The lateral area of the cylinder is approximately [tex]45.24 \, \text{cm}^2\)[/tex] and the volume is approximately [tex]\(45.24 \, \text{cm}^3\)[/tex].
To find the lateral area and volume of a cylinder, you can use the following formulas:
1. Lateral Area [tex](\(A_{\text{Lateral}})\)[/tex]:
[tex]\[ A_{\text{Lateral}} = 2 \pi r h \][/tex]
where r is the radius of the base and h is the height.
2. Volume (V):
[tex]\[ V = \pi r^2 h \][/tex]
Given that the diameter (D) is 4 cm, the radius (r) is half of the diameter, so [tex]\( r = \frac{D}{2} = \frac{4}{2} = 2 \)[/tex] cm, and the height (h) is 3.6 cm.
Now, let's calculate:
1. Lateral Area:
[tex]\[ A_{\text{Lateral}} = 2 \pi \times 2 \times 3.6 \][/tex]
2. Volume:
[tex]\[ V = \pi \times 2^2 \times 3.6 \][/tex]
Calculating these values:
1. Lateral Area:
[tex]\[ A_{\text{Lateral}} \approx 45.24 \, \text{cm}^2 \][/tex]
2. Volume:
[tex]\[ V \approx 45.24 \, \text{cm}^3 \][/tex]
So, the lateral area of the cylinder is approximately [tex]45.24 \, \text{cm}^2\)[/tex] and the volume is approximately [tex]\(45.24 \, \text{cm}^3\)[/tex].
Complete Question: Find the lateral area and volume of the cylinder whose diameter is 4 cm and height= 3.6cm.
Complete the sentences to make true statements.
6 is 100 times
Answer:
Step-by-step explanation:
0.06
you can solve it one of 2 ways
first : put 6 over 100 and make it a fraction so 6/100 then convert it to a decimal depending on how your teacher wants it
secondly: divide 6 by 100
Which inequality is represented by the graph?
A. y>−32x−2
B. y≤−32x−2
C. y≥−32x−2
D. y<−32x−2
Inequality that represents the graph
[tex]y>\:-\frac{3}{2}x-2[/tex]
Option A
Explanation :
Given the graph of a linear inequality
Lets frame the linear equation of the dotted line first
Slope intercept form of linear equation is y=mx+b
where m is the slope and b is the y intercept
In the graph y intercept is -2. So value of b=-2
Now find out slope m using any two point on the dotted line
Lets pick (0,-2) and (-2,1)
slope formula
[tex]\frac{y_2-y_2}{x_2-x_1}[/tex]
Substitute the values of two points and find out slope
[tex]slope =\frac{y_2-y_2}{x_2-x_1}=\frac{1+2}{-2-0}=-\frac{3}{2}[/tex]
Now replace the values in equation y=mx+b
[tex]y=-\frac{3}{2} x-2[/tex]
In the graph we have dotted line so we use < or >
Lets use test point (0,0) origin.
x=0 and y=0
[tex]y=-\frac{3}{2} x-2\\0=-\frac{3}{2} (0)-2\\0=-2\\0>-2\\[/tex]
So the inequality becomes
[tex]y>-\frac{3}{2} x-2[/tex]
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As a point moves in the positive x-direction along the line graphed, what is the rate of change of y with respect to x?
A.4/3
B.3/4
C.-4/3
D.-3/4
Answer:
B. 3/4
Step-by-step explanation:
Care with these types of graphs as the values are 2 rather than one on each axis.
Away from that, rate of change can also be named "slope" in which how many units up or down the y-value goes per x value. To find the slope or "rate of change" you want to use [tex]\frac{RISE}{RUN}[/tex] .
To find the rise over run you want to go up from any point where the x and y value line up to another. The origin or (0,0) can be used to do this. Look at point (8,6) to see this. Rise from the origin 6 times and run to the right 8 times. Rise OVER run so the rate of change can be shown as 6/8 which can be simplified to 3/4.
A pound of chocolate costs 7 dollars. Keiko buys p pounds. Write an equation to represent the total cost c that keiko pays.
