Solve the initial value problem

r''(t)=2/t^2, r'(1)=3, r(1)=-4

The best option that analogizes Cavalieri's Principle is D. A short, wide glass that can hold the same volume of water as a tall, thin glass.

To describe the relationship between solids, Cavalier introduced parallel planes and area. If every plane parallel to these two planes intersects both regions in equal-area cross-sections, the two regions have equal volumes.

The volume of a prism is calculated by multiplying the area of the base by the height.

Cavalieri's principle, named after Bonaventura Cavalieri, is a modern implementation of the method of indivisibles in geometry. It is as follows: Case in two dimensions: Assume two plane regions are included between two parallel plane lines.

The Cavalieri's Principle describes the relationship between the volumes of two solids given their cross-sections and heights. When comparing the areas of two solids given their respective bases and heights, this principle comes in handy.

It states that the volumes of two or more solids are equal when their areas and lengths are the same.

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Answer:

C: A straight column of 10 pennies having the same volume as a leaning column of 10 pennies.

Step-by-step explanation:

The transformation g(x) = -f(x) converts the graph of

f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.

What is transformation of graph?

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations, it is a typical kind of algebraic problem.

Given:  f(x) = 8x^2 - 7.

We have to find what kind of transformation converts the graph

f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.

Let,

f(x) = 8x^2 - 7

Multiply both sides by -1.

⇒ -f(x) = -8x^2 - (-7)

  - f(x) = -8x^2 + 7

Since g(x) = -8x^2 + 7

⇒    -f(x) = g(x)

⇒    g(x) = -f(x)

Therefore, the transformation g(x) = -f(x) converts the graph of

f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.

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Answer:

Equation: x/-9 = 16

Solution: x = -144

Step-by-step explanation:

The "number x divided by -9 is 16" means x/-9 = 16, then we solve for x by multiplying both sides by "-9" to solve for x

x/-9 = 16

-9x/-9 = 16(-9)

x = -144

(18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5).

Yes, the answers are same from both the expressions i.e. 133.

Given, an expression i.e. 4(3a + 7) + 3(2a + 5)

Now, we are asked to find an equivalent expression for the given expression.

So, on simplifying the given expression, we get

4(3a + 7) + 3(2a + 5)

12a + 28 + 6a + 15

12a + 6a + 28 + 15

18a + 43

So, (18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5)

Now, On putting the value of a = 5 in both the expressions, we get

4(3(5) + 7) + 3(2(5) + 5)

= 4(15 + 7) + 3(10 + 5)

= 4(22) + 3(15)

= 88 + 45

= 133

also in (18a + 43),

= 18(5) + 43

= 90 + 43

= 133.

Hence, (18a + 43) is an equivalent expression for the given expression i.e.

4(3a + 7) + 3(2a + 5).

Yes, the answers are same from both the expressions i.e. 133.

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Answer:

1. A

2. A, B, D

Step-by-step explanation:

The first one is pretty straightforward, divide 7^2 to both the denominator and numerator, so you get 1/7^2. 7^2 is 49, which is not 14, so A is false. Everything else produces 1/49 in some shape or form.

The second question is also relatively easy. A is correct because 1/4 is 4^-1 and (4^-1)^-1 is 4^1. B is also right because if you add all the exponents up, you basically get -5+6+1=2, and 2^2 is 4. C is wrong because (1/2)^2 is 1/4, not 4. D is correct because 2^(5-3) is 2^2, which is 4. E is wrong because 4^(4-2) is 4^2, which is 16, not 4.

Overall, it's not hard, nor does it take time, you just need to remember the basic formulas: [tex]\frac{1}{x^a} =x^{-a[/tex], [tex]x^a * x^b=x^{a+b[/tex], and [tex]\frac{x^a}{x^b} = x^{a-b[/tex]

Answer:

95,189

Step-by-step explanation:

98x972-67

95256-67

95189

Answer:95189

Step-by-step explanation:  First you ave to multiply 98 x 972 which  would equal to 95256 ten subtract 67 which would give you the answer 95189

Answer:

x-intercept(s): (2,0)

y-intercept(s): (0,9)

y=−9/2x+9

x=2−2y9

Step-by-step explanation:

I don't know what else you need

Answer:

y=9

x=2

y=-9

Step-by-step explanation:

we just replace the values with whatever numbers

9(0)+2y=18

2y=18

/2.  /2

y=9

9x+2(0)=18

9x=18

/9.   /9

x=2

9(4)+2y=18

36+2y=18

-36.     -36

2y=-18

/2.   /2

y=-9

Hopes this helps please mark brainliest

Jeffry will get greatest total revenue when he charges the lemonade $1.40

Given,

The price per servings of lemonade = $0.80

Number of servings = 200

For each $0.10 that he adds to the price, Jeffrey will lose 10 customers.

