Which formulas could you use to find the volume of a right circular
cone?
OA) V = B-h where B = I-w
OB) V=B-h where B=1r'
OC) V=B-h where B = Tr
OD) V=B-h where B=1-w
Answers
Answer:
The formula for the volume of a cone is V=1/3hπr².
Related Questions
Hola! Necesito ayuda con esto, tengo que encontrar el dominio y rango de esta gráfica. Les agradezco mucho si me ayudan.
Answers
Answer:
yo no se pero ahorita yo te ayudo
Suppose that a class has 60 students who were born in 1999. How many ways are there that no two students have the same birth date in that class
Answers
There are 60 students in the class.
They were all born in 1999. No two students in the class have the same birthday date.
Therefore, there are approximately 1.146 x 10^98 ways that no two students in the class have the same birthday date.
Summary: There are 60 students in the class who were all born in 1999. We want to find the total number of ways that no two students in the class have the same birthday date. We use the permutations formula and let n = 365 and k = 60 to get P(365, 60) = 1.146 x 10^98. Therefore, there are approximately 1.146 x 10^98 ways that no two students in the class have the same birthday date.
Learn more about permutations click here:
https://brainly.com/question/1216161
#SPJ11
Consider the two vectors A=4.00i^+5.00j^−3.00k^ and B=2.00i^−3.00j^−5.00k^ (a) Calculate A−B using the components of the two vectors. (b) Calculate the magnitude of the vector difference A−B. (c) Is it possible to calculate a direction for this vector? Explain. (d) Calculate the vector product between the two vectors, A×B.
Answers
(a) The components of the two vectors are A - B = 2.00i + 8.00j + 2.00k.
(b) The magnitude of the vector difference A - B is approximately 11.49.
(c) The vector product A × B is -16.00i + 14.00j - 22.00k.
(a) To calculate A - B, we subtract the corresponding components of the two vectors:
A - B = (4.00i + 5.00j - 3.00k) - (2.00i - 3.00j - 5.00k)
Simplifying:
A - B = 4.00i + 5.00j - 3.00k - 2.00i + 3.00j + 5.00k
Combining like terms:
A - B = (4.00i - 2.00i) + (5.00j + 3.00j) + (-3.00k + 5.00k)
A - B = 2.00i + 8.00j + 2.00k
Therefore, A - B = 2.00i + 8.00j + 2.00k.
(b) To calculate the magnitude of the vector difference A - B, we use the formula:
|A - B| = sqrt((A - B) · (A - B))
where (A - B) · (A - B) represents the dot product of A - B with itself.
|A - B| = sqrt((2.00i + 8.00j + 2.00k) · (2.00i + 8.00j + 2.00k))
Expanding and calculating the dot product:
|A - B| = sqrt((2.00i · 2.00i) + (2.00i · 8.00j) + (2.00i · 2.00k) + (8.00j · 2.00i) + (8.00j · 8.00j) + (8.00j · 2.00k) + (2.00k · 2.00i) + (2.00k · 8.00j) + (2.00k · 2.00k))
|A - B| = sqrt(4.00 + 16.00 + 4.00 + 16.00 + 64.00 + 4.00 + 4.00 + 16.00 + 4.00)
|A - B| = sqrt(132.00)
|A - B| ≈ 11.49
Therefore, the magnitude of the vector difference A - B is approximately 11.49.
(c) To calculate the vector product (cross product) between vectors A and B, we use the formula:
A × B = (A_yB_z - A_zB_y)i + (A_zB_x - A_xB_z)j + (A_xB_y - A_yB_x)k
Plugging in the values:
A × B = ((5.00)(-5.00) - (-3.00)(-3.00))i + ((-3.00)(2.00) - (4.00)(-5.00))j + ((4.00)(-3.00) - (5.00)(2.00))k
Simplifying:
A × B = (-25.00 + 9.00)i + (-6.00 + 20.00)j + (-12.00 - 10.00)k
A × B = -16.00i + 14.