Answer:
7xp=c
Step-by-step explanation:
since you have to multiply p by 7. to get the answer is c. Take for example
7 x 3 =21
p=3
c=21
distributive property to match equivalent expression -7(4-+x)
70.5 - 6.81 =
63.69
63.71
64.69
77.31
Answer:
63.69
Step-by-step explanation:
X is less than equal to nine in greater than four
derive sina
[tex]derive \: (sin(cos ^{2} x)) \: [/tex]
Answer:
the derivative of given function is
[tex]cos(cos^2 x )(-sin 2 x)[/tex]
Step-by-step explanation:
Step :-
using chain rule formula [tex]\frac{d y}{d x} = \frac{d y}{d u} X\frac{d u}{d x}[/tex]
let [tex]Y = sin(cos^2 x)[/tex] ...........(1)
[tex]\frac{d(sin x)}{d x} = cos x[/tex]
Differentiating equation (1) with respective to x,we get
[tex]\frac{d y}{d x} = cos(cos^2 x) \frac{d}{d x} (cos^2 x)[/tex]........(2)
we will use again formula
[tex]\frac{d(cos x)}{d x} = -sin x[/tex]
[tex]\frac{d (x^{2} )}{d x} =2 x[/tex]
From (2) equation we will get solution is
[tex]\frac{d y}{d x} = cos (cos^2 x) (2 cos x (\frac{d(cos x)}{dx} )[/tex] ........(3)
again simplification the equation (3) we will get
[tex]\frac{d y}{d x} = cos(cos^2 x)(2 cos x(-sin x))[/tex] ........(4)
by using trigonometry formula
[tex]2 sin x cos x = sin2x[/tex]
now the equation (4) we get final solution is
[tex]\frac{d y}{d x} = cos(cos^2 x)(- sin2x)[/tex]
Open Response 2
A glass containing water is in the shape of a right circular cylinder with a radius
of 3 centimeters. The height of the water in the glass is 10 centimeters.
a) What is the volume of the water in the glass? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer.
b) Five spherical marbles of equal size are dropped into the glass. The water in
the glass rises to a height of 11 centimeters. What is the increase in the
volume of the contents of the glass? Be sure to include units of measure in
your answer. Show or explain how you obtained your answer.
c) What is the volume of one of the marbles? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer.
d) What is the radius of one of the marbles? Be sure to include units of
measure in your answer. Show or explain how you obtained your answer.
Answer:
b
Step-by-step explanation:
Four times the larger of two numbers is equal to seven times the smaller the sum of the numbers is 22 find the numbers
Answer:
8 and 14
Step-by-step explanation:
X + Y = 22
X= 22-Y
4X= 7Y
4(22-Y) = 7Y
88-4Y=7Y
88= 11Y
8=Y
X= 22-Y= 22-8=14
F(x) is an even function and f(-6) = 8. If g(x) = 4f(x+2)-1, then which of the following is the value
of g(4)?
The value of function g (4) will be 31.
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
F(x) is an even function.
So, F(-x) = F(x)
And, f(-6) = 8
Now,
The function is,
g(x) = 4 f(x+2) - 1
Find the value of g(4), substitute x = 4 in above equation as;
⇒ g (4) = 4 f(4 + 2) - 1
⇒ g (4) = 4 f (6) - 1
Since, F(x) is an even function.
So, F(-8) = F(8)
Hence, We get;
⇒ g (4) = 4 × 8 - 1
⇒ g (4) = 32 - 1
⇒ g (4) = 31
Thus, The value of function g (4) will be 31.
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What is the number between 0.5 and 1.0
Answer:
0.6, 0.7, 0.8, 0.9
Step-by-step explanation:
0.5 < x < 1
Answer:
It could be 0.5, 0.6, 0.7, 0.8, 0.9 depending if it is in the tenths
While exercising, a person’s recommended target heart rate is a function of age. The recommended number of beats per minute, y , is given by the function y=f(x)=−0.85x+187 where x represents a person’s age in years. Determine the number of recommended heart beats per minute for your age. Show each step in the process of this calculation.
x=21
Answer:
170 heart beat per minute.
Step-by-step explanation:
While exercising, a person’s recommended target heart rate is a function of age. The recommended number of beats per minute, y, is given by the function y = f(x) = − 0.85x + 187 where x represents a person’s age in years.
So, if my age is 21 years i.e. x = 21, then the number of recommended heart beats per minute for my age will be
y = f(21) = - 0.85(21) + 187 = - 17.85 + 187 = 169.15 ≈ 170. (Answer)
{Taking the larger integer value}
Convert each degrees minutes seconds into decimal degrees
351°41’142”
Answer:
351.7227778°
Step-by-step explanation:
The conversion of 351°41’142” into decimal degrees involves expressing minutes and seconds as fractions of a degree. This results in approximately 351.7227 degrees.
Explanation:To convert degrees, minutes, and seconds to decimal degrees, we express the minutes and seconds as fractions of a degree. Degrees are already expressed in decimal form, so 351° remains 351. However, 1 minute equals 1/60 of a degree, while 1 second equals 1/3600 of a degree. So, to convert 41 minutes into decimal degrees, we divide 41 by 60, which equals approximately 0.6833. And to convert 142 seconds into decimal degrees, we divide 142 by 3600, which equals approximately 0.0394. Then we add these values together with the original degrees to get the final answer: 351 + 0.6833 + 0.0394 equals approximately
351.7227 degrees
.
