Rita is designing a building shaped like a pyramid that's cut off in a plane parallel to its base (this is called a truncated pyramid). The building has a 64×64 m end text square base and is 36 m tall. The cut off section has an a16×16m square base and is 12 m tall. What is the volume of the building? Round to the nearest cubic meter.

The measure of the value of [x] is x = √5/2

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle as shown in the image.

We can write -

sin(30) = x/(√5)

x = √5 sin (30)

x = √5/2

Therefore, the measure of the value of [x] is x = √5/2.

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The inequality states that the value of z must be greater than or equal to 0 and less than or equal to h, which ensures that all points within the slab are included.

The slab bounded by the planes 0 and ​(planes​ included) is a region in three-dimensional space that is defined by two parallel planes, one located at z = 0 and the other at

z = h.

Any point inside this region has a z-coordinate that is greater than or equal to 0 and less than or equal to h. Therefore, we can describe this region using an inequality in terms of z, as shown above.The inequality 0 ≤ z ≤ h is a useful one because it ensures that all points within the slab are included.

If we were to use a strict inequality like 0 < z < h, we would exclude points on the boundary of the slab. On the other hand, if we were to use an inequality like z ≤ h or 0 ≤ z, we would include points outside the slab. Therefore, the inequality 0 ≤ z ≤ h is the most appropriate one for describing this region. Inequalities are mathematical expressions that relate two quantities using a less than, greater than, less than or equal to, or greater than or equal to sign. Inequalities can be used to describe a variety of geometric shapes and regions in space, such as slabs bounded by two parallel planes.

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The percent yield is calculated as the ratio of the actual yield to the theoretical yield, multiplied by 100.

Percent yield is a measure of how efficient a chemical reaction or process is in producing the desired product.

The formula for percent yield is:

Percent Yield = (Actual Yield / Theoretical Yield) * 100

The actual yield is the amount of product obtained from the reaction or process, typically measured in grams or moles. It represents the actual amount of product obtained in the laboratory.

The theoretical yield, on the other hand, is the maximum amount of product that can be obtained based on stoichiometry and other factors. It is calculated using balanced chemical equations and the starting amounts of reactants.

By dividing the actual yield by the theoretical yield and multiplying by 100, we get the percent yield, which is expressed as a percentage.

This value provides insight into the efficiency of the reaction or process, with a higher percent yield indicating a more efficient conversion of reactants into products.

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We can make use of a slope field to sketch the two approximate solutions of the differential equation. The slope field for the differential equation is dy/dx.

a) We will now mark the point (0,4) on the slope field as shown in the image below.

Solution 1: We will begin at the point (0, 4) and move along the slope lines to obtain the first solution. This first solution is shown in blue in the image below,

Solution 2: For the second solution, we will begin at the point (0,4) and move along the slope lines in the opposite direction to obtain the second solution. This second solution is shown in red in the image below.

Substituting x = 0 and y = 4, we get: 4 = sin(0) + C4 = 0 + CC = 4

Therefore, the particular solution is: y = sin(x) + 4

Below is the graph of the solution: Graph of y = sin(x) + 4

We can compare this graph of the particular solution with the sketches in part (a).

The graph of the solution matches the first solution in blue.

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The Maximum possible error in the surface area of the cube is estimated to be 24 cm^2.

To estimate the maximum possible error when computing the volume and surface area of a cube, we can use differentials.

(a) Volume of the Cube:

The volume of a cube is given by V = s^3, where s represents the length of one edge. In this case, the edge of the cube is measured as 20 cm with a possible error of 0.1 cm. To estimate the maximum possible error in the volume, we'll use differentials.

Let's define V as the volume of the cube and s as the length of the edge. The differential of V, denoted as dV, can be approximated using the derivative of the volume equation:

dV ≈ (dV/ds) * ds

Now, let's find dV/ds:

dV/ds = 3s^2

Substituting the given value of s = 20 cm:

dV/ds = 3(20)^2 = 1200 cm^2

Since ds represents the possible error in the measurement of the edge, ds = 0.1 cm, we can substitute these values into the differential equation:

dV ≈ (1200 cm^2) * (0.1 cm) = 120 cm^3

Therefore, the maximum possible error in the volume of the cube is estimated to be 120 cm^3.