00j - 22.00k
Therefore, the vector product A × B is -16.00i + 14.00j - 22.00k.
Learn more about like terms here:
https://brainly.com/question/29169167
#SPJ11
Consider the two vectors A=4.00i^+5.00j^−3.00k^ and B=2.00i^−3.00j^−5.00k^ (a) Calculate A−B using the components of the two vectors. (b) Calculate the magnitude of the vector difference A−B. (c) Calculate the vector product between the two vectors, A×B.
How do artists use conventions such as line, color, and form to convey emotions in art? are these methods more or less effective than relying on subject matter?
Answers
Artists use conventions such as line, color, and form to convey emotions in art by manipulating these elements to create a certain mood or atmosphere.
For example, a jagged, frenzied line can convey a sense of anxiety or fear, while a smooth, flowing line can suggest calmness or tranquility. Similarly, warm colors like reds and yellows can create a sense of excitement or passion, while cool colors like blues and greens can suggest calm or sadness.
These methods can be very effective in conveying emotions in art because they allow the artist to communicate a feeling or idea without relying solely on subject matter. By using different techniques, an artist can create a sense of mood or emotion that transcends the specific subject matter depicted in the artwork.
However, it is important to note that relying solely on these conventions may not always be as effective as using subject matter to convey emotion. For example, if an artist creates a painting of a person crying, the viewer may immediately understand the emotion being conveyed. On the other hand, if an artist simply uses jagged lines and dark colors without any recognizable subject matter, the emotion being conveyed may not be as clear.
Ultimately, the effectiveness of using conventions such as line, color, and form to convey emotions in art depends on the artist's skill and intention, as well as the viewer's ability to interpret and understand the artwork.
To know more about Artists visit:
https://brainly.com/question/28804451
#SPJ11
Will award brainlest and 15 points!!!
A circle has a radius of 50 cm. Which one of these is closest to the area?
A. 314 cm
B. 15,708 cm
C. 7,854 cm
D. 157 cm
I need help ASAP!!!
Answers
Answer:
The answer is C!
Step-by-step explanation:
I don't have an explanation, it just came to me, sorry..Hope this helps though!
Answer:
7,854 cm
Step-by-step explanation:
We know that Area of the circle is given by:-
Area = \pi r^2πr2
, where r is the radius of the circle.
Given, A circle has a radius of 50 cm.
i.e. r= 50 cm
Then the circle would be Area = \pi(50)^2=(3.14)(2500)=7853.98163397\approx78547\ cm^2π(50)
=(3.14)(2500)=7853.98163397≈78547 cm
Thus, the area of the circle is approximately 7,854\ cm^27,854 cm
Write an inequality for the following statement.
9 is greater than a
Answers
Answer:
9>a
Step-by-step explanation:
The greater than symbol is >
The less than symbol is <
It can be helpful to imagine the signs as little crocodile mouths. They will turn their heads to the biggest catch, or in this case, the greater number. So the open end of the sign will be towards the greater number.
Answer:
9>a
Step-by-step explanation:
the side with the bigger opening means that side of the inequality has a greater value so since 9 is greater than a the bigger opening will go to 9.
On a coordinate plane, 2 rectangles are shown. Rectangle P Q R S has points (negative 3, negative 5), (negative 2, negative 5), (negative 2, negative 1), (negative 3, negative 1). Rectangle P double-prime Q double-prime R double-prime S double-prime has points (negative 5, 5), (negative 5, 4), (negative 1, 4), (negative 1, 5).
Which rule describes the composition of transformations that maps rectangle PQRS to P''Q''R''S''?
R0,270° ∘ T0,2(x, y)
R0,180° ∘ T2,0 (x, y)
T0,2 ∘ R0,270°(x, y)
R0,2 ∘ T0,180°(x, y)
Answers
The correct rule describing the composition of Transformations is: R0,2 ∘ T0,10 ∘ R0,270°
The rule that describes the composition of transformations mapping rectangle PQRS to P''Q''R''S'', we need to analyze the given coordinates and determine the sequence of transformations.
