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3 years ago

How do you take the antiderivative of (sinxcosx)^2?

1 answer:

8 0

∫(sinx cosx)^2dx = ∫(1/2sin 2x)^2 dx = 1/4∫sin^2 2x dx = 1/4∫1/2(1 - cos 4x)dx = 1/8∫(1 - cos 4x) dx = 1/8[x - sin 4x / 4] + c = 1/32(4x - sin 4x) + c

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A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced.

zzz [600]

Answer:

$CI=(66.54,78.46)$

Step-by-step explanation:

Given : A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed.

To find : A 99% confidence interval for the mean yield when the new catalyst is used ?

Solution :

Let X be the yield of the batches.

We have given, n=10 , $\bar{X}=72.5\%$ , s=5.8%

Since the size of the sample is small.

We will use the student's t statistic to construct a 995 confidence interval.

$\bar X\pm t_{n-1,\frac{\alpha}{2}}\frac{s}{\sqrt n}$

From the t-table with 9 degree of freedom for $\frac{\alpha}{2}=0.005$

$t_{n-1,\frac{\alpha}{2}}=t_{9,0.005}$

$t_{n-1,\frac{\alpha}{2}}=3.250$

The 99% confidence interval is given by,

$CI=72.5 \pm 3.25\frac{5.8}{\sqrt{10}}$

$CI=72.5 \pm 5.96$

$CI=(72.5+5.96),(72.5-5.96)$

$CI=(66.54,78.46)$

8 0

3 years ago

This shows a part of a multiplication table. Find the missing numbers. Explain how you found the numbers

DedPeter [7]

Well the first part of the table is 7 cause 7x5- 35 x 6 is 42 x 7 49. Second part of the table is 8 x 5 40 x6 is 48 x 7 is 56. once you know this it is easy just to common factor it or just simply add 5 6 or 7 to the numbers already given

5 0

3 years ago

Read 2 more answers

Anyone willing to help?? thank u to whoever does help :))

blsea [12.9K]

Answer and Step-by-step explanation:

Yes, the three side lengths could form a triangle.

To find out if the sides can form a triangle, you take the lowest side lengths and add them together. If they are greater than the longest side, then they can form a triangle. If it is equal or less than the longest side, then it CAN NOT form a triangle.

7.8 + 10.4 > 13

18.2 > 13

So, the answer is Yes.

#teamtrees #PAW (Plant And Water)

4 0

2 years ago

Read 2 more answers

If sin theta = -0.7660, which of the following represents an approximate value of tan theta, for 180 degrees < theta < 270

Elis [28]

We have that
sin ∅=-0.7660

the sin ∅ is negative
so
∅ belong to the III or IV quadrant
but
180°< ∅ < 270°
hence
∅ belong to the III quadrant
sin ∅=-0.7660
sin² ∅+cos² ∅=1
cos² ∅=1-sin² ∅------> cos² ∅=1-(0.7660)²-----> 0.4132
cos ∅=√0.4132-----> cos ∅=0.6428
the value of cos ∅ is negative-------> III quadrant
cos ∅=-0.6428

tan ∅=sin ∅/ cos ∅----> tan ∅=-0.7660/-0.6428----> tan ∅=1.1917

the answer is
tan ∅ is 1.1917

4 0

3 years ago

Can someone help??? Also if it wouldn’t bother can you also state how you got the answer. I don’t quite understand this concept.

Bond [772]

2/3 + x=4

x= 4 - 2/3

= (((4)(3) -2))/3

= (12-2)/3

= 10/3

7 0

3 years ago