Find the volume of a right circular cone that has a radius of 4 inches and a height of 12 inches
Final answer:
The volume of a right circular cone with a radius of 4 inches and a height of 12 inches is calculated using the formula V = (1/3)πr²h, resulting in a volume of 64π cubic inches.
Explanation:
The question asks to find the volume of a right circular cone with a specific radius and height. To calculate the volume of a cone, you use the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone. Since we're given the radius as 4 inches and the height as 12 inches, we substitute these values into the formula: V = (1/3)π(4²)(12).
Carrying out the calculation, we have V = (1/3)π(16)(12) = (1/3)π(192) = 64π inches³. Therefore, the volume of the cone is 64π cubic inches.
Effective rate (APY) is: Never related to compound table Interest for one year divided by annual rate Interest for one year divided by principal for 2 years Interest for one year divided by principal None of these
Leah likes to stretch 5 minutes for every 10 minutes of dancing. How many minutes should she stretch if she is doing a 50 minute dance class?
Leah should stretch for 25 minutes during a 50-minute dance class, as she stretches for 5 minutes for every 10 minutes of dancing.
Leah stretches for 5 minutes for every 10 minutes of dancing. To calculate how much time she should be stretching during a 50-minute dance class, we need to apply a simple ratio. For every 10 minutes of dance, she stretches for 5 minutes, which is half the time spent dancing. We can set up the proportion as follows: 5 minutes of stretching / 10 minutes of dancing = X minutes of stretching / 50 minutes of dancing.
Now, solving for X gives us 5/10 = X/50, which simplifies to X = (5/10) × 50 = 25 minutes. Therefore, Leah should stretch for 25 minutes during her 50-minute dance class.
Find the sum of a finite geometric sequence from n = 1 to n = 8, using the expression −2(3)^n − 1.
F(x,y)=eâ8xâx2+8yây2. find and classify all critical points of the function. if there are more blanks than critical points, leave the remaining entries blank.
To find and classify critical points of a two-variable function, calculate and set the first partial derivatives to zero to find critical points. Then, use the second derivatives to classify these points. The determinant of the Hessian matrix, made up of the second derivatives, contributes to this classification.
Explanation:To find the critical points of the function F(x,y)=e^8x - x^2 + 8y - y^2, you first need to find the partial derivatives F_x and F_y and set them both equal to zero.
F_x = 8e^8x - 2x and F_y = 8 - 2y. By setting these equal to zero and solving for x and y, you will find the critical points.
Once the critical points are found, we classify them using the second derivative test. This involves computing the second partial derivatives F_xx, F_yy, and F_xy, and evaluating them at the critical points.
Finally, we calculate the determinant D of the Hessian matrix, composed of the second derivatives, at the critical points. The signs and values of these results and the determinants help classifying the critical points.
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Gabrielle's age is two times Mikhail's age. The sum of their ages is 72 . What is Mikhail's age?
The age of Mikhail's is 24 years old.
To find Mikhail's age, let's denote Mikhail's age as ( x ) and Gabrielle's age as ( 2x ) (since Gabrielle is twice as old as Mikhail). We know the sum of their ages is 72. We can set up an equation to represent this information:
[tex]\[ x + 2x = 72 \][/tex]
Step 1: Combine like terms
Combine the (x) terms on the left side of the equation:
[tex]\[ x + 2x = 3x \][/tex]
So, the equation simplifies to:
[tex]\[ 3x = 72 \][/tex]
Step 2: Solve for ( x )
To find the value of ( x ), divide both sides of the equation by 3:
[tex]\[ x = \frac{72}{3} \][/tex]
[tex]\[ x = 24 \][/tex]
Therefore, Mikhail's age is 24 years old.
Mikhail's age is 24. Gabrielle is 48.
Let's solve it step by step:
1. Let's represent Gabrielle's age as [tex]\( G \)[/tex] and Mikhail's age as [tex]\( M \)[/tex].
2. According to the given information, Gabrielle's age is two times Mikhail's age, so we can express this as an equation:
[tex]\[ G = 2M \][/tex]
3. We also know that the sum of their ages is 72, which can be expressed as another equation:
[tex]\[ G + M = 72 \][/tex]
4. Now, we have a system of two equations:
[tex]\[ G = 2M \][/tex]
[tex]\[ G + M = 72 \][/tex]
5. Substitute the value of [tex]\( G \)[/tex] from the first equation into the second equation:
[tex]\[ 2M + M = 72 \][/tex]
[tex]\[ 3M = 72 \][/tex]
6. Divide both sides by 3 to solve for [tex]\( M \)[/tex]:
[tex]\[ M = \frac{72}{3} \][/tex]
[tex]\[ M = 24 \][/tex]
7. So, Mikhail's age is 24 years.
Now, to verify, we can find Gabrielle's age using the first equation:
[tex]\[ G = 2M \][/tex]
[tex]\[ G = 2(24) \][/tex]
[tex]\[ G = 48 \][/tex]
Gabrielle's age is indeed 48 years.