Let's compare the coordinates of the corresponding points:
P (−3, −5) ↔ P'' (−5, 5)
Q (−2, −5) ↔ Q'' (−5, 4)
R (−2, −1) ↔ R'' (−1, 4)
S (−3, −1) ↔ S'' (−1, 5)
From the comparison, we can observe the following transformations:
1. Translation: The x-coordinate of P'' is obtained by subtracting 2 from the x-coordinate of P. The y-coordinate of P'' is obtained by adding 10 to the y-coordinate of P. This suggests a translation of (−2, 10).
2. Reflection: The x-coordinate of Q'' is obtained by reflecting the x-coordinate of Q across the y-axis. The y-coordinate of Q'' remains the same. This indicates a reflection across the y-axis.
3. Rotation: The coordinates of R'' and S'' are obtained by rotating R and S 270 degrees counterclockwise about the origin (0, 0).
Now, let's determine the composition of transformations:
The sequence of transformations that maps rectangle PQRS to P''Q''R''S'' is as follows:
1. Translation by (−2, 10)
2. Reflection across the y-axis
3. Rotation of 270 degrees counterclockwise about the origin
Therefore, the correct rule describing the composition of transformations is:R0,2 ∘ T0,10 ∘ R0,270°
To know more about Transformations .
https://brainly.com/question/29788009
#SPJ8
Wendy is a waitress and has $15,000 toinvest, and wishes to gain $4,200 in interestover the next eight years. Approximatelywhat is the minimum simple interest rateWendy needs to reach her goal?
Answers
The formula for determining simple interest is expressed as
I = PRT/100
where
I = interest earned
R = interest rate
T = number of years
P = principal or amount invested
From the information given,
P = 15000
I = 4200
T = 8
Thus, we have
4200 = (15000 x R x 8)/100
4200 = 1200R
R = 4200/1200
R = 3.5
The required interest rate is 3.5%
Exercises Exercise 2.6.1. State what is wrong with each of the following write-ups; some have more than one error: We make use of the fact about the real numbers that if x > 0,2 > 0. To solve x2 +6x = 16: x2 +6x = 16 x2 +6x _ 16 = 0 (x_2)(x+8) = 0 and x = 2,x=-8_ In order to solve x2 +6x = 16, then x2 + 6x _ 16 = 0, (x- 2)(x+8) = 0, and therefore x = 2,x = -8 We want to solve the equation 12 _ 2x =x+10. then x2 _ 3x _ 10, so (x 5) (x+2) , so 5 and _2. We want t0 multiply the two polynomials +2y) and (y2 + Sy _ 6), which we do by computing (7+2y)60+Sy_6) 1y2 +35y-42+ 2y3 +10y2 _ 12y 2y3 +17y2 +23y-42 the answer is 2y3 +l7y2 +23y-42. A real number x is gloppy if there is some integer n such that.? _ n is sloppy Suppose that x is gloppy Because n is an integer; then its square is an integer; (The terms here are meaningless Let x be a real number: Then x2 > 0 for all real numbers x It is known that Va < a for all a > 1. Hence Va+ 3 < a +3. Hence Va+ 3)2 < (a+3)2
Answers
1. The first write-up is missing an equal sign before the 16 in the first line. The second line should be x² + 6x - 16 = 0 (instead of x² + 6x _ 16 = 0). The last line has an error in the second solution, where it says x = -8_ instead of x = -8.
2. In the second write-up, the equation should be 12 - 2x = x + 10 (instead of 12 _ 2x = x + 10). The sign error also carried over to the next line, where it should be x² - 3x - 10 (instead of x2 _ 3x _ 10). The correct solutions are x = 5 and x = -2 (instead of 5 and _2).
3. In the third write-up, there is a calculation error in the expansion of (7+2y)(y² + Sy - 6). The correct answer is 2y³ + 17y² - 23y - 42 (instead of 2y³ + l7y2 + 23y - 42).