(b) Surface Area of the Cube:

The surface area of a cube is given by A = 6s^2. Similar to the volume, we can use differentials to estimate the maximum possible error in the surface area.

Let's define A as the surface area of the cube. The differential of A, denoted as dA, can be approximated using the derivative of the surface area equation:

dA ≈ (dA/ds) * ds

Now, let's find dA/ds:

dA/ds = 12s

Substituting s = 20 cm:

dA/ds = 12(20) = 240 cm^2

Since ds = 0.1 cm:

dA ≈ (240 cm^2) * (0.1 cm) = 24 cm^2

Therefore, the maximum possible error in the surface area of the cube is estimated to be 24 cm^2.

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The particular solution is:

\(\(y = 3x^2 - 2x + 3\)\)

A function's derivative with respect to an independent variable can be used to define differentiation. Calculus differentiates to measure the function per unit change in the independent variable. A function of x is y = f(x).

To find the particular solution of the differential equation \(\(y''' = 0\)\) with the given initial conditions \(\(y(0) = 3\)\), \(\(y'(1) = 4\)\), and \(\(y''(2) = 6\)\), we can integrate the equation successively to find the antiderivatives.

1. Integrating \(\(y''' = 0\)\) once will give us \(\(y'' = C_1\)\), where \(\(C_1\)\) is a constant of integration.

2. Integrating \(\(y'' = C_1\)\) once more will give us \(\(y' = C_1x + C_2\)\), where \(\(C_2\)\) is another constant of integration.

3. Integrating \(\(y' = C_1x + C_2\)\) one last time will give us \(\(y = \frac{C_1}{2}x^2 + C_2x + C_3\)\), where \(\(C_3\)\) is the final constant of integration.

Now, let's use the initial conditions to determine the values of the constants.

Given (y(0) = 3), we substitute (x = 0) into the equation:

\(\(y(0) = \frac{C_1}{2}(0)^2 + C_2(0) + C_3\)\)

Simplifying, we get \(\(C_3 = 3\)\).

Next, given \(\(y'(1) = 4\)\), we substitute (x = 1) into the equation:

\(\(y'(1) = C_1(1) + C_2\)\)

Since we know \(\(y'(1) = 4\)\), we have\(\(C_1 + C_2 = 4\)\) (Equation 1).

Finally, given \(\(y''(2) = 6\)\), we substitute \(\(x = 2\)\) into the equation:

\(\(y''(2) = C_1\)\)

Since we know \(\(y''(2) = 6\)\), we have \(\(C_1 = 6\)\) (Equation 2).

Now, substituting Equation 2 into Equation 1, we can solve for \(\(C_2\)\):

\(\(6 + C_2 = 4\)\)

\(\(C_2 = 4 - 6\)\)

\(\(C_2 = -2\)\)

Thus, the constants are \(\(C_1 = 6\), \(C_2 = -2\), and \(C_3 = 3\)\).

The particular solution of the differential equation \(\(y''' = 0\)\) with the given initial conditions is:

\(\(y = \frac{C_1}{2}x^2 + C_2x + C_3\)\)

Substituting the values of the constants, we have:

\(\(y = \frac{6}{2}x^2 - 2x + 3\)\)

Simplifying further, the particular solution is:

\(\(y = 3x^2 - 2x + 3\)\)

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The answer is 30

Step-by-step explanation:

50-2=48 then divide 48 by 1.60 and you get 30!

Answer:

- \(\frac{3}{5}\) i

Step-by-step explanation:

Given

\(\frac{3}{5i}\)

Multiply numerator/ denominator by i

= \(\frac{3i}{5i^2}\) [ i² = - 1 ]

= \(\frac{3i}{-5}\)

= - \(\frac{3}{5}\) i

The volume of the right circular cone with a height of 15.4 m and a base circumference of 18 m is 15.68 cubic meters.

