The volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]
The volume of a right circular cone is given by the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cone.
Given that the height of the cone is multiplied by 3, the new height [tex](\( h' \))[/tex] becomes 3 times the original height [tex](\( h \))[/tex]:
[tex]\[ h' = 3h \][/tex]
Now, let's find the volume of the new cone with the updated height:
[tex]\[ V' = \frac{1}{3} \pi r^2 (3h) \][/tex]
[tex]\[ V' = \pi r^2 (h) \times 3 \][/tex]
So, the volume of the new cone is three times the original volume.
Now, let's dive into the explanation:
When the height of a cone is multiplied by a factor, the volume of the cone is directly proportional to the cube of that factor. This is because the volume formula contains the height term raised to the power of 3. So, if the height is tripled, the volume will be multiplied by[tex]\(3^3 = 27\).[/tex]
Alternatively, we can calculate it directly:
Original Volume: [tex]\(V = \frac{1}{3} \pi r^2 h\)[/tex]
New Volume:[tex]\(V' = \frac{1}{3} \pi r^2 (3h) = \pi r^2 h \times 3\)[/tex]
Therefore, the volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]
Complete question:
The height of a right circular cone is multiplied by 3, but its radius remains fixed. By what factor will the volume of the cone be multiplied?
Find two consecutive integers whose sum is 73. Which of the following equations could be used to solve the problem?
a:2x = 73
b: 2x + 1 = 73
c;2x + 2 = 73
d:x2 + 1= 73
Answer:
b: 2x + 1 = 73
Step-by-step explanation:
Let x be the smaller integer,
Then the larger integer consecutive to x is x + 1,
Sum of these integers = x + x + 1 = 2x + 1
According to the question,
The sum is 73
⇒ 2x + 1 = 73
Which is the required equation that could be used to solve the problem.
Option 'b' is correct.
How do I write the height h of the rectangle as a function of x.
To write the height h of the rectangle as a function of x, you need to understand the relationship between the height and the other variables involved.
To write the height h of the rectangle as a function of x, you need to understand the relationship between the height and the other variables involved. In a rectangle, the height is typically perpendicular to the base.
So, if we assume that x represents the base length, then the height h can be written as a function of x using an equation.
For example, if the rectangle has a fixed width, the height can be calculated using the following equation: h = f(x), where f is the function that describes the relationship between the base length x and the height h.
Learn more about Rectangle here:https://brainly.com/question/34750862
#SPJ3
How to rewrite the expression. With the steps. Use an exponent, rather than repeated multiplication. (–4)(–4)
For this case we have the following expression:
[tex](-4) (- 4)[/tex]
Using law of exponents we have:
[tex](a ^ m) (a ^ n) = a ^ {m + n}[/tex]
We use the definition to rewrite the given expression
Rewriting we have:
[tex](-4) (- 4) = (- 4)^{ 1 + 1}\\(-4) (- 4) = (- 4) ^ 2[/tex]
Answer:
The rewritten expression is given by:
[tex](-4) (- 4) = (- 4) ^ 2[/tex]
Simplify the product using FOIL. (2x – 7)(5x 5)
Answer:
[tex]10x^2-25x-35[/tex]
Step-by-step explanation:
The FOIL method is used to multiply two binomials.
FOIL stand for:
First : Multiply the first term in each set of parenthesis.
Outer : Multiply the outer term in each set of parenthesis.
Inner : Multiply the inner term in each set of parenthesis.
Last: Multiply the last term in each set of parenthesis.
Given that:
[tex](2x-7)(5x+5)[/tex]
Using the foil method:
[tex]2x(5x+5)-7(5x+5)[/tex] [Using distributive property]
⇒[tex]10x^2+10x -(35x+35)[/tex]
⇒[tex]10x^2+10x -35x-35[/tex]
Combine like terms:
⇒[tex]10x^2-25x-35[/tex]
Therefore, the product of (2x – 7)(5x+5) using FOIL method is, [tex]10x^2-25x-35[/tex]
Find the average rate of change for f(x) = x2 − 3x − 10 from x = 4 to x = 6
Answer:
what's the answer
Step-by-step explanation:
What are the amplitude and midline?
Amplitude: 1; midline: y = 1
Amplitude: 1; midline: y = 2
Amplitude: 2; midline: y = 1
Amplitude: 2; midline: y = 2
Answer:
D) Amplitude;2 ; midline: y= 2
Step-by-step explanation:
The total height of the curve = 4
Amplitude = 4/2 = 2
The middle line is y = 2
Therefore, answer is D) Amplitude;2 ; midline: y= 2
Hope this will helpful.
Thank you.