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84 is what percent of 105?
Answer:
80%
Step-by-step explanation:
84/105=0.8
0.8=80%
Answer:
The answer is 80 percent
20 points
Write as a power of a binomial.
[tex]125m^{2} -15m^2+\frac{3}{5} m-\frac{1}{125}[/tex]
Answer:
[tex](5m - \frac{1}{5})^{3}[/tex]
Step-by-step explanation:
We have to write the following expression as a power of a binomial.
The expression is [tex]125m^{3} - 15m^{2} + \frac{3}{5}m - \frac{1}{125}[/tex].
Now, we have to rearrange the given expression.
[tex]125m^{3} - 15m^{2} + \frac{3}{5}m - \frac{1}{125}[/tex]
= [tex](5m)^{3} - 3(5m)^{2}(\frac{1}{5}) + 3(5m)(\frac{1}{5})^{2} - (\frac{1}{5})^{3}[/tex]
= [tex](5m - \frac{1}{5})^{3}[/tex] (Answer)
Since we know the identity as (a - b)³ = a³ - 3a²b + 3ab² - b³.
Statement:5>4
Which is greater 5x or 4x
Answer:
5x
Step-by-step explanation:
Because the inequality sign means it greater and if it turned around than it means it less than and the = sign means it equal to
If x is positive, 5x is greater than 4x and if x is negative, 5x is less than 4x.
To determine whether 5x is greater than 4x, we need to consider the value of "x." The comparison between 5x and 4x depends on the value of "x."
If x is a positive number, then 5x will be greater than 4x because 5 is larger than 4, and multiplying by a positive number increases the value.
For example:
If x = 1, then 5x = 5, and 4x = 4. Since 5 is greater than 4, 5x is greater than 4x.
If x is a negative number, then 5x will be less than 4x because multiplying by a negative number changes the inequality sign.
For example:
If x = -1, then 5x = -5, and 4x = -4. Since -5 is less than -4, 5x is less than 4x.
Thus, it can be concluded that
If x is positive, 5x is greater than 4x. If x is negative, 5x is less than 4x.
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Which of the following units can be used to measure area?
inches
square centimeters
meters
square yards
cubic feet
Any measurement that can be used to measure area will have the word square or squared somewhere in the term, because you multiply two values to get the area. So the answers would be inches squared, and square yards.
Simply meters and centimeters would be used for length; cubic feet would be used for volume because three values have to be used to find an object's volume.
Hope This Helps! :)
QuezoMartiinez :)
Answer:
Square centimeters and Square yards
Step-by-step explanation:
the area of any object has to be squared. for volume it would need to be cubed
5x−7=−10x+8
x = ___
(type your answer as a number)
Answer:
x=1
Step-by-step explanation:
5x-7=-10x+8
5x=−10x+8+7
5x=−10x+15
5x+10x=15
15x=15
Answer: x=1
Answer:
x = 1
Step-by-step explanation:
Put the like terms to same side of equation
5x -7 = -10x +8 ➡ 5x + 10x = 8 + 7
15x = 15
x = 1
A line passes through the point (4, –6) and has a slope of Negative three-fourths. Which is the equation of the line?
A y = negative three-fourths x minus 3
B y = negative three-fourths x minus 6
C y = negative 3 x minus three-fourths
D y = negative 6 x minus three-fourths
Option A
The equation of line is [tex]y = \frac{-3}{4}x - 3[/tex]
Solution:
Given that line passes through the point (4, –6) and has a slope of Negative three-fourths
Given point is (x, y) = (4, -6)
[tex]slope = \frac{-3}{4}[/tex]
The equation of line passing through point (x, y) and slope "m" is given as:
y = mx + c ----- eqn 1
Where "m" is the slope of line and "c" is the y - intercept
Substitute (x, y) = (4, -6) and [tex]m = \frac{-3}{4}[/tex] in eqn 1
[tex]-6 = \frac{-3}{4} \times 4 + c\\\\-6 = -3 + c\\\\c = -6 + 3\\\\c = -3[/tex]
The required equation of line is given as:
[tex]\text{ Substitute } m = \frac{-3}{4} \text{ and } c = -3 \text{ in eqn 1 }[/tex]
[tex]y = \frac{-3}{4}x - 3[/tex]
Thus the equation of line is found
Answer:
the answer is A
Step-by-step explanation:
Hope this helps!
es -
Two linear functions of x are shown.
Which statement about the functions is true?
Function 2 can be described by the equation y= 25x - 100.
Function 2 can be described by the equation y = 13x - 11.
The y-intercept of function 1 is less than the y-intercept of function 2.
Rate of change of function 2 is less than the rate of change of function 1.