We have to find the greatest total revenue he got.

Lets check.

0.80 x 200 = $160

0.90 x 190 = $171

1.00 x 180 = $180

1.10 x 170 = $187

1.20 x 160 = $192

1.30 x 150 = $195

1.40 x 140 = $196

1.50 x 130 = $195

1.60 x 120 = $192

Here this continues

From the above data we came to know that Jeffry will get greatest total revenue when he charges the lemonade $1.40

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Answer:

Step-by-step explanation:

1. The diagonals of a parallelogram are congruent.

2. The diagonals of a rhombus form congruent acute angles.

3. To get each side length of the rhombus, double each diagonal. That means 24 times 2 will be 48 and 20 times 2 will be 40.

4. The perimeter is the sum of the sides. 48+40+48+40 = 176

The flower arrangements with $200 has lower unit price than the flower arrangements with $70 unit price.

The average price of a product is calculated by dividing the total sales income by the total number of units sold. When a same product is supplied in variants, such as bottle sizes, managers must define "similar" units. Average prices can be estimated by dividing distinct unit selling prices by the percentage of unit sales (mix) for each product variant. When we utilize a standard rather than an actual mix of sizes and product variations, the result is price per statistical unit. Statistical units are sometimes known as analogous units.

Unit price for 15 flower arrangements for $200 is,

200/15=13.33

Unit price for 5 flower arrangements for $70 is,

70/5=14

Therefore, 14>13.33

So, the flower arrangements with $200 has lower unit price than the flower arrangements with $70 unit price.

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If the domain of a​ one-to-one function f is ​[6​,&​), the range of its​ inverse, f-1 ​of the one to one function is [6​, &​)

In mathematics, functions are said to be one-to-one functions, when one input value only give an output. No two input values give same output value in a one to one function

Usually in mathematics, functions may have two inputs which give same outputs however for one to one functions one input value gives only one output value

Relating this to domain (input values) and range (output values) and inverse.

The domain of a one to one function will be the range of inverse of the one to one function

This is among the property of one to one function

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The whole plots he can make are 43/6=7.1666

A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, while that of lemons to oranges is 6:8 (or 3:4). (or 4:7).

A ratio can include any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values. Both numbers must be positive in the majority of situations.

Given, the covering land is 5(3/8) acres

That is 43/8 acres

By dividing the plots as 3/4 each, we get

(43/8)*(4/3)=43/6=7.1666

The whole plots he can make are 43/6=7.1666

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Answer:

15

Step-by-step explanation:

1. 2x + 3 = 33

2. 2x = 33 - 3

3. 2x = 30

4. x = 15

Answer:

Area = 12x + 66

Perimeter = 2x + 35

Step-by-step explanation:

Area= 12(5.5 + x)

= 12x + 66

Perimeter = 2[(5.5 + x)+12]

= 2(17.5 + x)

= 2x + 35

The equivalent fraction using the least common denominator for 5/6 is 25/30 and for  4/5 is 24/30  .

In the question ,

it is given that ,

the fraction is 5/6 and 4/5 ,

the least common denominator of 6 and 5 is 30 .

the first fraction is 5/6 ,

since the least common denominator is 30,

we multiply the numerator and denominator by 5 ,

we get

= (5×5)/(6×5)

= 25/30

the second fraction is 4/5 ,

since the least common denominator is 30,

we multiply the numerator and denominator by 6 ,

we get

= (4×6)/(5×6)

= 24/30

Therefore , The equivalent fraction using the least common denominator for 5/6 is 25/30 and for  4/5 is 24/30  .

The given question is incomplete , the complete question is

Write Equivalent fractions for 5/6 and 4/5 using the least common denominator .

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Answer:

solve for the supplementary angles:

140 + x = 180

x = 40

then solve for 5x

40 + 5x = 90

5x = 50

x = 10

TADA!!

