Answers
To calculate the volume of a composite figure, individual volumes of simple geometric shapes that make up the figure are calculated using dimensionally consistent formulas and then summed up to find the total volume.
Explanation:To find the volume of a composite figure, we must analyze each part of the figure separately and then combine their volumes. Volume is a measure of how much space an object occupies and for common shapes like cylinders, prisms, and cones, there are specific volume formulas. According to the information given, dimensionally consistent volume formulas would be those where volume is calculated by combining length measurements in such a way that the result has dimensions in cubic units. For example, for a cylinder, the volume is found by multiplying the area of the base by the height (V = πr²h), which is dimensionally consistent because it's the product of an area (with units squared) with a length (with a unit), resulting in units cubed, i.e., cubic units which represent volume.
For example, if we are to find the volume of a cylinder with a radius 'r' and height 'h', we would use the formula V = πr²h, where π is approximately 3.14159. If the radius is 2 cm, and the height is 5 cm, then the volume would be V = 3.14159 * (2²) * 5 cm³, which simplifies to V = 3.14159 * 4 * 5 cm³ = 62.8 cm³, after rounding to the nearest tenth.
As per the subject of composite figures, when the figure is made of multiple simple geometric shapes, we first find the volume of each part separately and then sum them all up to get the total volume of the composite figure. Understanding the dimensional analysis principles helps identify and correct potential errors in geometric formulas by ensuring that the dimensions on either side of an equation are consistent.
To solve the composite volume of the figure, we will subtract the volume of the cylinder from the volume of the cube.
The formula to find the volume of a cube is V = s^3, where s is the length of the side. It is shown in the figure that the length is 8 feet. Substitute this into the formula to find the volume of the cube.
V = s^3
= (8 ft)^3
= 512 ft^3
The formula to find the volume of a cylinder is V = πr^2h, where "r" is the radius and "h" is the height of the cylinder. It is shown in the figure that the diameter of the cylinder is 8 feet and its height is 8 feet. However, we need the value of the radius, not the diameter. To find the radius, we will divide the length of the diameter by 2 since the radius is half the length of the diameter.
r = d/2
= 8/2
= 4 ft
We already solve the length of the radius. Substitute the length of the height and radius to the formula to find the volume of the cylinder.
Volume (V) = πr^2h = π(4 ft)^2(8 ft) = π(16 ft^2)(8 ft) = 128π ft^3
We have solved the volume of the cube, which is 512 ft^3, while the volume of the cylinder is 128π ft^3. To solve the composite volume of the figure, we will subtract the volume of the cylinder from the volume of the cube.
V = V_cube - V_cylinder
V = 512 ft^3 - 128π ft^3
V = 109.9 ft^3
Related Questions
write the equations for the basic absolute value equation y=|x-h|+k under the given transformations:
1. shift 1 unit to the right and up 2 units
2. shift 3 units to the left and 7 units down
3. vertical shrink by a factor of 1/3
4. vertical stretch by a factor of 3
Answers
Up & Down affect the k,
Shrink & Stretch affect the "a" (which is in front of the absolute value expression).
1. shift 1 unit to the right and up 2 units → y = |x-1| + 2
2. shift 3 units to the left and 7 units down → y = |x + 7| - 7
3. vertical shrink by a factor of 1/3 → y = [tex] \frac{1}{3} [/tex]|x|
4. vertical stretch by a factor of 3 → y = 3 |x|
The spheres radius is 1/3 the radius of the hemisphere how does the volume of the hemisphere compare with the volume of the sphere
Answers
the volume of the sphere will be:
V=4/3πr³
V=4/3×π×(1/3x)³
V=4/81πx³
Volume of the hemisphere will ve:
V=1/2×4/3πr³
v=2/3×π×x³
v=2/3πx³
comparing the two volume by dividing the the volume of the hemisphere by that of the sphere we obtain:
(2/3πx³)/(4/81πx³)
=13.5
this implies that the volume of the hemisphere is 13.5 times the volume of the sphere.
Answer:
It is greater than the volume of the sphere
Step-by-step explanation:
Factor the polynomial completely.
x2 + 16
A) (x + 4)(x + 4)
B) (x - 4)(x - 4)
Answers
Its D
cannot factor this
Write as a mixed fraction: 22 / 3
Answers
1. You have the following fraction:
22/3
2. To write that fraction as a mixed number, you must divide the numerator by the denominator.
3. Then, write the whole number and next to it, the reminder as the numerator and the quotient as the denominator.
4. Therefore, the answer is:
7 1/3
The fraction 22/3 can be written as the mixed fraction 7 1/3.