Answer:
The answer is D
Step-by-step explanation:
Answer:
THE ANSWER D ON USATESTPREP
What is 7y + 12 - 6 +(-8y)
Answer:
-1y+6
Step-by-step explanation:
Here’s why:
Combine like terms. -8y and 7y added together becomes -1y giving the first term.
The second term is from subtracting 12 and 6.
Hope this helps!
Answer:
-y + 6
Step-by-step explanation:
7y + 12 - 6 + (- 8y) =
7y + 12 - 6 - 8y =
7y - 8y = -y
12 - 6 = 6
- y + 6
Find the slope of the line that passes through (2,11) and (7,9).
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{11}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{2}}}\implies \cfrac{-2}{5}[/tex]
Answer:
it should be -2/5 if you're looking for the slope
which of the binomials below is a factor of this trinomial? x^2+12x+35
Answer:
(x+5) (x+7)
Step-by-step explanation:
Will mark as BRAINLIEST!!
Answer:
a= 2s-b-c
Step-by-step explanation:
s=a+b+c/2
1) Multiply everything by 2, to get rid of the /2.
2s=a+b+c
2s-b=a+c
2s-b-c=a
Answer:
Its D TRUST ME IT IS
Step-by-step explanation:
He messed up but i got it right
Twenty one hundredth as a common fraction
Answer:
21/100
Step-by-step explanation:
Select all of the quotients that have the same value as 5.04 divided by 7
1. 5.04 divided by 70
2. 50.4 divided by 70
3. 504,000 divided by 700
4. 504,000 divided by 700,000
Answer: 2 and 4
Step-by-step explanation: the quick way is by dividing all the answer options
(05.07 MC)
The correlation coefficient for poor hearing and loud music in a group of people is 0.67 Analyze the following statement:
Poor hearing is caused by listening to loud music.
Is this a reasonable conclusion?
Final answer:
While a correlation of 0.67 suggests a positive relationship between loud music and poor hearing, it does not confirm causation. Many factors contribute to hearing loss, and while loud music is a significant risk factor for noise-induced hearing loss, one cannot definitively conclude it causes poor hearing without considering other variables.
Explanation:
The correlation coefficient of 0.67 between poor hearing and loud music indicates a positive and moderate relationship between the two variables, suggesting that people who listen to loud music tend to have poorer hearing. However, correlation does not imply causation. While loud music can be one of the factors contributing to poor hearing, it is important to remember that other factors can also lead to hearing loss, such as age, genetics, infections, and other environmental noises. Therefore, while the correlation is significant, we cannot conclude with certainty that poor hearing is exclusively caused by listening to loud music.
Noise-induced hearing loss can indeed happen from prolonged exposure to sounds of high intensity. For example, listening to music through earbuds at maximum volume, which can be around 100-105 decibels, increases the risk of hearing loss and can cause noise-induced hearing loss after 15 minutes of exposure. The impact of sound intensity on hearing health is undeniable, but when determining causality, a deeper investigation into other possible contributing factors must also be taken into account.
Enter the numerator and the denominator of the fraction in simplest form that is equal to the decimal shown.
0.63
To convert the decimal 0.63 to a fraction, write it as 63/100, and simplify if possible. Since 63 and 100 do not have a common divisor larger than 1, the fraction is already in its simplest form, which is 63/100.
Explanation:The question involves converting a decimal to a fraction in simplest form. To convert the decimal 0.63 into a fraction, you can write it as 63/100 because there are two digits after the decimal point, which equates to the hundredth place. To simplify the fraction, you look for the greatest common divisor (GCD) of both the numerator and the denominator. In this case, both 63 and 100 can be divided by the GCD which is 1. Thus, the fraction is already in its simplest form and the answer is 63/100.
The decimal 0.63 written as a fraction in simplest form is 63/100, which cannot be reduced further since 63 and 100 share no common factors other than 1.
Explanation:The numerator and denominator of the fraction in simplest form that is equal to the decimal 0.63 can be found by moving the decimal point two places to the right. This gives us the fraction 63/100 which can be simplified to 9/15 by dividing both the numerator and denominator by the greatest common factor, which is 9. To convert the decimal 0.63 into a fraction in simplest form, you can start by writing it as ⅓ over 100, since the last digit is in the hundredths place. This gives you the fraction 63/100. However, the question asks for the simplest form, so you should reduce the fraction by finding the greatest common factor of the numerator and denominator.
The greatest common factor of 63 and 100 is 1, so 63/100 cannot be reduced any further - it is already in its simplest form. Thus, the answer is simply ⅓ over 100 or 63/100.
The sum of 9 times a number and 5 equals 7.
Answer:
9x+5=7
9x=2
x=2/9