Find the maximum and minimum values of the function g(theta) = 2theta - 4sin(theta) on the interval Big[0, pi 2 Bigg\

Hello!

\(\boxed{ \bf The~radius~of~the~sphere~is~6~mm.}\)

We know that:

V = \(\frac{4}{3}\)πr³

904.32 = \(\frac{4}{3}\)πr³

To figure out the radius, we have to undo the above. We can undo the fraction by multiplying by it's reciprocal:

\(\frac{3}{4}\) × \(\frac{904.32}{1}\) = \(\frac{4}{3}\)πr³ × \(\frac{3}{4}\)

678.24 =  πr³

Next, we're going to divide both sides by pi:

\(\frac{678.24}{\pi } = \frac{\pi r^{2} }{\pi }\)

215.90 = r³

To undo the, we must find the cube root of 215.90.

r = 6

Answer:

\(radius = 6mm\)

Step-by-step explanation:

Volume of a sphere.

Use this formula

\(v = \frac{4}{3} \pi {r}^{3} \)

Now solve for r

\(r = (3 \frac{v}{4\pi} ) ^{ \frac{1}{3} } \\ = (3 \times \frac{904.32}{4 \times \pi} ) ^{ \frac{1}{3} } \\ ≈

5.99899mm

\)

Answer:

19

Step-by-step explanation:

tan35=x/20

20tan35=x

x=14.0041507641942

x+5=19.0041507641942

The nearest foot is 19

The length of the wire used to make the cuboid is 36 meters.

To find the length of the wire used to make the cuboid, we need to calculate the perimeter of all the edges of the cuboid.

The cuboid has dimensions:

Length = 4m

Width = 2.5m

Height = 2.5m

Let's calculate the perimeter of each face of the cuboid and then sum them up to find the total length of the wire.

Face 1: Length x Width

Perimeter of face 1 = 2(Length + Width) = 2(4m + 2.5m) = 2(6.5m) = 13m

Face 2: Length x Height

Perimeter of face 2 = 2(Length + Height) = 2(4m + 2.5m) = 2(6.5m) = 13m

Face 3: Width x Height

Perimeter of face 3 = 2(Width + Height) = 2(2.5m + 2.5m) = 2(5m) = 10m

Now, let's sum up the perimeters of all three faces to find the total length of the wire:

Total wire length = Perimeter of face 1 + Perimeter of face 2 + Perimeter of face 3

                 = 13m + 13m + 10m

                 = 36m

Therefore, the length of the wire used to make the cuboid is 36 meters.

for more such question on length visit

https://brainly.com/question/28322552

#SPJ8

Answer:

$1400

Step-by-step explanation:

Take $3500 and multiply by 4% (0.4) and then get the product of 140 then multiply by 10 for the years and get $1400. Hope this answer helped!

Given: Object = Figure A

Image = Figure B

Step 1: write out the values of the coordinates of polygon A

(-6, 1)

(-7,3)

(-7,8)

(-4,5)

(-3,8)

(-5,6)

Step 2: write out the corresponding values of the coordinates of polygon B in relation to Polygon A.

Let the transformation mapping be T. Then, we have

T(-6, 1) = (1,6)

T(-7,3) = (3,7)

T(-7,8) = (8,7)

T(-4,5)= (5,4)

T(-3,8) =(8,3)

T(-5,6)=(6,5)

From these steps, we can see that T must be defined as shown below

Hence, the transformation T is a counter-clockwise rotation of 270°

Answers:

Triangle ABC is an acute triangle. It's also a scalene triangle.

====================================================

Work Shown:

x = measure of angle B

2x+2 = measure of angle A, since we're told its "2 more than twice angle B"

2x-7 = measure of angle C, for similar reasoning

The three angles add to 180. This is true for any triangle

A+B+C = 180

(2x+2)+(x)+(2x-7) = 180

5x-5 = 180

5x = 180+5

5x = 185

x = 185/5

x = 37

This means angle B is 37 degrees. The other two angles are

A = 2x+2 = 2*37+2 = 74+2 = 76

C = 2x-7 = 2*37-7 = 74-7 = 67

----------------

In summary, we have these three interior angles

As a way to check, note how A+B+C = 76+37+67 = 180. This confirms the answer. All three angles mentioned are smaller than 90 degrees, so this triangle is acute.