We have,
To write the fraction 22/3 as a mixed fraction, we need to divide the numerator (22) by the denominator (3) and express the result as a whole number plus a proper fraction.
When we divide 22 by 3, we get a quotient of 7 and a remainder of 1.
The quotient represents the whole number part, and the remainder becomes the numerator of the proper fraction.
Thus,
22/3 can be written as the mixed fraction 7 1/3.
This means that we have 7 whole units and an additional 1/3 unit.
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A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function shown below. After how many seconds will the grasshopper land on the ground? Round to the nearest tenth.
h(t) = -t^2 + 4/3t + 1/4
A. -0.2 seconds
B. 0.5 seconds
C. 1.5 seconds
D. 0.7 seconds
Answers
The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function , which is
[tex] h(t) =-t^2+\frac{4}{3}t+ \frac{1}{4} [/tex]
When the grasshopper land on the ground,
[tex] h(t)=0 [/tex]
that is,
[tex] -t^2+\frac{4}{3}t+ \frac{1}{4}=0 [/tex]
Multiplying whole equation by 12 to get rid of denominators 3 and 4
[tex] -12t^2+16t +3=0 [/tex]
[tex] (3-2t)(6t+1)=0
\\
3-2t=0 , 6t+1=0
\\
t= \frac{3}{2} , \frac{-1}{6} [/tex]
And time cant be negative, so the correct option is
[tex] t = \frac{3}{2}=1.5 seconds [/tex]
Correct option is C .
The correct option is (D) 0.7 seconds.To determine when the grasshopper lands on the ground based on its height function, solve the quadratic equation and round to the nearest tenth for the time in seconds.
The height of the grasshopper above the ground is given by the function h(t) = -t² + 4/3t + 1/4. To find when the grasshopper lands on the ground, set h(t) = 0 and solve for t.
By setting -t² + 4/3t + 1/4 = 0 and solving the quadratic equation, you'll find the solutions for t. Round to the nearest tenth to get the time when the grasshopper lands.
The correct answer is 0.7 seconds (D).
James has 16 balloons.1/4 of his balloons are red.How many red balloons does he have?
Answers
First you have to convert the fraction to a decimal
1/4 = 0.25
Multiply the amount of balloons by the amount that are red
16 * 0.25 = 4
The answer is 4
Hope this helps!
What is the distance between the points (14, 29) and (14, 58) in the coordinate plane?
Answers
∞∞∞∞∞∞∞∞∞
Explanation:
∞∞∞∞∞∞∞∞∞
[tex]\textnormal {Formula : Distance }= \sqrt{(Y_2 - Y_1) ^2+(X_2 - X_1)^2}[/tex]
[tex]\textnormal {Plug }(X_1 ,Y_1) = (14, 29) \textnormal { and } (X_2 , Y_2) = (14, 58) \textnormal { into the formula: }[/tex]
[tex]\textnormal {Distance }= \sqrt{(58 -29) ^2+(14-14)^2} = \sqrt{29^2 + 0^2} = \sqrt{841} = 29 \textnormal { units} [/tex]
A gardener measured the heights of pepper plants in his garden. The results, rounded to the nearest inch, are shown on the line plot.Based on the graph, which statement about the heights of the pepper plants is true?
More than half of the plants are taller than 6 inches.
Fewer than one-quarter of the plants are taller than 4 inches and shorter than 7 inches.
More than half of the plants are less than 6 inches tall.
Fewer than one-quarter of the plants are taller than 7 inches and shorter than 10 inches.
Answers
Answer:
D) Fewer than one-quarter of the plants are taller than 7 inches and shorter than 10 inches.
Step-by-step explanation:
There are 17 total plants, 17/4=4.25
Plants taller than 7 inches and less than 10 are 8 or 9 inches tall
There are 3, 8 inch plants
There is 1, 9 inch plant
The total plants between 7 and 10 inches is 4
Answer:
D
Step-by-step explanation:
took the test
Proof: all radii of a circle are congruent, so , and since and , then are right triangles by the __________ congruency theorem. the corresponding sides of the triangles, and , are congruent, so zv = yx. thus, we know that 2zv = 2yx by the multiplication property of equality. by a congruency theorem that states, "if a diameter of a circle is perpendicular to a chord, then the __________," bisects and bisects , so vu = 2zv and xw = 2yx. therefore, we can conclude that vu = xw, or .
a. hl (hypotenuse-leg) . . . diameter bisects the chord and its other chord
b. sss (side-side-side) . . . diameter bisects the arc and its measurement
c. hl (hypotenuse-leg) . . . diameter bisects the chord and its arc
d. asa (angle-side-angle) . . . chord but not the diameter
Answers
A survey was conducted on 800 students regarding the number of automobiles in their household. A sample mean of 2.7 automobiles was determined, with a standard deviation of 0.7 automobiles. Assuming a 95% confidence level, which of the following statements holds true?
