For problems 12-15 find the unknown factor.


. 3/4 x ? =9/16

2/5 x ? =8/15

5/7 x ? = 5/9

Answer:

7a) To show that r^2 = R^2 - h^2, one can use the Pythagorean theorem and the fact that the distance from the center of the sphere to the surface of the cylinder is h/2.

7b) To find the volume of the cylinder, one can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height.

7c) To find the maximum volume of the cylinder, one can differentiate the expression for the volume with respect to h, set the derivative equal to zero, and solve for h.

7d) The ratio of the volume of the sphere to the maximum volume of the cylinder can be found by dividing the volume of the sphere by the maximum volume of the cylinder.

To find the ratio of radius to height for the desired can, one can set up an expression for the surface area of the can and differentiate it with respect to the radius and height. Setting the partial derivatives equal to zero, one can find the critical points, and evaluate which one is the minimum.

10a) To find the area of the rectangle, one can use the formula for the area of a rectangle, A = xy, where x is the length and y is the width.

10b) To find the maximum area of the rectangle, one can differentiate the expression for the area with respect to x and y, set the partial derivatives equal to zero, and solve for x and y.

Step-by-step explanation:

Cosine of ∠U is 28/53 in proper fraction, 28/53 in improper fraction, 0.52609 in whole number.

The cosine of an angle in a right triangle can be found using the ratio of the adjacent side to the hypotenuse. In this triangle, the adjacent side to ∠U is 28 and the hypotenuse is 53.

cos(∠U) = adjacent side ÷ hypotenuse = 28 ÷ 53 = 28/53

So, the cosine of ∠U is 28/53, written as a proper fraction.

Now let's convert cosine of ∠U is 28/53 in improper fraction:

The cosine of ∠U, which is 28/53, can be expressed as an improper fraction by dividing both the numerator and denominator by their greatest common factor.

gcd(28, 53) = 1, so the fraction cannot be further simplified.

Therefore, the cosine of ∠U, expressed as an improper fraction, is 28/53.

Now let's convert cosine of ∠U is 28/53 in whole number:

The cosine of ∠U, which is 28/53, can be expressed as a whole number by dividing the numerator by the denominator.

28 ÷ 53 = 0.526087

So, the cosine of ∠U expressed as a whole number is approximately 0.52609

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_____ The given question is not correct, so correct Question is:

Find the cosine of ∠U in Triangle UTV with side:

UV=28

VT=45

TU=53

Simplify your answer and write it as a proper fraction, improper fraction, or whole number.

Answer:

Below

Step-by-step explanation:

Cross multiply the fractions to get

3 (x+4 ) = 4(x+3)

3x + 12  = 4x + 12     subtract 12 from both sides

3x = 4x      <======obviously , this can only happen when x = 0  

ONE SOLUTION

Answer: 14.64m^2

Step-by-step explanation:

Base area = volume/height

Substitute:

86.376/5.9 = 14.64cm^2

Hope that helps!

The value of x in the angle is 56 degrees

From the question, we have the following parameters that can be used in our computation:

The figure

On the figure, we have teh following equation

64 + x + 60 = 130

The above is by the sum of angle theorem

So, we have

124 + x = 130

Evaluate the like terms

x = 6

Hence, the value of x is 6

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Answer:

6

Step-by-step explanation:

As you can see from the graph, it intercepts the y-axis at -4 and x-axis at 6

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

The equations that are solutions when c = 9 are B and C, and D and E.

When c = 9, the solutions for the equations are:

(A) 4 - c = 5: substituting 9 for c, we get 4 - 9 = -5, which is not true, so this equation is not a solution.

(B) 20 = 14 + c: substituting 9 for c, we get 20 = 14 + 9, which is true, so this equation is a solution.

(C) 15 = c - 6: substituting 9 for c, we get 15 = 9 - 6, which is true, so this equation is a solution.

(D) c/3 = 3: substituting 9 for c, we get 9/3 = 3, which is true, so this equation is a solution.

(E) 36 = 4c: substituting 9 for c, we get 36 = 4 * 9, which is true, so this equation is a solution.

So the equations that are solutions when c = 9 are B and C, and D and E.

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Answer:



Step-by-step explanation:

Answer:

Step-by-step explanation:

   Ted's balcony

       |\

       | \

       |  \ <- 40 degrees

       |   \

       |    \  <-- line of sight to the dog

       |     \

       |      \

       |       \

       |        \

       |         \

       |__________\

          Ted's

          eye level

Let d be the distance the dog needs to walk to get to the donut. We can use trigonometry to solve for d.

Since the angle of depression from Ted's line of sight to the dog is 40 degrees, the angle between the ground and Ted's line of sight is 90 - 40 = 50 degrees.

We can use the tangent function to find d:

tan(50) = opposite / adjacent

The opposite side is the height of Ted's eye level above the ground, which is 16 feet. The adjacent side is d, the distance the dog needs to walk to get to the donut.

tan(50) = 16 / d

d = 16 / tan(50)

d ≈ 12.6 feet

Interest on amount after 4 years = $256

Simple interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest for a given time.