So, to recap, Mikhail's age is 24 years.
solve for m
2m = -6n -5; n = 1, 2 ,3
A music company executive must decide the order in which to present 6 selections on a compact disk. how many choices does she have
What expression is equivalent to 10x2y+25x2
A ship traveled at an average rate of 22 miles per hour going east. It then traveled at an average rate of 17 miles per hour heading north. If the ship traveled a total of 212 miles in 11 hours, how many miles were traveled heading east?
A package contains 3 cups of trail mix. A serving of trail mix is ⅓ cup. How many servings of trail mix is in the package?
if log75=1.875
then what is the value of log (sub 100) 75?
Answer: The required value of [tex]\log_{100}75[/tex] is 0.9375.
Step-by-step Explanation: Given that [tex]\log 75=1.875.[/tex]
We are to find the value of the following logarithm :
[tex]log_{100}75.[/tex]
We will be using the following properties of logarithm :
[tex](i)~\log_ba=\dfrac{\log a}{\log b}\\\\\\(ii)~\log a^b=b\log a.[/tex]
Therefore, we have
[tex]\log_{100}75\\\\\\=\dfrac{\log 75}{\log100}\\\\\\=\dfrac{1.875}{\log10^2}\\\\\\=\dfrac{1.875}{2\times\log10}\\\\\\=\dfrac{1.875}{2}~~~~~~~~~~~[since~\log10=1]\\\\\\=0.9375.[/tex]
Thus, the required value of [tex]\log_{100}75[/tex] is 0.9375.
The average winter snowfall in City A is 105 cm. City B usually gets 2.8 m of snow each winter. Compare the yearly snowfall in the two cities. Complete parts a and b. (A) the difference in one year is __ m. (B) the difference over two years is ___ cm
help which statement is true
Divide and state the quotient in simplest form.
The house shown is a composite of more than one shape. Which of these methods would you use to find the volume of the house?
The method that can be used to find the volume of the house is:
Add the volume of a rectangular prism to the volume of the triangular prism.
Step-by-step explanation:In order to find the volume of the house we need to find the volume of the bottom part of the house which in the shape of a rectangular prism or cuboid and volume of the top of the house which is in the shape of a triangular prism.
Hence, the total volume of the house is:
Volume of rectangular prism+Volume of triangular prism.
Can someone answer this ASAP? I got 52 which as a decimal would be 0.52 but it was wrong. What is the correct answer?
since cone B is bigger it needs to weigh more than 20 lbs.
5/13 = 20/X
x=52 LBS
Theo started to solve the quadratic equation (x + 2)2 – 9 = –5. He added 9 to both sides and the resulting equation was (x + 2)2 = 4. Next, he took the square root of each side. Which was the resulting equation of that step?
we have
[tex](x + 2)^{2}-9=-5[/tex]
Adds [tex]9[/tex] both sides
[tex](x + 2)^{2}-9+9=-5+9[/tex]
[tex](x + 2)^{2}=4[/tex]
square root both sides
[tex](x+2)=(+/-)\sqrt{4}\\(x+2)=(+/-)2\\x1=2-2=0 \\x2=-2-2=-4[/tex]
therefore
the answer is
the resulting equation is [tex](x+2)=(+/-)2[/tex]
Answer: [tex](x+2) = \pm 2[/tex]
Step-by-step explanation:
If the given expression is,
[tex](x + 2)^2 - 9 = -5[/tex]
For solving this expression, By adding 9 on both sides,
[tex](x+2)^2 = 4 [/tex]
By taking square root on both sides,
[tex]\sqrt{(x+2)^2} = \sqrt{4}[/tex]
[tex]({(x+2)^2)^{\frac{1}{2} = \pm 2[/tex] [tex]( \text{ Because, }\sqrt{4} = \pm 2 \text { and }\sqrt{x} = x^{\frac{1}{2}})[/tex]
[tex]{(x+2)^{2\times \frac{1}{2} = \pm2[/tex] [tex]((a^m)^n=a^{m\times n})[/tex]
[tex](x + 2) = \pm2[/tex]
Which is the required next step.
what is the midpoint of 45-53
Ruby is visiting a wildlfe center to gather information for he paper . The center has circular pond with a diameter if 20. What is the approximate area of the pond ?
area = PI x r^2
r = 20/2 = 10
3.14 x 10^2 = 314 square units
How can you use models find the volume of composite figures
The altitude of a triangle is increasing at a rate of 1 cm/ min while the area of the triangle is increasing at a rate of 2 cm2 / min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm2 ?
The rate of change of the base of a triangle, given an increase of the altitude at 1 cm/min and an increase in area at 2 cm2/min, when the altitude is 10 cm and the area is 100 cm2, is 4 cm/min.