To find the volume of a right circular cone, we can use the formula:

Volume = (1/3) × π × r² × h,

where π is the mathematical constant pi, r is the radius of the base, and h is the height of the cone.

Given that the base has a circumference of 18 m, we can calculate the radius using the formula:

Circumference = 2 × π × r

18 = 2 × π × r

r = 18 / (2 × π) = 2.864 m.

Now we can substitute the values into the volume formula:

Volume = (1/3) × π × (2.864 m)² × 15.4 m,

Volume = 15.68 m³

Therefore, the volume of the right circular cone with a height of 15.4 m and a base circumference of 18 m is 15.68 cubic meters.

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Answer:

Step-by-step explanation:

I am taking q as some integer.

Let a be the positive integer.

And, b = 4 .

Then by Euclid's division lemma,

We can write \(a = 4q + r\) ,for some integer \(q\ \text {and}\ 0 \leq r < 4 .\)

°•° Then, possible values of r is 0, 1, 2, 3 .

\(\texttt {Taking} \ r = 0 .\\\\a = 4q .\)

\(\texttt {Taking} \ r = 1 .\\\\a = 4q + 1 .\\\\\texttt {Taking} \ r = 2\\\\a = 4q + 2 .\\\\\texttt {Taking} \ r = 3 .\\\\a = 4q + 3 .\)

But a is an odd positive integer, so a can't be 4q , or 4q + 2

[ As these are even ] .

•°• a can be of the form 4q + 1 or 4q + 3 for some integer q .

Answer:

84

Step-by-step explanation:

Multiply 35 by 2.5

Answer:

75 windows

Step-by-step explanation:

35 ---- 7

x ----- 15

\(x=\frac{(35)(15)}{7} =75\)

Hope this helps

Step-by-step explanation:

x = ml of the 60% solution

y = ml of the 45% solution

x + y = 600

and therefore

x = 600 - y

0.6x + 0.45y = 0.5×600

we use the above identity in this equation :

0.6(600 - y) + 0.45y = 300

360 - 0.6y + 0.45y = 300

60 - 0.15y = 0

60 = 0.15y

y = 400 ml

x = 600 - y = 600 - 400 = 200 ml

Answer:

b

Step-by-step explanation:

in order to find the mean you have find the sum of the numbers and divide them by the amount of numbers.without 68 the sum is 310 divide it by 5 and tge answer is 62.however if you add 68 the sum is 378 divide it by 6 and the answer is 63.

therefore the answer increased by 1.

hope this helps :)

The possible area of the region that is shaded is given as 462cm.

The picture here shows us two rectangles.

The area of a rectangle is given as L * w

= length x width

We have to find the area of the first rectangle

21cm x 42cm

= 882 cm

Next we find the area of the rectangle inside

15cm x 28cm

= 420

To get the area of the shaded region

= 882 - 420

= 462cm

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The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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Answer:

1.)  1 ,2, 31, 62

2.)  1, 3, 5, 9

3.) 540

Step-by-step explanation:

1.)  1x62= 62

2x31= 62

31x2= 62

62x1=62

Each of these number are a multiple of 62.

2.) 1x45=45

3x15=45

5x9= 45

9x5= 45

3.) 420÷2= 210

420÷3= 140

420÷5= 84

420÷6= 70

420÷9= 46.667 This number is not a multiple of 420 because the answer is in decimals which means 9 is not divisible by 420

540÷2= 270

540÷3= 180

540÷5= 108

540÷6= 90

540÷9= 60

540÷10= 54

2, 3, 5, 6, 9 and 10 is divisible by all of these numbers

Answer:

1)  1 ,2, 31, 62

2)  1, 3, 5, 9

3.) 540

Step-by-step explanation:

1)  62 would be divisible by 2 because its an even number, and if you split 62 in half, you would get 31.

2) 4+5 = 9. 3 and 9 are both divisible by 9, and 5 is divisible by 5.

3) All of the numbers are divisible by 10, 5, and 2 in the list. 250 is not divisible by 3, so we can take it off the list.  The rest of the numbers are all divisible by 6. All we have left is 9. Both 420 and 510 add their values up to 6, which is not divisible by 9. That leaves us with 540 as our answer.