4. In the fourth write-up, there is an incomplete sentence that is cut off.
5. In the fifth write-up, the inequality should be Va > a for all a > 1 (instead of Va < a for all a > 1). The last line is missing an explanation of how Va+3 is less than (a+3) in order to justify the inequality (Va+ 3)² < (a+3)².
Math problems errorsThe write-ups that provided are about different topics in mathematics, including algebra, calculus, and number theory.
The first write-up involves solving a quadratic equation using algebraic manipulation.The second write-up involves solving an equation with algebraic manipulation and factoring a quadratic expression.The third write-up involves multiplying polynomials using distributive property and simplifying the resulting expression.The fourth write-up appears to be incomplete and does not relate to a specific topic.The fifth write-up involves inequalities and specifically the concept of the square root function.Learn more about Math problems errors here:
https://brainly.com/question/17738182
#SPJ4
2.
MP Attend to Precision Gilbert needs
to move 20 pounds of soil from a truck
to a garden. His wheelbarrow can move
6 pounds at one time. How many loads of soil will he have to move?
Explain.
the Snot The area of a rectangular garden is 53 square feet
is the width?
Answers
Answer:
3⅓ moves he have to make in garden
please help me in maths this is composite so find the area and perimeter
Answers
The area will be 40 for the small rectangle because 5*8=40 and 99 for the big rectangle because 11*9=99. To get the whole area, we add those, so 40+99=139.
Area is 139
Perimeter is 66
which box plot a, b, or c is a reasonable summary of the data used to create the histogram? there are 16 data points.
Answers
The boxplot which is reasonable to the summary of the data used to create the histogram is equals to boxplot A. So, correct answer is option (c).
Histogram is a graph which discribes the distribution of data by using of bars of different heights and same width. In this problem, we'll have a histogram and 3 box plots as box plot A, box plot B and box plot C, and we have to choose here which of these 3 box spots is a reasonable summary of the data. We can see that the histogram in above figure is skewed to left because it's maximum data present on the right end. The box plot C, is representing a normally distributed data, but are data is right side distributed so, it is wrong. Similarly, as we see box plot B shows distribution of data in left end, which is also not right choice. So, boxplot A is correct because it's showing the maximum data and the median where we have. We can see the median line over her median on the right hand. Thus, data is very highly negatively skewed hence boxplot A is appropriate.
To learn more Histogram , refer:
https://brainly.com/question/2962546
#SPJ4
Complete question:
See the above figure, which box plot a, b, or c is a reasonable summary of the data used to create the histogram? there are 16 data points.
a) boxplot C
b) boxplot B
c) boxplot A
- Which function is equivalent to y= 3( x + 2) ^2 + 7?
Answers
Answer:
3x² + 12x + 19
Step-by-step explanation:
I'm assuming this is a multiple choice question and you just didn't provide the choices so I will just simplify and hope for the best.
(x+2)(x+2) = x² + 2x + 2x + 4
3(x² + 4x + 4) + 7
3x² + 12x + 12 + 7
3x² + 12x + 19
There are thirty three students in the chess club. There are five more boys than girls in the club. Write and solve a system of equations to find the number of boys and girls in the chess club.
Answers
There are 14 girls and 19 boys in the chess club.
Step-by-step explanation:Let x be girls and y be boys in the chess club. First, we need to write the system.
We know there are 33 students in total.
x + y = 33
We also know there are five more boys than girls in the club.
x + 5 = y
Here is our system of equations and the solving process:x + y = 33
x + 5 = y
First, we will solve for y with substitution:
x + y = 33
x + (x + 5) = 33
2x = 28
x = 14
Now, we will plug in this x-value:
x + y = 33
(14) + y = 33
y = 19
There are 14 girls and 19 boys in the chess club.
two cards are chosen at random from a deck of 52 cards containing 4 kings. the first card is not replaced. which expression could be used to find the probability of choosing two kings?
