first, notice that since both have 550A, they cancel, so we obtain

120B = 8520

Now divide by 120 into both sides to solve for B, we get

B= 8520/120 = 71

So Pablo used 71lbs of blend B.

Step-by-step explanation:

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