Given,

Principal = $3200

Rate = 2%  = 0.02

Time =  4 years

Simple Interest = Principal × rate × time

                         = 3200 × 0.02 × 4

                         = $256

Hence $256 is simple interest on Principal amount after 4 years.

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The order of the numbers from least to greatest is -3, √3, 3, 3².

√3  is an irrational number

Arranging numbers in order from least to greatest is the arrangement of numbers in such a way that the smallest number comes first and the highest number comes last.

We have 3, 3², √3, -3

where 3² = 9 and √3 = 1.73

Thus, the order from least to greatest will be:

-3, √3, 3, 3²

Irrational numbers are mostly in the form of square roots, which when evaluated cannot be expressed in the form a/b e.g √7, π, 2/√5, 3√11, etc.

Thus, √3  is irrational

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The amount company will make in 6 months is $24327.43.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Given the interest rate = 12.5% = 0.125

principal  = $12,000

time period = 6 months

CI is given by,

CI = [tex]p(1 + \frac{r}{n})^{nt}[/tex]

n = 1

substitute the values,

A  = 12000(1 + (0.125/1))¹ˣ⁶

A = 12000(1.125)⁶

A = 24327.43

A = $24327.43

Hence the amount will be $24327.43.

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sum of roots is 0 , -5 , 4

product of roots is -9, 25/4, 8

Discriminant = 36, 0 , - 16

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

When a quadratic equation is solved, the two values of x that result are known as the roots of the equation. The zeros in the equation are another name for these quadratic equation roots. For instance, x = -1 and x = 4 are the roots of the equation x² - 3x - 4 = 0 since they each fulfill it.

The easiest method for locating a quadratic equation's roots is the quadratic formula. There are some quadratic equations that are difficult to factor, and in these cases we can quickly discover the roots by using the quadratic formula. The quadratic equation's roots also aid in determining the quadratic equation's sum of roots and product of roots. The quadratic formula's two roots are shown as a single statement.

The equation are :

x² - 9 = 0 ⇒ (x-3)(x+3) = 0 ,

sum of roots is 0

product of roots is -9

Discriminant = 0²  - 4*3(-3) = 36

The second equation :

4x² + 25 = - 20x ⇒ 4x² + 20x + 25 = 0 ⇒ 4x² + 10x + 10x + 25 ⇒2x(2x + 5) +5(2x+5) = 0  ⇒ (2x +5)²

sum of roots is -5

product of roots is 25/4

Discriminant = 0

x²/2 - 2x + 4 = 0 ⇒ x² - 4x + 8 = 0

Sum of roots 4

Product of roots 8

Discriminant = (-4)² - 4*1*8 = 16 - 32 = -16

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Answer: y = 1/4x + -5/4

Step-by-step explanation:

Step 1: add -4x to both sides

step 2:  Divide both sides by -16.

Answer:

Slope is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Rearranging the equation:

[tex]4x - 20 = 16y[/tex]

The coefficient of y needs to be '+1' for the above equation to be considered as the slope-intercept form:

Dividing both sides of the equation by '16':

[tex]\frac{16}{16}y = \frac{1}{16}(4x -20)[/tex]

[tex]y = \frac{4}{16}x - \frac{20}{16}[/tex]

Divide the numerator and denominator present in the coefficient of x  by the Highest Common Factor '4'. Also divide the numerator and denominator present in the coefficient of 'non-x' term by the Highest Common Factor '4':

[tex]y = \frac{1}{4}x - \frac{5}{4}[/tex]

The simplified form of the slope-intercept of the equation has been achieved. The coefficient of x is the slope of the graph:

m = Slope of graph =

Answer:$1.097

Step-by-step explanation:

3.29/3

then you will get 1.0967 (round up)

For the given grid a. The area of the triangle is 21 square units. b. The area of the rectangle is 42 square units.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

Given that the points on the grid are 1 units apart we have:

The height of the triangle is 6 units and the base of the triangle is 7 units.

The area of the triangle is:

A = 1/2 (b)(h)

A = 1/2(7)(6)

A = 21 square units.

The area of the triangle is 21 square units.

The length of the rectangular grid is 7 units and the width is 6 units.

The area of the rectangle is:

A = (l)(b)

A = (7)(6)

A = 42 square units.

The area of the rectangle is 42 square units.

Hence, a. The area of the triangle is 21 square units. b. The area of the rectangle is 42 square units.

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The expected number of 3's would be 5.

What is probability?

Probability is a field of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of inaccuracy in study by using probability.

The probability of rolling a 3 on a single roll of a fair six-sided die is 1/6, since there is one favorable outcome (rolling a 3) out of a total of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

However, it's important to keep in mind that the actual number of 3's obtained in 30 rolls of a die can vary, as the outcome of each roll is inherently random.