Answers
The correct answer is: As the sample size is appropriately large, the margin of error is ±0.049.
The statement that holds true with a 95% confidence level is true population mean of the number of automobiles in households of students is between 2.6524 and 2.7476."
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
To determine which of the following statements holds true, we need to use the confidence interval formula:
Confidence Interval = sample mean ± (critical value x standard error)
where the critical value is determined by the confidence level and the standard error is calculated using the formula:
standard error = standard deviation / sqrt(sample size)
With a 95% confidence level, the critical value is 1.96. Plugging in the values given in the question, we get:
standard error = 0.7 / sqrt(800) = 0.0247
Confidence Interval = 2.7 ± (1.96 x 0.0247) = (2.6524, 2.7476)
Therefore, the statement that holds true with a 95% confidence level is:
"The true population mean of the number of automobiles in households of students is between 2.6524 and 2.7476."
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A company is looking to design a new cover for their smartphone. The scale drawing of the design is shown below. The coordinates of the actual cover are: R' (12, 0); S' (0, 0); T' (0, 16); U' (12, 16). Is the design of the cover similar to the actual cover?
Rectangle RSTU is shown. Point R is at 3,0. S is at 0,0. T is at 0,4. U is at 3,4.
Yes; the corresponding sides are proportional.
No; the corresponding sides are not proportional.
Yes; the corresponding angles are proportional.
No; the corresponding angles are not proportional.
Answers
R '(12, 0); S '(0, 0); T '(0, 16); U '(12, 16)
The vertices of the design are:
R (3, 0); S (0, 0); T (0, 4); U (3, 4)
We then have the following relationship:
((1/4) x ', ((1/4) y') -----> (x, y)
Equivalently:
(1/4) R '= R
(1/4) S '= S
(1/4) T '= T
(1/4) U '= U
Therefore, the points are proportional and the proportionality constant is:
k = 1/4
Answer:
Yes; the corresponding sides are proportional.
HELP ME PLEASE
Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.
an = 8(1/2)n − 1; average rate of change is −3
an = 10(1/2)n − 1; average rate of change is 3
an = 8(1/2)n − 1; average rate of change is 3
an = 10(1/2)n − 1; average rate of change is −3
Answers
Average rate from n = 1 to n = 3 is -3
Its choice 1
Answer:
Option A
Step-by-step explanation:
To find nth term we use the given options.
[tex]a_n= 8(\frac{1}{2})^{n-1}[/tex]
Lets pick any point from the graph and plug it in the given option
LEts pick (1,8) and (2,4)
[tex]a_n= 8(\frac{1}{2})^{n-1}[/tex], n=1, an=8
[tex]8= 8(\frac{1}{2})^{1-1}[/tex]
[tex]8= 8(\frac{1}{2})^{0}[/tex]
8=8 True
LEts check with (2,4), n=2 and an=4
[tex]4= 8(\frac{1}{2})^{2-1}[/tex]
4=4 True
Average rate of change from n=1 to n=3= [tex]\frac{a_3-a_1}{3-1} =\frac{2-8}{2} =-3[/tex]
Average rate of change from n=1 to n=3 is -3
Marcus painted 1/3 of his bedroom in 4/5 of an hour. at this rate how long will it take him to paint his entire room
Answers
Answer:
So it took him 4/5 of an hour to paint 1/3
that means there is still 2/3 to go
so that means that he will have two times that time to paint the rest of the room
4/5 = ?
1/3 2/3
using cross multiplication
(4/5)(2/3) = (1/3) (?)