-kiniwih426

Answer: From the graph, we see that Anna needs to sell 300 pre-sale tickets and 100 at-the-door tickets to reach her goal. Therefore, she needs to sell 100 at-the-door tickets to make her goal. Answer: 100.

Step-by-step explanation:

Answer:

3:5

Step-by-step explanation:

24:40

24 cars without sunroof

24+16=40

40 total cars

reduce the ratio of 24:40

12:20

6:10

3:5

the answer is 3:5

Answer:

angle 2 = 37⁰

angle 3 = 153⁰

angle 4 = 37⁰

Step-by-step explanation:

I guess this refers to two intersecting lines which form 4 angles.

Angles 1 and 2 are supplementary angles whose sum is 180⁰.

Angle 1 + angle 2 = 180⁰

143⁰ + angle 2 = 180⁰

angle 2 = 180⁰ - 143⁰

angle 2 = 37⁰

Angles 1 and 3 are vertical angles so do with angles 2 and 4. Therefore it is easy to find their measures because vertical angles are congruent in measures.

Hope this helps...

Answer:

m∠1 = 143°

m∠2 = 37°

m∠3 = 143°

m∠4 = 37°

Answer:

\(x=\frac{5\±i√203}{6}\)(the lanky a is a square root)

Step-by-step explanation:

I suppose the equation is \(3x^2-5x+19=0\)?

A good old quadratic equation! Back to the good old days when we are memorizing the formula...

\(x=\frac{-b\±√(b^2-4ac)}{2a}\)

(Yes that little lanky a is a square root)

\(x=\frac{-(-5)\±√((-5)^2-4(3)(19))}{2(3)} \\x=\frac{5\±√(25-228)}{6}\\x=\frac{5\±√-203}{6} \\x=\frac{5\±i√203}{6}\)

Since the discriminant is negative, there are no real solutions, but instead, we have complex solutions shown above.

Answer:

X'= (-3,6)

Y'=(7,8)

Z'=(11,2)

Step-by-step explanation:

when a point is reflected over the y axis, (x,y) becomes (-x,y). so the x value is just multiplied by -1

Answer:

X′(−3, 6), Y′(7, 8), Z′(11, 2)

Step-by-step explanation:

Imagine you are a spy who needs to infiltrate a secret base located at the origin of the coordinate plane. You have three accomplices, X, Y, and Z, who are waiting for you at different points on the plane. X is at (3, 6), Y is at (-7, 8), and Z is at (-11, 2). You have a device that can reflect any point over the y-axis, which you plan to use to confuse the enemy guards. You decide to reflect X, Y, and Z over the y-axis to create X', Y', and Z', respectively. What are the coordinates of these new points?

To find the coordinates of X', you simply change the sign of the x-coordinate of X. So, X' is at (-3, 6). Similarly, to find the coordinates of Y' and Z', you change the sign of the x-coordinates of Y and Z. So Y' is at (7, 8) and Z' is at (11, 2). Now you have three new points that are symmetric to the original ones over the y-axis.

But wait! There's a problem. The enemy guards have noticed that something is wrong. They see four points on their radar: one at the origin (you) and three on the right side of the y-axis (X', Y', and Z'). They realize that these points are reflections of some other points on the left side of the y-axis. They quickly deduce that there must be a spy among them. They start searching for you.

You need to act fast. You use your device again to reflect yourself over the y-axis. This creates a new point at (-0, 0), which is exactly the same as (0, 0). You have effectively disappeared from their radar. You sneak into the base while they are busy looking for you on the wrong side of the plane.

You have successfully completed your mission. Congratulations! You are a master of reflections.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer:

Z

Step-by-step explanation:

Just graph it bro

An equation represents the slope-intercept form of the given line is y= 1/2 x+8. Therefore, option D is the correct answer.

Given that, y-intercept = (0, 8) and slope = 1/2.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Substitute m=1/2 and c=8 in y=mx+c, we get

y= 1/2 x+8

Therefore, option D is the correct answer.