Furthermore, because all three angles are different measures, this means all three sides are different lengths. This leads to triangle ABC being scalene.

Answer:

z = 30

Step-by-step explanation:

All angles of a triangle add up to 180:

z + 120 + 30 = 180

z + 150 = 180

z = 180 - 150

z = 30

In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10."

How to solve the question?

a. The set of natural odd numbers greater than 2, but less than 11 can be expressed using the roster method as {3, 5, 7, 9}. The set includes all the odd natural numbers between 2 and 11, excluding the endpoints, since 2 is not odd, and 11 is not less than 11.

b. The set {x|x (N and 4<x<10)} can be expressed using the roster method as {5, 6, 7, 8, 9}. The set includes all the natural numbers greater than 4 and less than 10, since x is a natural number (N) and satisfies the condition 4 < x < 10.

In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10." The vertical bar separates the description of the elements of the set (the condition) from the set itself.

The roster method and set-builder notation are both ways of describing sets, but the roster method lists all the elements of a set, while the set-builder notation describes the properties or conditions that define the set. Both methods are useful in different situations and depend on the specific context and the purpose of the set description.

To know more about numbers visit :-

https://brainly.com/question/25734188

#SPJ1

Your complete question is :-

express each set using the roster method.

a. the set of the natural odd numbers greater than 2, but less than 11

b.{x|x (N and 4

Answer:

(−∞,1/3)∪(1/3,∞),{yly≠1/3}

Step-by-step explanation:

Answer:

$478.8

Step-by-step explanation:

1 sparkler costs= $3.99

120 sparklers cost= $3.99 x 120 = $478.8

Answer:

42/7

Step-by-step explanation:

Change 6 to a fraction by putting a 1 under the 6.

6 becomes 6/1

Then multiply by 7/7 to change the denominator to 7 as was asked for in the question.

6/1 × 7/7

= 42/7

When you multiply fraction × fraction, you multiply top×top and bottom×bottom.

6 rewritten as a fraction with the 7 on the bottom is 42/7

Answer:

70.48% probability that it was infected with Dummy

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Fixed by Bob

Event B: Infected with Dummy

65% of the customers with virus problems are bothered by Dummy

This means that \(P(B) = 0.65\)

If the computer is infected by Dummy, Bob has a 90% chance of fixing the problem.

This means that \(P(A|B) = 0.9\)

Probability of Bob Fixing

90% of 65%(fixing a Dummy-infected virus)

70% of 35%(fixing a Smarty-infected virus).

So

\(P(A) = 0.9*0.65 + 0.7*0.35 = 0.83\)

What is the probability that it was infected with Dummy

\(P(B|A) = \frac{0.65*0.9}{0.83} = 0.7048\)

70.48% probability that it was infected with Dummy

The number that produces an irrational number when multiplied by 0.4 is 3π. The correct option is A. \(3\pi\)

To determine which number produces an irrational number when multiplied by 0.4

First and foremost, 0.4 is a rational number.

A rational number is a number that is of the form \(\frac{p}{q}\) where p and q are integers and q is not equal to 0.

0.4 can be written as \(\frac{4}{10}\) or \(\frac{2}{5}\), hence, it is a rational number.

Now,

Any irrational number when multiplied by a rational number other than zero will also be irrational.

Therefore, we are to determine which of the given options is an irrational number.

