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Arte-miy333 [17]
3 years ago
5

Simplify the expression and find its value: (2x+0.5)^2–(2x–0.5)^2 for x=−3.5

Mathematics
1 answer:
lys-0071 [83]3 years ago
6 0
The answer is -70.25
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How do you do these questions?
Lady bird [3.3K]

Answer:

(e) csc x − cot x − ln(1 + cos x) + C

(c) 0

Step-by-step explanation:

(e) ∫ (1 + sin x) / (1 + cos x) dx

Split the integral.

∫ 1 / (1 + cos x) dx + ∫ sin x / (1 + cos x) dx

Multiply top and bottom of first integral by the conjugate, 1 − cos x.

∫ (1 − cos x) / (1 − cos²x) dx + ∫ sin x / (1 + cos x) dx

Pythagorean identity.

∫ (1 − cos x) / (sin²x) dx + ∫ sin x / (1 + cos x) dx

Divide.

∫ (csc²x − cot x csc x) dx + ∫ sin x / (1 + cos x) dx

Integrate.

csc x − cot x − ln(1 + cos x) + C

(c) ∫₋₇⁷ erf(x) dx

= ∫₋₇⁰ erf(x) dx + ∫₀⁷ erf(x) dx

The error function is odd (erf(-x) = -erf(x)), so:

= -∫₀⁷ erf(x) dx + ∫₀⁷ erf(x) dx

= 0

7 0
3 years ago
A cylinder has a height of 23 m and a volume of 18,488 m³. What is the radius of the cylinder? Round your answer to the nearest
diamong [38]
The radius to this cylinder is 16.
3 0
3 years ago
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A student is making cookies for a bake sale. He sells 8 snickerdoodles and 12 chocolate chip
lions [1.4K]

Answer:

Snickerdoodles are 0.22$ each and chocolate chip are 0.43$ each

Step-by-step explanation:

using the information in the problem, you can make 2 separate equations: 8x+12y=6.92 and 5x+5y=3.25, let x= the cost of a snickerdoodle and y= the cost of a chocolate chip cookie.

With the 2 equations, we can isolate the y variable of the first equation and simplify which will give us y= -2/3x +6.92/12.

You can now take that equation and plug it into equation number 2:

5x+5(-2/3x + 6.92/12)=3.25.

solve that equation by multiplying 5 through the brackets: 5x-10/3x+34.6/12=3.25

add common terms: 5/3x=4.4/12

find the value of x, you will get x=0.22

plug the value of x (0.22) into one of your equations and solve for the y-value

8 0
3 years ago
Please help!! Greatly appreciated <3
Margaret [11]

Answer:

30?

Step-by-step explanation:

divide 20 by 8 and then times the answer by 12

7 0
3 years ago
Write <br> 108<br> 13<br> as a mixed number.
gayaneshka [121]

Answer:

8 4/13 Is the Correct Answer!

Step-by-step explanation:

Numerator. This is the number above the fraction line. For 108/13, the numerator is 108.

Denominator. This is the number below the fraction line. For 108/13, the denominator is 13.

Improper fraction. This is a fraction where the numerator is greater than the denominator.

Mixed number. This is a way of expressing an improper fraction by simplifying it to whole units and a smaller overall fraction. It's an integer (whole number) and a proper fraction.

Now let's go through the steps needed to convert 108/13 to a mixed number.

Step 1: Find the whole number

We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

108/13= 8.3076923076923 = 8

Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.

Step 2: Get the new numerator

To work this out we'll use the whole number we calculated in step one (8) and multiply it by the original denominator (13). The result of that multiplication is then subtracted from the original numerator:

108 - (13 x 8) = 4

Step 3: Our mixed fraction

We've now simplified 108/13 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

8  

4

13

Step 4: Simplifying our fraction

In this case, our fraction (4/13) can be simplified down further. In order to do that, we need to calculate the GCF (greatest common factor) of those two numbers. You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 4 and 13 is 1.

xXxAnimexXx

6 0
3 years ago
Read 2 more answers
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