If f(x)=2x^2sqrt(x-2), complete the following statement f(6)

using 3.14 for pi

area = pi x r^2

 since he can see 12 miles in any direction 12 would be the radius

 so 3.14 x 12^2 = 452.16 square miles

 round the answer as needed.

The equation that represents the number of hours the mountaineer climbed is t = 1000/V1 + 2600(V1 - 5).

Based on the information given, V1 = 1000 and V2 = 2V1 - 10.

The time taken will be:

= 1000/V1 + 5000/V2

Well substitute the equations. This will be:

t = 1000/V1 + 5000//(2V1 - 10)

t = 1000/V1 + 5000/2(V1 - 5)

t = 1000/V1 + 2600(V1 - 5).

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Answer:

Solve the following inequality: 2(x + 1) – (–x + 5) ≤ –18. A. x ≤ –9 B. x ≤ –20 C. x ≤ –37 D. x ≤ –5

Step-by-step explanation:

2 (x + 1) - (-x + 5) ≤ -18

2x + 2 + x - 5 ≤ - 18

3x - 3 ≤ - 18

3x ≤ - 15

x ≤ - 15/3 ≤ - 5

The answer is: D. x ≤ - 5

Final answer:

To eliminate the parameter 't' from the equations x = 5 cos t and y = 5 sin t, use the Pythagorean identity which leads to the non-parametric equation of a circle: x^2 + y^2 = 25.

Explanation:

To eliminate the parameter 't' from the parametric equations x = 5 cos t, y = 5 sin t, we can use the Pythagorean identity sin^2(t) + cos^2(t) = 1. Plugging in the given expressions for x and y:

(x/5) = cos(t)

(y/5) = sin(t)

We can square both sides of these equations and then add them together:

(x/5)^2 + (y/5)^2 = cos^2(t) + sin^2(t)

As cos^2(t) + sin^2(t) equals 1, the equation simplifies to:

(x/5)^2 + (y/5)^2 = 1

Thus, the eliminated parameter equation representing the same curve without the parameter 't' is:

x^2 + y^2 = 25

This is the equation of a circle with a radius of 5, centered at the origin.

Using logarithmic function concepts, it is found that for values of b > 1, [tex]f(x) = \log_b{x}[/tex] will be an increasing function.

A logarithmic function is modeled by:

[tex]f(x) = \log_b{x}[/tex]

The coefficient b determines the behavior of the function, as follows:

Hence, for values of b > 1, [tex]f(x) = \log_b{x}[/tex] will be an increasing function.

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The final amount is = $ 959.779

Compound interest is when you earn a hobby on both the cash we've got stored and the hobby we earn.

calculation:-

principal amount = $765.13

rate if interest = 12%

for 1st year:-

interest amount= $765.13*12/100

                            = $ 91.8156

final amount = $765.13 + $ 91.8156

                     = $ 856.9456

for 2nd year:-

principal amount = $ 856.9456

       12% interest on $ 856.9456 = $ 102.833472

final amount = $ 856.9456+$ 102.833472

                      = $ 959.779 answer

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The value of cosx if "tanx cscx = 2" is 1/2. The correct option is D)1/2

From the question, we are to determine the value of cosx

From the given information,

tanx cscx=2

Recall that,

[tex]tan(x )= \frac{sin (x)}{cos(x)}[/tex]

and

[tex]csc(x) = \frac{1}{sin(x)}[/tex]

Then,

Substitute these values into the given equation

tanx cscx = 2 becomes

[tex]\frac{sin (x)}{cos(x)} \times \frac{1}{sin(x)} = 2[/tex]

[tex]\frac{1}{cos(x)} = 2[/tex]

∴ [tex]cos(x) = \frac{1}{2}[/tex]

Hence, the value of cosx if "tanx cscx = 2" is 1/2. The correct option is D)1/2

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Answer:20 !

Step-by-step explanation:

To find what percent 187.05 is of 645, one can use the following formula:

[tex]\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \][/tex]

In this case, the Part is 187.05 and the Whole is 645. Plugging these values into the formula gives:

[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 \][/tex]

Now, calculate the fraction:

[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 = \left( 0.29155 \right) \times 100 \][/tex]

[tex]\[ \text{Percentage} = 29.155 \][/tex]

Therefore, 187.05 is approximately 29.155% of 645. To express this as a fraction, one can write:

[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \approx 29.155\% \][/tex]

To get the exact fraction, we can simplify:

[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \times \frac{20}{20} = \frac{374100}{12900} \][/tex]

Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 300, we get:

[tex]\[ \text{Percentage} = \frac{374100 \div 300}{12900 \div 300} = \frac{1247}{430} \][/tex]

So, the exact fraction representing the percentage is:

[tex]\[ \text{Percentage} = \frac{1247}{430} \times 100 \][/tex]

[tex]\[ \text{Percentage} = \frac{1247}{4.3} \][/tex]

[tex]\[ \text{Percentage} = 29.00 \% \][/tex]

Thus, 187.05 is exactly 29% of 645.

Let us say that the procedure of completely filling up the pool with water is called “1 job”. Therefore the rates of the equipment in doing the job would be:

Rate of handheld hose = 1 job / 8 minutes                  ---> 1

Rate of lawn sprinkler = r                                             ---> 2

Rate of the two combines = 1 job/ 5 minutes               ---> 3

So we are to find the equation to use, in this case, we simply have to add equations 1 and 2 to get 3:

1 / 8 + r = 1 / 5

Multiplying both sides by 5:

(5 / 8) + 5 r = 1                                                               ---> ANSWER

Answer:

5/8 + 5r = 1

Step-by-step explanation:

Right on edge!

Answer:

4.6

Step-by-step explanation:

Allow me to revise your question and hope it will be the same as the original one:

In a certain town 22% of voters favor a given ballot measure for groups of 21 voters find the variance for the number who favor the measure

a. 1.9

b. 13

c. 4.6

d. 3.6

Here is my answer:

Given:

So the variance is: 21*0.22 = 4.6

We choose B

To find the volume of the solid enclosed by the given cylinder and planes, you convert to cylindrical coordinates. Then, you set up a triple integral with respect to these coordinates as ∫∫∫ dz dr dθ where the bounds of integration are 0<=θ<=2π, 0<=r<=3, and 2<=z<=14-r.

The volume of the solid can be found using a triple integral in cylindrical coordinates. First, we need to identify the boundaries of the solid. From the cylinder equation, we see that x² + y² = 9, which in cylindrical coordinates converts to r^2 = 9, so 0<=r<=3. Then, from the plane equations y + z = 14 and z=2, we can determine that in cylindrical coordinates, 2<=z<=14-r.

Therefore, the volume V can be found by:

V = ∫∫∫ dz dr dθ

with bounds for integration being 0<=θ<=2π, 0<=r<=3, and 2<=z<=14-r.

Running this triple integral will provide the volume of the solid.

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42 x 61 = 2562

2562/215 = 11.92

 12 total bags are needed