π is an irrational number, therefore 3π is also an irrational number

0.444... can be expressed as 4/9, therefore it is a rational number

\(\sqrt{9}\) = 3, which can be expressed as 3/1, therefore it is a rational number

\(\frac{2}{7}\) is a rational number

The only irrational number among the given options is 3π

Hence, the number that produces an irrational number when multiplied by 0.4 is 3π. The correct option is A. \(3\pi\)

Learn more here: https://brainly.com/question/11763957

Answer: B

Step-by-step explanation: Hope this helps:)

Answer:

x = -12

Step-by-step explanation:

4x - 2(x + 1) = 3x + 10

First, you use distribution for - 2(x + 1) to better simplify teh equation:

4x - 2x - 2 = 3x + 10

Then, you subtract 4x - 2x:

2x - 2 = 3x + 10

Next, you subtract 2x from both sides of the equation to get x on one side:

(2x - 2x) - 2 = (3x - 2x) + 10

-2 = x + 10

Finally, you subtract 10 on both sides to get your answer:

(-2 - 10) = x (+ 10 - 10)

-12 = x

x = -12

the anwser is

Step-by-step explanation:

the anwser is 5 kg

Answer: 35, 48, 63

Step-by-step explanation:

This sequence is known as an arithmetic progression sequence.

      3 - 0 = 3

      8 - 3 = 5

      15 - 8 = 7

      24 - 15 = 9

Using this pattern, we will add 11 to 24 for the next term in the sequence. Then, we will continue this pattern for the next two terms.

➜ The pattern is resulting odd numbers from subtracting two terms in a row; 3, 5, 7, 9, [11], [13], [15].

      24 + 11 = 35

      35 + 13 = 48

      48 + 15 = 63

Answer: 24

Step-by-step explanation: 6 x 4 = 24
24 - 8 = 16

The attached figure represents the image of A"B"C" after the transformation

The transformation rule is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle

From the figure, the coordinates of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of 90 degrees clockwise rotation is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The translation of the triangle by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the transformation

Read more about transformation at:

https://brainly.com/question/11709244

#SPJ1

Answer:

- 1/2

Step-by-step explanation:

turn 2/5 to have the same denominator as 10

2 ( 2 ) = 4

5 ( 2 ) = 10

4/10 - 9/10

= -5/10

simplify

-5/10 = -1/2

hope this helps

Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001

Answer: 1 m is 9 there are 7 m so 7X9 =63

Step-by-step explanation:

Answer:

the answer would be 9

expination:

because 63 divide by 7 would be 9

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

For more such answers on coordinates

https://brainly.com/question/30227780

#SPJ8

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

For more questions on simplified form of the expression:

https://brainly.com/question/28323654

#SPJ8

Divide 18 by 40 %

18/0.40 = 45

Answer: 45

Answer:

Step-by-step explanation:

18 is 40% of what number?

18 : 40 * 100 =

45

-----------------------------

check

45 : 100 * 40 = 18

the answer is good

The amount he pays back using simple interest is $4860

Since Taylor plans to borrow $4,500 from the bank to purchase a used vehicle. If he borrows the money at a rate of 4% for 2 years, to find the amount he pays back, A we use the simple interest formula which is given by

A = P(1 + rt) where

Given that

Substituting the values of the variables into the simple interest equation, we have

A = P(1 + rt)

A = 4500(1 + 0.04 × 2)

A = 4500(1 + 0.08)

A = 4500(1.08)

A = 4860

So, the amount he pays back is $4860

Learn more about simple interest here:

https://brainly.com/question/28193741

#SPJ1

The value of x that makes the given pair of ratios equivalent is: A. 32.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.

This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;

x/16 = 50/25

Cross-multiplying, we have the following:

25x = 16 × 50

25x = 800

x = 800/25

x = 32.

Read more on ratio here: brainly.com/question/27817533

#SPJ1

Answer:

Reflection across \(x=4\)

Step-by-step explanation:

You must measure the distance between the rightmost point on the blue figure and the leftmost point on the orange figure. Then divide it in half and these dots will be the answer, how are they asking for a line you need to specify if it is horizontal or vertical, because the interchanged points are \(B\) with \(C\) and \(D\) with \(A\) we know that is a vertical line, so the answer is:

Reflection across \(x=4\)