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Answer:

The linear function f(x) = -6x - 4

Step-by-step explanation:

The equation of the linear function f(x) is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where  

∵ f(x) = y ⇒ is the function of the set of ordered pairs (x, y)  

∴ f(-2) = 8 is the point (-2, 8)  

∴ f(1) = -10 is the point (1, -10)

∴ x1 = -2 and y1 = 8

∴ x2 = 1 and y2 = -10

→ Substitute them in the rule of the slope to find it

∵ m = \(\frac{-10-8}{1--2}\) = \(\frac{-18}{1+2}\) =  \(\frac{-18}{3}\)

∴ m = -6

→ Substitute it in the form of the equation above

∵ y = -6(x) + b  

∴ y = -6x + b

→ To find b substitute x by 1 and y by -10

∵ x = 1, y = -10

∴ -10 = -6(1) + b

∴ -10 = -6 + b

→ Add 6 to both sides

∵ -10 + 6 = -6 + 6 + b

∴ -4 = b

∴ b = -4

→ Substitute it in the equation

∴ y = -6x + -4

∴ y = -6x - 4

∵ y = f(x)

∴ The linear function f(x) = -6x - 4

For a normal distribution with mean µ = 40 and σ = 10. The proportion of the scores in this distribution are smaller than X = 35 is equals to the 0.3085. So, option(a) is right answer here.

The mean of the normal distribution lies at the center, it is called symmetric distribution. The score smaller than the mean is denoted by the negative z-score while the score greater than the mean is denoted by the positive z-score. Let X be a random variable. We have X is normally distributing, that is X ~ N( 0,1). So, population mean µ = 40

Standard deviations, σ = 10

If X< 35, tge we have to determine the proportion of the scores in this distribution. Using the Z-Score formula, \(Z = \frac{X - \mu}{\sigma}\)

=> \(Z = \frac{35 - 40}{10}\)

= - 0.5 --(1)

The proportion of the scores to the left side of x, \(P(X< 35) = P( \frac{X - \mu}{\sigma}<\frac{36 - 40}{10})\)

= P( Z<−0.5) ( from equation (1))

Using the normal distribution table, the P( Z< - 0.5) is equals to 0.3085. So, P(X < 35) = P( Z< -0.5). Hence, required value is 0.3085.

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Answer:

11/31 11/12 11/5

Step-by-step explanation:

because 11/5 is a mixed number and the bigger the denominator the smaller the number

Answer:

x = 4, y = 3

x = 3, y = 4

Step-by-step explanation:

Set equation 2 equal to x or y

y = 7 - x

Sub in place of y in equation 1

x

2 + (7 – x)

2 = 25

x

2 + (7 – x)(7 – x)= 25

Set equal to zero

Expand Brackets and simplify

x

2 + 49 - 14x + x2 = 25

2x2

- 14x + 49 = 25

2x2

- 14x + 24 = 0

Factorise and remove a factor first if

possible!

x

2

- 7x + 12 = 0

(x – 4)(x – 3)= 0

x = 4 and x = 3

Sub values of x into ‘y = 7 – x’

x = 4, y = 3

x = 3, y = 4

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Answer:

V would be at (-4,5)

U would be at (-4,7)

T would be at (-9,7)

Answer:

V: (-4,5) U: (-4,7) T: (-9,7)

Step-by-step explanation:

reflect the shape across the x axis like a mirror

Hope this helps :)

Answer:

So this is an inequality and can be easily solved if its opposite number is done with both the sides. There are some inequality rules which are:

1. when absolute values removed; the number in the oppostite side becomes negative and if negative then positive. And the signs are changed to its opposite sign. Like greater than to less than or vise versa.

2. When both the sides are divided or multiplied by a negative number the signs are changed.

I - 7b + 5 I ≤ 33

- 7b + 5 ≥ -33

- 7b + 5 - 5 ≥ - 33 - 5

- 7b ≥  - 38

-7b/-7 ≥ -38/-7

b ≤ 5.428

Brainliest pls if it was correct!