The expected value provides us with a guide for what to expect on average, but in any given sequence of rolls, the actual number of 3's may be higher or lower.

So, if you roll the cube 30 times, the expected number of 3's would be 30 * 1/6 = 5.

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The required time taken by the Devin to complete 5.8 laps is 24.36 minutes.

To find out how long it takes Devin to complete 5.8 laps, we need to multiply the time it takes to complete one lap by the number of laps. If it takes Devin 4.2 minutes to walk a lap, then to complete 5.8 laps, it would take.

time = 4.2 minutes/lap * 5.8 laps

= 24.36 minutes.

So, it would take Devin 24.36 minutes to complete 5.8 laps.

This information can be useful for determining Devin's walking pace, comparing his time to that of others, or calculating the total distance he has covered. It's important to note that this calculation assumes that Devin's pace remains constant throughout the entire walk, which may not always be the case.

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The geometric sequence is given as follows:

1, 2, 4, 6, 8, ...

The recursive formula is given as follows:

The explicit formula is given as follows:

[tex]f(n) = 2^{n - 1}[/tex]

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, meaning that each term is obtained by the multiplication of the previous term by the common ratio q.

The explicit formula of a geometric sequence is given by:

[tex]f(n) = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

For the recursive formula, we have that:

f(n) = q x f(n - 1).

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In this question, the length of the chord LN will be 15 inches long. It will be equal to PM.

Given,

At the circle's Centre, the Arc PL subtends an angle of 10 degrees.

At the circle's Centre, the Arc LM subtends an angle of 14 degrees.

At the circle's Centre, the Arc LN subtends a 24 degree angle.

The PM chord measures 15 inches in length.

What are the circle's chord theorems?

Considering the attached figure now,

The angle that the Arc PM creates at the Centre is equal to the sum of the angles that the Arc PL and Arc LM make there.

So,

At the middle, Arc PM will create the following angle: 10+14=24 degree.

We are aware that if the chords that make up the arc are equal, then the angle that it subtends in the Centre of the circle will likewise be equal.

Since, PM= 15 inches, therefore LN will also be 15 inches.

LN is therefore 15 inches as well.

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Based on the given angles:

From the given lines and angles, we can identify:

Vertical angles are pair of angles with no adjacent line but share one meeting point and have congruent angles. Four pairs of vertical angles are:

Alternate interior angles are pair of angles within the parallel line (inside) that have congruent angles. Each pair cross the transversal line "t". Two pairs of alternate interior angles are:

Cogruent angles might come from several types of relationships, such as:

All angles congruent to angle ∠1 are:

All angels congruent to angle ∠2 are:

Supplementary angles are a pair of angles whose its sum is 180°. Supplementary angles might formed by several types of angles relationship, such as:

Pairs of supplementary angles are:

Consecutive interior angles:

Adjacent angles:

Corresponding angles are a pair of unadjacent angles but have congruent angles because they face the same direction. Pairs of corresponding angles:

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Answer:

Step-by-step explanation:

4

The three subcategories in the previous scratch list are high-end linens, affordability, and food and drink-free snacks.

High-end linens include double-thick bath towels and 600-thread-count sheets. Affordability includes $100/night for four-star rooms. Food and drink-free snacks include coffeemakers and selected teas.

This scratch list provides guests with luxurious amenities and convenience. High-end linens enhance the comfort of a room, while affordability makes it accessible to many.

Food and drink-free snacks add to the convenience of a stay by providing guests with refreshments. All of these amenities contribute to a pleasant and comfortable stay.

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There are 172 boys in the introductory geology course.

The ratio of boys to girls is 4:5. We can know that the number of boys in the class is four multiplied by the common value that the ratio is based on.

We can call this usual value x and say that the number of boys in the class is 4x. Applying the same logic to the girls, we can say that there are 5x girls in the class. Hence, a total of 9x children. We divide the total value by 9 to get x, which equals 43.

We can then calculate the number of boys by calculating 4x, which equals 172.

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The bird is flying at a height of 404.9 feet above the ground

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

Let h represent the height of the bird.

Using trigonometric ratio:

tan(39) = h / 500

h = 500 * tan(39)

h = 404.9 feet

The height of the bird is 404.9 feet

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As a result, the extreme stem values may contain fewer rows than the other stem values. In our graph, the extreme stem values are 1 and 4, and they both have fewer rows than the middle values (2 and 3).

The shape and spread of a continuous data distribution are depicted by stem and leaf plots. These graphs are similar to histograms, but instead of bars, they display numbers.

Statistical software packages use an algorithm to improve our ability to read stem and leaf plots by displaying multiple rows of each stem value based on the properties of the data, as shown in the body fat percentage graph. There are two ones, five twos, five threes, and four fours.

The graph divides stem values into five rows for the body fat percentage data. Each row only has two leaf values (e.g., 0 and 1, 2 and 3, etc.) The leaf values terminate at the dataset's minimum and maximum values.

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