Please help please help please help

Answers

Answer 1

Answer:

Answer:

rules of algebra

A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement.

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Problem 5.Joseph is told to dissolve a medicine he has to take in 1 pint 4 ounces of water. He has a
measuring cup marked in ounces. How many ounces of water should he pour?

Answers

Answer:

The amount of water he should pour in ounces(that is the only units the cup measures) is 16 + 4 = 20 ounces

Step-by-step explanation:

He is told to dissolve a medicine he has in 1 pint 4 ounces of water . He has a measuring cup marked in ounces .This means he can only measure the water quantity in ounces.

He definitely have to convert the pints to ounces.

1 pint = 16 ounces

Recall he has to dissolve the medicine in 1 pint 4 ounces of water.

Since 1 pint is equals to 16 ounces therefore, 16 ounces + 4 ounces = 20 ounces.

The amount of water he should pour in ounces(that is the only units the cup measures) is 16 + 4 = 20 ounces

What is 6=- x/8
Plz help

Answers

Answer:

1 .Multiply both sides by 88.

6\times 8=-x6×8=−x

2 .Simplify 6\times 86×8 to 4848.

48=-x48=−x

3. Multiply both sides by -1−1.

-48=x−48=x

4. x=−48

Step-by-step explanation:

Evaluate ∫C ysin(z)ds, where C is the circular helix given by the equations x = cos(t), y = sin(t), z = t, 0 ≤ t ≤ 2π. SOLUTION The formula for a line integral in space gives the following. ∫y sin(z)ds = sin2(t) dt = (sin(t))2√ (cos(t))2 + (sin(t))2 + 1dt = 1 2 (1 - cos(2t))dt = √2 2 =

Answers

The line integral is

$\displaystyle\int_Cy\sin z\,\mathrm ds=\int_0^(2\pi)y(t)\sin z(t)\,\sqrt{\left((\mathrm dx)/(\mathrm dt)\right)^2+\left((\mathrm dy)/(\mathrm dt)\right)^2+\left((\mathrm dz)/(\mathrm dt)\right)^2}\,\mathrm dt$

We have

$x=\cos t\implies(\mathrm dx)/(\mathrm dt)=-\sin t$

$y=\sin t\implies(\mathrm dy)/(\mathrm dt)=\cos t$

$z=t\implies(\mathrm dz)/(\mathrm dt)=1$

so the integral reduces to

$\displaystyle\int_0^(2\pi)\sin^2t√((-\sin t)^2+\cos^2t+1^2)\,\mathrm dt=\frac{\sqrt2}2\int_0^(2\pi)(1-\cos2t)\,\mathrm dt=\boxed{\frac\pi{\sqrt2}}$

The line integral ∫C ysin(z) ds over the circular helix C, parametrized by x = cos(t), y = sin(t), z = t for 0 ≤ t ≤ 2π, evaluates to π√2.

To evaluate the line integral ∫C ysin(z) ds over the circular helix C given by x = cos(t), y = sin(t), z = t for 0 ≤ t ≤ 2π, we follow these steps:

1. Parameterize the curve: C is already parameterized as x = cos(t), y = sin(t), z = t.

2. Find the differential ds: ds = √(dx² + dy² + dz²) = √(sin²(t) + cos²(t) + 1)dt = √(1 + 1)dt = √2 dt.

3. Evaluate the integral: ∫C ysin(z) ds = ∫[0, 2π] sin(t) * sin(t) * √2 dt = ∫[0, 2π] sin²(t) * √2 dt.

Now, we'll integrate sin²(t) * √2 with respect to t:

∫ sin²(t) * √2 dt = (1/2) * ∫ (1 - cos(2t)) * √2 dt.

Using the power rule for integration, we get:

(1/2) * [(t - (1/2) * sin(2t)) * √2] | [0, 2π].

Plugging in the limits:

(1/2) * [(2π - (1/2) * sin(4π) - (0 - (1/2) * sin(0))) * √2].

Since sin(4π) = sin(0) = 0:

(1/2) * [(2π - 0 - 0) * √2] = π√2.

So, ∫C ysin(z) ds = π√2.

For more such questions on Line Integral :

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Solve for X
x+3 1/3=8 1/2

Answers

Answer:x= 31/6

Step-by-step explanation:

Solve for

by simplifying both sides of the equation, then isolating the variable.

Find the square root of 8-2√5

Answers

Answer:

The square root of 8 - 2√5 is

$\sqrt{4 + √(11) } \: - \sqrt{4 - √(11) }$

Step-by-step explanation:

To find the square root

8-2√5 must be in the form √a - √b where a > b

√ 8 - 2√5 = √a - √b

Square both sides

8 - 2√5 = (√a - √b)²

That's

8 - 2√5 = (a + b) - 2√ab

Since the two surd expressions are equal we can equate them

That's

8 = a + b ........ 1

a = 8 - b ........ 2

2√5 = 2√ab

Simplify

Divide both sides by 2

√5 = √ab

square both sides

We have

5 = ab ....... 3

Substitute a = 8 - b into equation 3

5 = ( 8 - b)b

5 = 8b - b²

b² - 8b + 5 = 0

After solving

b = 4 + √ 11 or 4 - √ 1

Since b is less than a

b = 4 - √11

a = 4 + √11

So the square root of 8 - 2√5 is

$\sqrt{4 + √(11) } \: - \sqrt{4 - √(11) }$

Hope this helps you.

Answer:

1.88

Step-by-step explanation:

8-2√5=3.527864045

square root of 3.527864045=1.87826090972

the question will probably want it to 2d.p (decimal places) which means the answer would be 1.88

A professor at a university wants to estimate the average number of hours of sleep the students get during exam week. The professor wants to find a sample mean that is within 4.266 hours of the true average for all college students at the university with 99% conconfidence. If the professor knows the standard deviation of the sleep times for all college students is 2.539, what sample size will need to be taken