Answers
Answer: the probability is 1/221
Status
Exam
Find the missing length.
10
4
C=
✓ [?]
Pythagorean Theorem: a? + b2 = ?
Enter
![StatusExamFind the missing length.104C= [?]Pythagorean Theorem: a? + b2 = ?Enter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/070z5amBHeIaHpP5TzyOmxhOZyDqkdJo.png)
Answers
Answer:
116
Step-by-step explanation:
Write a function rule for the statement, “The output is 4 less than the input.” Then, complete the table.
Slope:
y-intercept:
equation:
Answers
Answer:5
Step-by-step explanation:
Answers:
Slope: 1y-intercept: -4equation: y = x-4y outputs: -4, -3, -2, -1, 0Those y outputs are placed into the table in the order shown. For instance, -1 goes right underneath the '3'.
========================================================
Explanation:
Let's find the equation first. The function rule is "the output is 4 less than the input". So whatever the input x is, we subtract off 4 to get the output y.
This leads directly to the equation y = x-4
This is the same as saying y = 1x-4 which is in the form y = mx+b
m = 1 is the slope and b = -4 is the y intercept
------------
Once we have the equation, we plug in the given input x values one at a time to find their corresponding y values.
For example, if x = 0, then,
y = x-4
y = 0-4
y = -4
So we have x = 0 pair up with y = -4. We write -4 underneath the 0 in the table given.
Then we write -3 under the "1" in the table because
y = x-4
y = 1-4
y = -3
And so on. Repeat this process until you get to x = 4.
You should have these ordered pairs
x = 0, y = -4x = 1, y = -3x = 2, y = -2x = 3, y = -1x = 4, y = 0Evaluate the intergral ∫R(6x+5y)2dAwhere R is a triangle with vertices (-2,0), (0,2), and (2,0). Enter the exact answer. Evaluating the Integral:The objective is to evaluate the given integral function. The given integral function is ∬R(6x+5y)2dABy using the given vertices we have find the limits for integration and get a solution. We have to integrate the function with respect to dyanddx
Answers
The given integral function is ∬R(6x+5y)²dA, where R is a triangle with vertices (-2,0), (0,2), and (2,0). To evaluate this integral, we need to find the limits of integration for both x and y.
The triangle can be split into two regions, one with y ranging from 0 to 2 and x ranging from -2 to 0, and the other with y ranging from 0 to 2 and x ranging from 0 to 2. Therefore, the integral can be written as:
∫₀² ∫₋₂⁰ (6x+5y)²dxdy + ∫₀² ∫₀² (6x+5y)²dxdy
Simplifying the integral using algebraic expansion, we get:
∫₀² ∫₋₂⁰ (36x² + 60xy + 25y²)dxdy + ∫₀² ∫₀² (36x² + 60xy + 25y²)dxdy
Evaluating the integral and simplifying, we get the final answer as 320/3.
In summary, to evaluate the given integral function, we needed to find the limits of integration for both x and y, which were obtained by splitting the triangle into two regions. Then, we simplified the integral using algebraic expansion and evaluated it to get the final answer.
To learn more about integral click here :
brainly.com/question/31401227
#SPJ11
1. What is the m2<5? Explain how you know. (2 points)
2.What is the measure of the sum of the angles in a triangle? (2 points)
3. L3 is in a triangle with L4 and L5. Write and solve an equation to find the m L3. (2 points)
4. What is the measure of a straight angle? (2 points)
5. L2 is in a straight line with L1 and L3. Write and solve an equation to find the m L2 (2 points)
Answers
What is the value of z in the image.
Answers
13 is the value of z from the given figure.