Explanation:The subject of this question is related to the field of calculus, specifically dealing with determining the rate of change, or the derivative, of a function. We're asked to determine the rate at which the base of the triangle is changing when the altitude is 10 cm and the area is 100 cm2, given that the altitude of the triangle is increasing at a rate of 1 cm/ min and the area of the triangle is increasing at a rate of 2 cm2 / min.
We know that the area of a triangle is given by the formula 1/2 * base * height. When it comes to rates, we can differentiate this with respect to time t to get dA/dt = 1/2 * (base * dh/dt + height * db/dt) where dA/dt is the rate of change of the area, dh/dt is the rate of change of the height, and db/dt is the rate of change of the base.
Given that dA/dt = 2 cm2/min and dh/dt = 1 cm/min, and we are finding db/dt when the height is 10 cm and the area is 100 cm2, we substitute these values to solve for db/dt. This simplifies to find that the base is increasing at a rate of 4 cm/min.
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Thomas works as an underwater photographer he starts at a position that is 15 feet below sea level he rises 9 feet then descends 12 feet to take a photo of a coral reef write and evaluate an expression to find his position relative to sea level when he took a photo
Find the maximum and minimum values of f(x,y) = 8x+y for the polygonal convex set having vertices at (0, 0), (4, 0), (3, 5), (0, 5).
What is the third step when factoring the trinomial ax^2+bx+c, after you have factored out a common factor in each term?
a.) Add the linear terms together
b.)Multiply the factors together to check
c.)Factor the simplified trinomial
d.) Distribute the common factor
After factored out a common factor in each term. Factor the simplified trinomial. Option c) is correct.
Step after the the third step when factoring the trinomial ax^2+bx+c to be determine.
Factors is are the sub multiples of the value.
Here,
After factored out a common factor in each term. The next step come is to factor the simplified term which implies taking common and kept in parenthesis.
Thus, after factored out a common factor in each term. Factor the simplified trinomial.
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Charles can type 675 words in 9 minutes. How many words can Charles types in 13 minutes?
Addison has 15 fewer pieces of candy than Ronny does. Is this situation modeled by an expression or equation? How do you know?
Equation, because Addison's candy is equal to 15 less than Ronny's candy.
i hope this help you
Answer:
Equation, because Addison's candy is equal to 15 less than Ronny's candy.
Step-by-step explanation:
Write an equation of the line perpendicular to the line 8x+15y=12 and containing the point (11,17) write the answer in standard form
The slope of a line perpendicular to another line has a slope which is the negative reciprocal of that line or:
m1 = -1/m2
First, we convert the given equation into slope-intercept form of a line: y = mx + b
8x + 15y = 12
15y = -8x + 12
y = (-8/15) x + 0.8
m1 = -8 / 15
Therefore the slope of the perpendicular line is:
m2 = 15 / 8
Since the perpendicular line crosses the point (11, 17), therefore using the slope formula:
m = (y2 – y1) / (x2 – x1)
15 / 8 = (y2 – 17) / (x2 – 11)
1.875 (x2 – 11) = y2 – 17
1.875 x2 – 20.625 = y2 – 17
y2 = 1.875 x2 – 3.625
y = (15/8) x – 3.625
multiplying both sides by 8:
8y = 15x – 29
rewriting in standard form:
15x – 8y = 29 (ANSWER)
Which of these ordered triples indicates where the plane cuts the x-axis for this equation? 7x +2y +3z =42 A. (14,0,0) B. (7,0,0) C. (21,0,0) or D. (6,0,0)
Answer:
Option D is correct.
Step-by-step explanation:
Given Equation of plane is 7x + 2y + 3z = 42
We need to find ordered triplet where plane cuts the x-axis.
To find point of x-axis when plane cuts it. we put other coordinates equal to 0.
So, put y = 0 and z = 0 in equation plance to get x-coordinate of the required ordered triplet.
7x + 2 × 0 + 3 × 0 = 42
7x + 0 + 0 = 42
7x = 42
[tex]x=\frac{42}{7}[/tex]
x = 6
⇒ ordered triplet = ( 6 , 0 , 0 )
Therefore, Option D is correct.
If f(x) = 3/x+2 - √x-3, complete the following statement (round to the nearest hundredth) f(7)= PLEASE HELP ME
The value of given function f(7) is -1.8.
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
According to the given problem,
f(x) = [tex]\frac{3}{x + 5}- \sqrt{x - 3}[/tex]
At x = 7,
⇒ f(7) = [tex]\frac{3}{7 + 5} - \sqrt{7-3}[/tex]
⇒ f(7) = [tex]\frac{1}{4} - 2[/tex]
⇒ f(7) = [tex]-\frac{7}{4}[/tex]
⇒ f(7) = - 1.75
≈ -1.8
Hence, we can conclude, the value of function f(7) is -1.8.
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