Verify the identity Cotx/tanx+cotx = 1-sin^2x

Answers

Answer 1

Answer: $\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \n\n\n tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\n\n -------------------------------\n\n \cfrac{cot(x)}{tan(x)+cot(x)}=1-sin^2(x) \n\n\n \textit{doing the left-side}\implies \cfrac{(cos(x))/(sin(x))}{(sin(x))/(cos(x))+(cos(x))/(sin(x))}\implies \cfrac{(cos(x))/(sin(x))}{(sin^2(x)+cos^2(x))/(cos(x)sin(x))}$

$\bf \cfrac{(cos(x))/(sin(x))}{(1)/(cos(x)sin(x))}\implies \cfrac{cos(x)}{\underline{sin(x)}}\cdot \cfrac{cos(x)\underline{sin(x)}}{1}\implies cos^2(x)\implies 1-sin^2(x)$

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Find the volume of the cone below.

Answers

Answer:

$V =(1)/(3) \pi r^2 h$

For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:

$V=(1)/(3) \pi (7cm)^2 (11cm)= (1)/(3) \pi (49cm^2) (11 cm)=(539)/(3) \pi cm^3$

And the best option would be:

$V = (539)/(3) \pi cm^3$

Step-by-step explanation:

For this case we know that the volume of the cone is given by:

$V =(1)/(3) \pi r^2 h$

For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:

$V=(1)/(3) \pi (7cm)^2 (11cm)= (1)/(3) \pi (49cm^2) (11 cm)=(539)/(3) \pi cm^3$

And the best option would be:

$V = (539)/(3) \pi cm^3$

Does it seem plausible that employment has a normal distribution for each gender

Answers

yes it is reasonable that employment has a normal distribution for each gender

How many 3/4 inch strips for caulk to cover 10 1/2 inches

Answers

The Number of 3/4 inch strips required to cover 10 1/2 inches of caulk will be 14

The total inches of caulk to be covered = 10 1/2 inches

The fraction of inch strip to be used = 3/4 inches

To obtain the number of 3/4 inch strop required ;

We divide the total inches of caulk by 3/4

Hence,

10 1/2 ÷ 3/4

21/2 ÷ 3/4

Change the sign to × and take the reciprocal of 3/4 ;

21/2 × 4/3

(21 × 4) / (2 × 3) = 84 / 6

84 / 6 = 14

Hence, the number of 3/4 inch strip required is 14

Learn more : brainly.com/question/2610134

Answer:

Step-by-step explanation:

So let's think smart. If you look at the image I made a diagram. The 3 squares I colored in represent 3/4. It takes 14 3/4 strips to cover 10 1/2 inches.

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