A charity fair raised $6,000 by selling 500 lottery tickets. There were two types of lottery tickets: A tickets cost $10 each, and B tickets cost $60 each. How many tickets of each type were sold?
A.5, 185
B.370, 230
C.410, 90
D.480, 20
E.250, 250
What is the Solution of the following system?
{-3x -2y = -12
{9x + 6y= -9
Imagine those two bracket things are one big one connecting both equations, and the answers are A (2,1) B No Solutions C (-2, -1) D Infinitely Many Solutions
@Emma11234
What is the surface area of the prism?
a. 82 yd2
b. 90 yd2
c. 96 yd2
d. 108 yd2?
Answer:
d. 96
Step-by-step explanation:
on usa test prep
Cody is twice as old as evan and seven years ago the sum of their age was 1010. find the age of each boy now.
Use complete sentences to describe how a postulate becomes a theorem.
Final answer:
A postulate becomes a theorem through a process of logical deduction and proof. Starting from basic assumptions or postulates, mathematicians derive theorems using step-by-step logical inferences, forming the basis for further deductions, such as with Newton's second law or the Schrödinger equation in physics.
Explanation:
A postulate is a statement assumed to be true without proof and serves as a starting point for deducing and inferring other truths. The transformation from a postulate into a theorem involves a process of logical deduction and rigorous proof. When we establish a theorem, what we're doing is showing that the statement necessarily follows from the previously accepted postulates and theorems by a sequence of logical deductions. For example, in geometry, one might postulate that a straight line can be drawn between any two points, and from there, using a series of logical steps, derive the Pythagorean theorem. The Pythagorean theorem's validity is then supported by the fact that it can be derived from these fundamental postulates through a sequence of unassailable logical steps within a proof.
To illustrate, a textbook might first introduce a straightforward theorem like: "If we start out with four lines that form a rectangle, we can draw a new, fifth line that divides the rectangle into two identical triangles." From this, using the fifth line as a postulate, more complicated theorems can be constructed. Similarly, in physics, Newton's second law (f = ma) and the Schrödinger equation in quantum mechanics begin as postulates that explain a wide range of observations. Once propositions like these are established, they can be used to deduce further principles that build upon them.
Evaluate the integral of the quotient of the sine of x and the square root of the quantity 1 plus cosine x, dx.
Answer:
[tex]-2\sqrt{1+\cos(x)}+C[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus[tex]\boxed{\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))}[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{\sin(x)}{\sqrt{1+\cos(x)}}\;\text{d}x[/tex]
To evaluate the given integral, we can use the method of substitution.
Integration by substitution is a way of integrating a function of a function by simplifying the integral. To integrate by substitution, write part of the function in terms of u, where u is some function of x.
Use the substitution u = 1 + cos(x).
Start by differentiating u with respect to x:
[tex]\begin{aligned}u&=1+\cos(x)\\\\\dfrac{\text{d}u}{\text{d}x}&=0-\sin(x)\\\\\dfrac{\text{d}u}{\text{d}x}&=-\sin(x)\end{aligned}[/tex]
Now rearrange the equation for du/dx to get dx on its own:
[tex]\text{d}u=-\sin(x)\:\text{d}x[/tex]
[tex]\text{d}x=-\dfrac{1}{\sin(x)}\:\text{d}u[/tex]
Substitute everything into the original expression:
[tex]\begin{aligned}\displaystyle \int \dfrac{\sin(x)}{\sqrt{1+\cos(x)}}\;\text{d}x&=\int \dfrac{\sin(x)}{\sqrt{u}}\cdot -\dfrac{1}{\sin(x)}\:\text{d}u\\\\ &=\int -\dfrac{1}{\sqrt{u}}\:\text{d}u\end{aligned}[/tex]
Simplify the integral and evaluate:
[tex]\begin{aligned}&=\displaystyle \int -u^{-\frac{1}{2}}\:\text{d}u\\\\&=\dfrac{-u^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+C\\\\&=\dfrac{-u^{\frac{1}{2}}}{\frac{1}{2}}+C\\\\&=-2\sqrt{u}+C\end{aligned}[/tex]
[tex]\textsf{Finally, substitute $u=1+\cos(x)$ back in:}[/tex]
[tex]=-2\sqrt{1+\cos(x)}+C[/tex]
Learn more about integration by substitution here:
https://brainly.com/question/32631646
What is the value of x?
a. 86.5°
b. 43.25°
c. 133.25°
d. 46.75°
Answer:
x = 43.25
Step-by-step explanation:
In the given figure :
In ΔDEF ,
DF = FE
⇒ ∠DEF = ∠FDE = x ( Angles opposite to equal sides are equal)
Now, using angles sum property of a triangle in ΔDEF
∠DEF + ∠FDE + ∠DFE = 180
⇒ ∠FDE + ∠FDE + 93.5 = 180
⇒ x + x = 180 - 93.5
⇒ 2x = 86.5
⇒ x = 43.25
Answer: D. 43.25
Step-by-step explanation:
I have just taken the test
WILL MARK BRAINLIEST!!