What are the properties of Triangle?The properties of the triangle are:
The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.From the given figure,
∠ABE + ∠EBC =. 180
∠EBC = 180- ∠ABE
∠EBC = 180 - 9z -----(1)
∠ECB + 115 = 180
∠ECB = 65-----(2)
IN ∆EBC
∠BEC + ∠ECB + ∠EBC = 180
4Z + 180- 9Z + 65 = 180 ---------(from eq i & ii)
-5Z = -65
Z = -65/-5y
Z = 13
The value of z from the given figure is 13.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
Complete question:
Each vertical cross-section of the triangular prism shown below is an isosceles triangle.
What is the height, h, of the triangular prism?
Round your answer to the nearest tenth.
The height is
units.
Answers
Answer: The height is 3 units.
Step-by-step explanation:
By using the give figure we can form right angle out of the whole figure with a base of 4 and an hypotenuse of 5.
By using this information we can use the Pythagorean Formula to find the height
a^2 + b^2 =c^2 a= base, b = height and c will be the hypotenuse.
4^2 + b^2 = 5^2 Solve for B
16 + B^2 = 25
-16 -16
b^2 = 9
b = \(\sqrt{9}\)
b = 3
The height, h, of the triangular prism is 3 units.
What is an isosceles triangle?Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.
Given that, vertical cross-section of the triangular prism shown in the given figure is an isosceles triangle.
Here, equal sides of an isosceles triangle is 5 units and base of the isosceles triangle is 8 units.
By using Pythagoras theorem,
5²=h²+4²
25=h²+16
h²=9
h=3
Therefore, the height, h, of the triangular prism is 3 units.
To learn more about an isosceles triangle visit:
https://brainly.com/question/10147636.
#SPJ7
Find the equation of the line.
Answers
the line go through 2 points ( -4 ; -5 ) and ( 6 ; 4 )
ANSWER: \(y=\frac{9}{10}x -\frac{7}{5}\)
ok done. Thank to me :>
the graphs of f(x)=-2x and g(x)=(1/2)^x are shown. what are the solutions to thr equation -2x=(1/2)^x? select each correct answer.
-2
-1
2
4
Answers
Answer:
-2Step-by-step explanation:
hello :
f(x)=-2x and g(x)=(1/2)^x
f(-2)=-2(-2) =4
g(-2)=(1/2)^-2 = 1/2^-2 = 2²=4
Determine the value of x for the triangle below if K is the incenter.E9.x-16X =لاGDHK184x + 9
Answers
Solution:
Given the triangle below where K is in the incenter:
Thus, we have
step 1: In the triangle DGK, find DK.
Thus, by Pythagoras theorem, we have
\(DK=\sqrt{18^2+(9x-16)^2}\)step 2: In the triangle KDI, find DK.
Similarly, we have
\(DK=\sqrt{18^2+(4x+9)^2}\)Step 3: Equate the equations in steps 1 and 2.
This gives
\(\begin{gathered} \sqrt{18^2+(9x-16)^2}=\sqrt{18^2+(4x+9)^2} \\ take\text{ the square of both sides,} \\ \Rightarrow18^2+(9x-16)^2=18^2+(4x+9)^2 \\ thus,\text{ we have} \\ 9x-16=4x+9 \\ add\text{ -4x to both sides,} \\ 9x-4x-16=-4x+4x+9 \\ 5x-16=9 \\ add\text{ 16 to both sides,} \\ 5x-16+16=9+16 \\ \Rightarrow5x=25 \\ divide\text{ both sides by the coefficient of x, which is 5} \\ \frac{5x}{5}=\frac{25}{5} \\ \Rightarrow x=5 \end{gathered}\)The value of x is
\(5\)
What is the equation for the line of symmetry in this figure?
Answers
Answer:
Step-by-step explanation:
Y-axis is the line of symmetry as it divides the figure into two equal parts
4.89 x 2.2 find the product
Answers
Answer: Hi!
4.89 * 2.2 = 10.758 (rounded is 10.76 or 10.8)
Tip: Line up the terms vertically and multiply.
Hope this helps!
can someone help me here
NONSENSE=REPORT
topic: Circles and its Concept
Answers
Answer:
Step-by-step explanation:
Circumference of a circle: 2πrArea of a circle: πr²π = 3.14r (radius) = d/21. Circumference: 2(3.14)(4.2) = 26.38 in.