Answer: x = 10

Step-by-step explanation:

J - E has to be 180. 180 - 140 is 40. DHF has to be a 90 degree angle. 90-40 is 50. 5x, 50/5 is 10 so X would be ten.

Answer:

x = -10

y = 9

z = 0

Step-by-step explanation:

Answer:

3.75

Step-by-step explanation:

2.5 teaspoons for 18 people

divide by two to get

1.25 teaspoons for 9 people

9 * 3 = 27 so we multiply 1.25 by 3 to get

3.75 for 27 people

Answer:

  (b)  52y +15

Step-by-step explanation:

You want an algebraic expression for 15 more than the product of 52 and a number.

If y represents "a number", then "the product of 52 and a number" can be written as ...

  52 × y = 52y

The wording "15 more than ..." means the value 15 is added to the product. That makes the expression ...

  (b)  52y +15

<95141404393>

Range of the given function A(t)=487-264t is (-∞, +∞)

Domain of the given function A(t)=487-264t is also (-∞, +∞)

What is domain?

it is the values which x can take in the function. so that it does not get indefined.

It is all the values which comes after x is put in the equation.

The domain and range are defined for a given function and they are the sets of all the x-ordinates and all the y-ordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then.

Given function

A(t)=487-264t

Hence, Range of the given function is (-∞, +∞)

and Domain of the given function is also (-∞, +∞)

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Answer:

xy

Step-by-step explanation:

if you take xy out of xy^2z it will become yz

if you take you xy out of xy it becomes 1 so this is the greatest factor

(please tell me if i got any digits wrong i assumed some were exponets)

hopes this helps please mark brainliest

Answer:

1. x² 2. x

Step-by-step explanation:

For these problems, there actually pretty easy. What you do is the numbers like x2 are x times 2. So, like if x is 3, it would be equal to 6 because 3 times 2 is 6. Easy, right?

But this time, it is asking you for GCF. It's harder, but it will be easy after you understand it.

#1

So, it organizes the equation. So x2 gets simplified to x times 2. x*2 is double the amount. x + y and x - z. Take the x's that is 2 x's. So x2. Then y and z which are unknown has the value left. And 1 more thing. Since there is no operation, it turns in to times/multiply. Please don't ask why. Ask it in a new question. So you can cross them off and multiply x2 with y times z. The equation now is basically x2 y times z). y times z. Again, the numbers are unknown. So you need to count them as zero. Add 2 zero's together is 0. Add x2 to 0. Which is x2.

You can now do problem 2 by yourself after you read the explanation. Remember, your answer isn't always like this type of explanation. Some one's work, try this for all your problems related. See if it works.

Therefore, the GCF of x2(x + y) (x - z) is x2

The graph g has a minimum value at it's vertex, (3, -1).

What is vertex?

The point where a parabola's line of symmetry intersects with the parabola itself is known as the vertex. The vertex of a parabola whose equation is given in standard form will be the lowest point on the graph and the highest point on the graph depending on certain conditions.

The given graph g is a upward parabola.

Since the upward parabola having a minimum value at it's  vertex.

And the downward parabola having a maximum value at it's vertex.

Here, the vertex of the upward parabola is, (3, -1).

Therefore, the minimum value of g is, (3, -1).

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An investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250 situation is best modeled by an exponential function with time as the independent variable

Two or more expressions with an Equal sign is called as Equation.

We need to find the exponential function with time as the independent variable.

Exponential growth refers to the original value from the range increases by the same percentage over equal increments found in the domain.

an investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250

an investment that increases by a constant factor of 1.03, or at a

rate of 3%, every year

an investment that increases by $30 every year

an investment that increases by $1 every 2 weeks

Hence, an investment that takes 2 years to increase in value by $50 and

10 years to increase in value by $250 situation is best modeled by an exponential function with time as the independent variable

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Answer: Total interest: $399

Balance = $2,299

Step-by-step explanation:

Total interest=

1900 * 7/100 * 3

= 133 * 3

= 399

Balance at maturity:

1900 + 399

= 2299

Answer:

28

Step-by-step explanation:

Draw a line segment.  Put A on one end and C on the other. Put B between these two points.  Mark the distance between A and B as 16 and the distance between B and C 12.  Add these two numbers together to get the distance of 28.