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3 years ago

Find the surface area of a cylinder with a helght of 6 in and a base diameter of 8 in.

Mathematics

1 answer:

Diano4ka-milaya [45]3 years ago

4 0

Answer:

we know surface area=pi*d*h=3.14*8*5=125.6sqm

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Please help me!!!!!

Bas_tet [7]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)

Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)

Use the Unit Circle to evaluate tan (π/4) = 1

Use Pythagorean Identity: cos²A + sin²A = 1

<u>Proof LHS → RHS</u>

$\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}$

$\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}$

$\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}$

$\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}$

$\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}$

$\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}$

$\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}$

$\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}$

= cos A

LHS = RHS: cos A = cos A $\checkmark$

4 0

3 years ago

Mitch is buying candy bars for his friends. He wants to give 2 bars to each friend, and he wants to have 10 spare bars. He can a

gregori [183]

Answer:

A. 2f + 10 = 28

Step-by-step explanation:

28 candy bars.

He wants 10.

28 - 10.

18 candy bars.

He gives each friend 2.

18 divided by 2.

He can treat 9 friends.

Step 1: Subtract 10 from both sides.

2f+10=28

which would take away the 10 and subtract 10 from 28. (That would be Jack's bars.)

2f = 28.

Step 2: Divide by 2 on both sides.

2f = 28

which would cancel out the 2f. And Whatever is done to the left is done to the right, meaning you would divide 28 by 2 aswell. (Dividing up the candy bars among his friends).

f = 9

6 0

3 years ago

The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls

kumpel [21]

Answer:

standard error = 1.63

Step-by-step explanation:

To calculate the standard error we need to know the standard deviation (σ) and the sample size (n) (see the attached formula).

To obtain the standard deviation we use the given sample variance of 77.4 years:

σ²= variance

Therefore:

σ = √77.4 = 8.8

Now we can calcuate the estimated standard error:

standard error = σ /√n = 8.8/√29 = 1.63

The standard error gives us an estimation about how far the mean of the sample is from the mean of the entire population, and in this case is 1.63.

7 0

3 years ago

Scientists measure a bacteria sample in a petri dish

zimovet [89]

Answer:

to grow bacterial cultures

4 0

2 years ago

Laura walks 3/5 mile to scool each day isaiahs walk to school is 3 times as long as laura how far dose isaiah walk to school eac

KonstantinChe [14]

Isaiah walks 9/5 or 1 and 1/5 miles to school

7 0

3 years ago