Write log3 6 as a logarithm of base 2.
log base 2 of 3 over log base 2 of 6
log base 2 of 6 over log base 2 of 3
log base 3 of 2 over log base 6 of 2
log base 6 of 2 over log base 3 of 2
Answer:
Option 2 - log base 2 of 6 over log base 2 of 3
Step-by-step explanation:
Given : Expression [tex]\log_3 6[/tex]
To find : Write the expression as a logarithm of base 2?
Solution :
Expression [tex]\log_3 6[/tex]
Applying the change-of-base formula,
[tex]\log_a(x)= \frac{\log_b(x)}{\log_b(a)}[/tex]
On comparing, a = 3, x = 6, b = 2
Substitute in the formula,
[tex]\log_3 (6)= \frac{\log_2(6)}{\log_2(3)}[/tex]
Therefore, Option 2 is correct.
Option 2 - log base 2 of 6 over log base 2 of 3
Number 5555555555555
Formula for calculating commission
Commission is calculated by multiplying sales revenue by the commission rate; this incentivizes sales, aiming to balance salary, commission, and overall business objectives like profitability and customer satisfaction.
The formula for calculating commission is usually based on the sales revenue multiplied by the commission rate. If, for example, a sales employee sells $10,000 worth of products and the commission rate is 5%, the calculation would be $10,000 x 0.05 = $500.
Commissions serve as a motivational tool in sales. They provide sales employees with an incentive to increase sales, as their earnings are directly linked to the success of their efforts. Optimal sales volume, profitability, and customer satisfaction are central to a well-balanced compensation plan that incorporates both a base salary and a commission structure.
BRAINLIESTTTT ASAP PLEASE
The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x – 1. What is the value of x?
Answer:
10 or answer B.
Step-by-step explanation:
Relationship B has a greater rate than Relationship A.
This graph represents Relationship A. Which equations could represent Relationship B?
Select each correct answer.
a) y = 3/4x
b) y = 0.6x
c) y = 1/4x
d) y = 2/3x
The equation (a) y = 3/4x, equation (b) y = 0.6x, equation (d) y = 2/3x are correct option because they have greater rate than A
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
We have;
Relationship B has a greater rate than Relationship A.
From the graph, the rate of A or slope will be:
A(m) = (4-2)/(8-4) = 2/4
A(m) =1/2 = 0.5
From the given option, the equation y = 3/4x, y = 0.6x, and y = 2/3x has a greater rate than A which is 3/4, 0.6, and 2/3 respectively.
Thus, the equation (a) y = 3/4x, equation (b) y = 0.6x, equation (d) y = 2/3x are correct option because they have greater rate than A
Learn more about the slope here:
brainly.com/question/3605446
#SPJ2
The graph of the function B is shown below. If B(x) = -1, then what is x?
A. -1
B. 1
C. 2
A is NOT The answer, the answer is either B or C!!!
What number can you add to 7√ to get a rational number?
The number that can be added to √7 to get a rational number is -√7.
What are rational numbers?A number of the form a/b where a and b are integers and b ≠ 0 is called a rational number.
The given number is √7.
√7 is an irrational number.
Note that the square root of prime numbers is irrational, therefore, to get a rational number by addition, the only way is to add the negative reciprocal of the given irrational number.
The negative reciprocal of √7 is -√7, therefore, add -√7 to √7:
√7 + (-√7) = 0 (a rational number).
Hence, the number that can be added to √7 to get a rational number is -√7.
Learn more about rational numbers here:
https://brainly.com/question/24398433
#SPJ2
H E L P P L E A S E Franklin deposited $1,400 in a savings account that earns simple interest of 6.75%. What is the balance in his account at the beginning of the third quarter?
A. $78.75
B. $1,447.25
C. $1,505
D. $105
Please explain your answer CLEARLY so I can use the principles for future reference. PLEASE no formulas of A = whatever or D = whatever. I don't get that. I try but it doesn't fit if it makes sense. :/ Thanks!
For the following figure, complete the statement for the specified points.
Points A, B, C, and Q are _____.
collinear
coplanar
both collinear and coplanar
neither collinear nor coplanar
Points A, B and Q are coplanar.
What are coplanar points?Points or lines are said to be coplanar if they lie in the same plane. Example 1: The points P , Q , and R lie in the same plane A . They are coplanar.