Area: πr² = 3.14(4.2)² = 55.39 in.²
2. Circumference: 2(3.14)(1) = 6.28 m.
Area: πr² = 3.14(1)² = 3.14 m.²
Hope this helps!
The position vector r describes the path of an object moving in space. Position Vector Time r(t) = √ti + 5tj + 4t²k t = 9 (a) Find the velocity vector, speed, and acceleration vector of the object.
Answers
The velocity vector is 3i + 5j + 72k, the speed is √(58), and the acceleration vector is 0i + 0j + 8k.
Given the position vector r(t) = √(t)i + 5tj + 4t^2k, we need to find the velocity vector, speed, and acceleration vector of the object at t = 9.
To find the velocity vector, we differentiate the position vector with respect to time. Each component of the position vector will be differentiated separately.
The derivative of √(t) with respect to t is (1/2√(t)), the derivative of 5t with respect to t is 5, and the derivative of 4t^2 with respect to t is 8t.
Thus, the velocity vector v(t) = (1/2√(t))i + 5j + 8tk.
To find the velocity vector at t = 9, we substitute t = 9 into the velocity vector:
v(9) = (1/2√(9))i + 5j + 8(9)k = (1/6)i + 5j + 72k.
Therefore, the velocity vector of the object at t = 9 is 3i + 5j + 72k.
To find the speed of the object, we calculate the magnitude of the velocity vector:
Speed = |v(9)| = √[(3)^2 + (5)^2 + (72)^2] = √(9 + 25 + 5184) = √(58).
Thus, the speed of the object at t = 9 is √(58).
To find the acceleration vector, we differentiate the velocity vector with respect to time. Since the velocity vector does not have any t-dependent terms, its derivative will be zero.
Therefore, the acceleration vector a(t) = 0i + 0j + 8k.
Thus, the acceleration vector of the object is 0i + 0j + 8k.
In summary, at t = 9, the velocity vector of the object is 3i + 5j + 72k, the speed is √(58), and the acceleration vector is 0i + 0j + 8k.
To learn more about position vector, click here: brainly.com/question/31401563
#SPJ11
Triangles ABC and EDC are outlined on a bridge. The triangles share vertex C and angles D and B are right angles. A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 5x − 5 and EC = 3x + 9, find the distance between the top and bottom of the bridge, in feet.
Answers
CHECK THE ATTACHED FIQURE FOR THE BRIDGE
Answer:
60 ft
Step-by-step explanation:
From the question we know that triangles ABC and EDC are in a 1:1 with this given ratio it implies that
triangles ABC and EDC are congruent then we can say
side EC = side AC
3x + 9 = 5x - 5
Then we can simplify to know value of x
3x + 14= 5x
2x = 14
x = 7
But we know that AC= 5x - 5 , then substitute value of x into it
AC = 5x + 5 = 5(7) - 5
= 35 - 5
AC= 30 ft
Also EC= 3x + 9 then substitute value of x into it
EC = 3x + 9 = 3(7) + 9
= 21 + 9
EC= 30 ft
Then the the distance between the top and bottom of the bridge, in feet, = EC+AC
= 30 + 30 = 60 ft
Answer:
60 ft
Step-by-step explanation:
i did the test
write the equations of all the circles
Answers
The equation of a circle with center (a, b) and radius r is:
(x - a)^2 + (y - b)^2 = r^2
(x, y) represents any point on the circle
What is a circle?A circle is described as a shape consisting of all points in a plane that are at a given distance from a given point, the center.
The properties of the circle are as follows:
The circles are said to be congruent if they have equal radii.The diameter of a circle is the longest chord of a circle.Equal chords of a circle subtend equal angles at the centre.The radius drawn perpendicular to the chord bisects the chord.Learn more about properties of the circle at: https://brainly.com/question/4244936
#SPJ1