8/15 = 1/3 ?
divide both sides by 1/3
so that will be 8/5
that means it will take 8/5 of an hour to complete the rest
or 12/5 total to do entire room
Hope this helps ;)
Step-by-step explanation:
7,24,25. 7 , 23,24 7, 25,26
Which of the following will form a right triangle
Answers
In a right triangle
c²=a²+b²
where
a and b are the legs of triangle
c is the hypotenuse of the triangle
so
case 1)7,24,25
25²=7²+24²
25²-----> 625
7²+24²----> 625
625 is equal to 625----------> form a right triangle
case 2) 7,23,24
24²=7²+23²
24²------> 576
7²+23²-----> 578
576 is not 578-------------> not form a right triangle
case 3) 7,25,26
26²=7²+25²
26²-----> 676
7²+25²-----> 674
676 is not 674-----> not form a right triangle
the answer is
7,24,25 form a right triangle
Answer:
7, 24, 25
Step-by-step explanation:
7^2=49
24^2 = 576
25^2 = 625
576 + 49 = 625.
therefore, its a right angle
I dont inderstand this at all
Answers
Tan θ=opposite/adjacent
adjacent=opposite/tan θ
thus:
x=500/tan 12-500/tan 16
x=500/0.2126-500/0.2868
x=608.61 yd
~609 yd
Answer: D] about 609 yd
18] The angle of depression will be:
tan θ=opposite/adjacent
thus
tan θ=0.5/13
tan θ=0.0385
θ=arctan 0.0385
θ=2.2°
19] This will be evaluated like #17 above.
Tan θ=opposite/adjacent
adjacent=opposite/tan θ
thus
x=95/tan 31-95/tan42
x=95/0.6009-95/0.9004
x=52.598
~53
answer: A] about 53
20] The horizontal length will be calculated as follows:
sin θ=opposite/hypotenuse
opposite=73 m
hypotenuse=177 m
thus
sinθ=73/177
sinθ=0.4124
θ=arcsin 0.4124
θ=24.357~24.4°
Answer: D]24.4°
A certain arithmetic sequence has the following explicit formula for the nth term: an = 3 + (n - 1)(8) The same sequence has the following recursive formula: an = an-1 + _____ What number belongs in the blank space in the recursive formula? A. 5 B. 3 C. 8 D. 24
Answers
an=3+(n-1)8
simplifying this we get:
an=3+8n-8
an=8n-5
thus
the recursive formula is:
an=an-1+
the missing part is the common difference which is 8
What is the slope of the line that passes through the points (-4, 6) and (2, 4)?
A. -3
B. -1/3
C. 1/3
D. 3
Answers
= (4 - 6) / (2 - - 4)
= -2 / 6
= -1/3
Need help on this question
Answers
radius of the circle = r = 6
the length of one side of the equilateral triangle = L
the height if the triangle = h
The shaded area is the required area.
∴The area = (1/3) (area of circle - area of triangle )
area of circle = π r² = π * 6² = 36 π
An equilateral triangle is inscribed in a circle of radius r
∴ The length of one side of the triangle = √3 * r
= 6√3
and the height of the triangle = (√3 /2) * 6√3 = 9
∴ Area of the triangle = 0.5 * 9 * 6√3 = 27√3
The required area = (1/3) (area of circle - area of triangle )
= (1/3) * ( 36π - 27√3 )
= 12π - 9√3
Harry was given an assignment. He had 32 days to get 256 tasks done at work.Which operation would he use to figure out how many tasks he needs to complete each day?
Answers
Answer:
d
Step-by-step explanation:
Whats the average cost to put wood floors in a 12 ft x 16 ft room?
Answers
Determine whether the graph of the quadratic function y = –x2 – 10x + 1 opens upward or downward. Explain.
a. Because a > 0, the parabola opens downward.
b. Because a < 0, the parabola opens upward.
c. Because a < 0, the parabola opens downward.
d. Because a > 0, the parabola opens upward.
Answers
When a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards and from the given equation a < 0 that is why the graph of the quadratic equation is a parabola that opens downward.
Given :
Quadratic Function --- [tex]y = -x^2-10x + 1[/tex]
The graph of the quadratic equation is in the shape of the parabola. The generalized quadratic equation is given by:
[tex]ax^2 + bx +c = 0[/tex]
Now, compare the given equation ([tex]y = -x^2-10x + 1[/tex]) with the generalized quadratic equation which is given above.
[tex]a = -2[/tex]
b = -10
c = 1
According to the rules of the graph, when a is greater than 0 then the parabola opens upwards and if the value of 'a' is less than 0 then the parabola opens downwards.
Therefore, the correct option is c).
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Need help asap for this math problem !!!!!!
Answers
i believe the answer is d
please help me with this pre-calc question?
Answers
The explanation of this exercise is:
To solve this problem you must apply the proccedure shown below:
1- You have that:
W (-2,8,-3) and X(1,4,-1)
2- Therefore, you can calculate the magnitude as below:
|WX|=√[(1-(-2)]²+(4-8)²+[(-1-(-3)]²)
|WX|=√29
Use the given information to find the amount aa in the account earning compound interest after 6 years when the principal is $3500. r=2.16%r=2.16%, compounded quarterly the amount after 6 years is $ .