What are coplanar lines?A line which is in the same plane as another line. Any two intersecting lines must lie in the same plane, and therefore be coplanar.
What are collinear points?Three or more points that lie on the same line are collinear points . Example : The points A , B and C lie on the line m.
From the figure we can observe
Points A, B and Q are not in the same line.
Three points are collinear only if they are on the same line
3 points are collinear if we can draw a line that connects the points.
In the image A, Q are in a same line but B is not in the line of A and Q.
Points A, B and Q are on the base, So the three points are coplanar but not collinear.
So, Points A, B and Q are coplanar.
Find out more information about coplanar and collinear here
https://brainly.com/question/24250339
#SPJ2
please help me out with this simple question I REALLY NEED THIS :((((((((
PLEASE HELP ILL GIVE MEDALS AND MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!! NEEDS TO BE ALEGABRA 2 MEATHOD!!!!!!!!
Solve 1/b = 6/5b + 1
20 points!!
The coordinates of the vertices of quadrilateral JKLM are J(−3, 2) , K(3, 5) , L(9, −1) , and M(2, −3) .
Which statement correctly describes whether quadrilateral JKLM is a rhombus?
Quadrilateral JKLM is not a rhombus because there is only one pair of opposite sides that are parallel.
Quadrilateral JKLM is a rhombus because opposite sides are parallel and all four sides have the same length.
Quadrilateral JKLM is not a rhombus because there are no pairs of parallel sides.
Quadrilateral JKLM is not a rhombus because opposite sides are parallel but the four sides do not all have the same length
Using the distance formula, we can calculate the distances between the vertices of quadrilateral JKLM. After performing these calculations, we can determine that not all sides have the same length, thus quadrilateral JKLM is not a rhombus.
Explanation:To determine if quadrilateral JKLM is a rhombus, we need to check if all four sides are of equal length because a defining property of a rhombus is that it has all sides of equal length. The length between two points (x1, y1) and (x2, y2) can be found using the distance formula which is √[(x2-x1)² + (y2-y1)²].
After calculating, we find:
J-K distance = √[(5-2)² + (-3-3)²] = √42
K-L distance = √[(-1-5)² + (9-3)²] = √52
L-M distance = √[(-3- -1)² + (2-9)²] = √52
M-J distance = √[(2- -3)² + (-3-2)²] = √42
Therefore, the distance between vertices J-K and L-M are the same, and the distance between vertices K-L and M-J are the same, but the two pairs are not in themselves equal to each other. As such, quadrilateral JKLM is not a rhombus because all sides do not have the same length.
Learn more about Quadrilateral JKLM here:https://brainly.com/question/34198104
#SPJ13
An 8-ounce bottle of lotion costs $4.50. What is the cost per ounce?
What is the average rate of change of d(t) between 2 seconds and 6 seconds, and what does it represent? 128 m/s; it represents the average speed of the object between 2 seconds and 6 seconds 80 m/s; it represents the average speed of the object between 2 seconds and 6 seconds 128 m/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds 80 m/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds
If a(x) = 3x + 1 and b(x)= √x-4 , what is the domain of (b*a)(x)
Answer: The correct option is C. The domain of [tex](b\circ a)(x)[/tex] is [tex][0,\infty)[/tex].
Explanation:
It is given that,
[tex]a(x)=3x+1[/tex]
[tex]b(x)=\sqrt{x-4}[/tex]
First we have to find the composite function [tex](b\circ a)(x)[/tex].
[tex](b\circ a)(x)=b(a(x))[/tex]
[tex](b\circ a)(x)=b(3x+1)[/tex]
[tex](b\circ a)(x)=\sqrt{3x+1-4}[/tex]
[tex](b\circ a)(x)=\sqrt{3x-3}[/tex]
We know that a root function is defined for only positive values therefore the composite function is defined if,
[tex]3x-3\geq 0[/tex]
[tex]3x\geq 3[/tex]
[tex]x\geq 1[/tex]
The function is defined for all the values of x which are greater than or equal to 1. Therefore the domain of [tex](b\circ a)(x)[/tex] is [tex][0,\infty)[/tex] and option C is correct.
How do I do this my Calculator will not do this
The numbers in order from least to greatest are:
√12,3.6,25/7,49 √4To order the numbers from least to greatest, we need to convert them all to decimals.
25/7 = 3.57142857...
√12 = 3.4641016151377544
49 V4 = 49/4 = 12.25
Therefore, the numbers in order from least to greatest are:
√12,
3.6,
25/7,
49 √4
For such more question on numbers
https://brainly.com/question/30765230
#SPJ12