Answers
Equation for compound interest:
A = P (1+r/n)^nt
P = 3500
r = .0216
n = 4
t = 6
Answer: $3,982.92
Step-by-step explanation:
$3,982.92
Equation for compound interest:
A = P (1+r/n)^nt
P = 3500
r = .0216
n = 4
t = 6
Which statement follows from the given theorem? Theorem: The diagonal of a parallelogram divides it into two congruent triangles.
A. Diagonals of a parallelogram bisect opposite angles.
B. Consecutive sides of a parallelogram are congruent.
C. Consecutive angles of a parallelogram are congruent.
D. Consecutive angles of a parallelogram are supplementary.
Answers
Answer:
Opposite sides of a parallelogram are congruent.
Step-by-step explanation:
The correct answer is A. Diagonals of a parallelogram bisect opposite angles.
The theorem states that the diagonal of a parallelogram divides it into two congruent triangles. This means that the two triangles have the same corresponding side lengths and angles. Since the diagonal is a common side to both triangles, the opposite angles must also be congruent.
Option B, "Consecutive sides of a parallelogram are congruent," is not always true. For example, in a rectangle, which is a type of parallelogram, the consecutive sides are not congruent.
Option C, "Consecutive angles of a parallelogram are congruent," is also not always true. For example, in a rectangle, which is a type of parallelogram, the consecutive angles are not congruent.
Option D, "Consecutive angles of a parallelogram are supplementary," is not always true. For example, in a square, which is a type of parallelogram, the consecutive angles are not supplementary.
Therefore, the only statement that follows from the given theorem is A. Diagonals of a parallelogram bisect opposite angles.
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The circumference of a circle is 18.84 millimeters. what is the circle's area
Answers
18.84 = 2 [tex] \pi [/tex] r
9.42/[tex] \pi [/tex] = r
Area = [tex] \pi [/tex] r²
= [tex] \pi [/tex] (9.42/[tex] \pi [/tex])²
= 9.42²/[tex] \pi [/tex]
= 28.25 mm²²
Solve the system of equations using any method. 6x + 4y = −8 4x − 2y = 2 A) ( 11 7 , 2 7 ) B) ( 2 7 , 11 7 ) C) (− 2 7 , 11 7 ) D) (− 2 7 , − 11 7 )
Answers
6x + 4y = -8
4x - 2y = 2
To solve it we can use the graphic method.
The solution is then the point of intersection of both lines.
We have then:
x = -2 / 7
y = -11 / 7
Answer:
D) (- 2/7, - 11/7)
See attached image
the perimeter of Jared's property is 56 yards. how many feet of fence will Jared need if he wants to enclose the whole property?
Answers
Multiply 56 × 3 = 168
Jared will need 168 feet of fence to enclose his property.
Given:In quadrilateral WXYZ , WY and XZ bisect each other at point A. Prove: Quadrilateral WXYZ is a parallelogram.
Answers
Given that the diagonals WY and XZ in a quadrilateral WXYZ bisect each other, we can confidently say that quadrilateral WXYZ is a parallelogram. This is based on the property of a parallelogram which states that its diagonals bisect each other.
Explanation:To prove that a quadrilateral is a parallelogram given that the diagonals bisect each other, we'll apply the properties of a parallelogram. According to the properties of a parallelogram, the diagonals bisect each other. That is to say, if WY and XZ bisect each other at point A (i.e., WA=AY and AZ=ZX), then WXYZ is a parallelogram. This satisfies the condition for the given quadrilateral and hence WXYZ is a parallelogram.
We use this information along with the parallelogram rule and the Pythagorean theorem to prove the quadrilateral is, in fact, a parallelogram. The rule states that if a quadrilateral has diagonals that bisect each other then it is a parallelogram.
In this case, since WY and XZ bisect each other at point A, we know that the lengths WA = AY and XA = AZ. Hence, quadrilateral WXYZ is indeed a parallelogram.
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6x – 2y = 10 2x + 3y = 51 Solving the first equation above for y gives
Answers
Answer with Step-by-step explanation:
6x – 2y = 10
2x + 3y = 51
Solving the first equation above for y:
6x-2y=10
⇒ 2y=6x-10
dividing both sides by 2
y=3x-5
Putting value of y in second equation
2x + 3(3x-5) = 51
2x+9x-15=51
11x=51+15
11x=66
⇒ x=6
y=3×6-5
=18-5
= 13
Hence, solution is: x=6 and y=13
and Solving the first equation above for y gives: y=3x-5