Answer:
The volume of the solid = 1444
Step-by-step explanation:
Given that:
The region of the solid is bounded by the curves [tex]y = 38 \sqrt{cos \ x}[/tex] and the axis on [tex][-\dfrac{\pi}{2}, \dfrac{\pi}{2}][/tex]
using the slicing method
Let say the solid object extends from a to b and the cross-section of the solid perpendicular to the x-axis has an area expressed by function A.
Then, the volume of the solid is ;
[tex]V = \int ^b_a \ A(x) \ dx[/tex]
However, each perpendicular slice is an isosceles leg on the xy-plane and vertical leg above the x-axis
Then, the area of the perpendicular slice at a point [tex]x \ \epsilon \ [-\dfrac{\pi}{2},\dfrac{\pi}{2}][/tex] is:
[tex]A(x) =\dfrac{1}{2} \times b \times h[/tex]
[tex]A(x) =\dfrac{1}{2} \times(38 \sqrt{cos \ x})^2[/tex]
[tex]A(x) =\dfrac{1444}{2} \ cos \ x[/tex]
[tex]A(x) =722 \ cos \ x[/tex]
Applying the general slicing method ;
[tex]V = \int ^b_a \ A(x) \ dx \\ \\ V = \int ^{\dfrac{\pi}{2} }_{-\dfrac{\pi}{2}} (722 \ cos x) \ dx \\ \\ V = 722 \int ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}} cosx \dx[/tex]
[tex]V = 722 [ sin \ x ] ^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}}[/tex]
[tex]V = 722 [sin \dfrac{\pi}{2} - sin (-\dfrac{\pi}{2})][/tex]
[tex]V = 722 [sin \dfrac{\pi}{2} + sin \dfrac{\pi}{2})][/tex]
[tex]V = 722 [1+1][/tex]
[tex]V = 722 [2][/tex]
V = 1444
∴ The volume of the solid = 1444
you can transform 4x + 12 = 9x - 3 again into a simpler form by subtracting 4x form both sides to get 12 = 5x - 3, if you subsitute 3 for x in 12 = 5x - 3, do you still get a true statement
Answer: Yes you will still get a true statement because 3 is the solution to the equation.
Step-by-step explanation:
Well substitute 3 for x into the equation and solve for to see if they equal each other.
12 = 5(3) - 3
12 = 15 - 3
12 = 12
So if you substitute 3 you get the solution .
Now solve for x in the real equation to see if you get 3.
4x + 12 = 9x -3
-4x -4x
12 = 5x -3
+3 +3
15 = 5x
x = 3
Two angles form a linear pair. The measure of one angle is twice the measure of the other angle. Find the measure of each angle.
The smaller angle measures
The larger angle measures
Answer:
Smaller Angle = 60°
Larger Angle = 120°
Step-by-step explanation:
Step 1:
2x + x = 180°
Step 2:
3x = 180°
Step 3:
x = 60°
Step 4:
60° times 2 = 120°
Answer:
Smaller Angle = 60°
Larger Angle = 120°
Hope This Helps :)
Fill in the blanks to complete the equation that describes the diagram.
Answer:
-1+7 =-7
Step-by-step explanation:
if f(x)= {2 for x>0, 0 for x=0, , then what is the value of -2 for x<0, f(7)-f(-4)?
Are you sure you've written the problem right...it says x can not equal 0 or 1
Answer:
C -2,1 or 3 0nly
Step-by-step explanation:
Just did it mark it brainliest
For what values of x will the result of 5 x be greater than 1?
Answer:
2&3
Step-by-step explanation:
2+3=5 or 3+2=5
You can continue on but you would need to use one and these are the two that are greater than 1 but make up 5.
The values of x for which the result of 5 x be greater than 1 would be 2 and 3.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE need to find the values of x for which the result of 5 x be greater than 1
WE can have that as;
2+3=5
or
3+2=5
Also we can continue on but we would need to use one and these are the two that are greater than 1 but make up 5.
Therefore, the values of x for which the result of 5 x be greater than 1 would be 2 and 3.
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Jennifer paid $13.37 for a pack of 12 pairs of sport socks. What was the price of a pair of sport socks
Answer:
Each pair of socks cost around $1.11 excluding taxes.
Step-by-step explanation:
To find how much it costs for one pair of socks, divide the cost with how many pairs there are.
13.37/12 = 1.11426...
Since we are determining the cost of each pair of socks, it's only justifiable if we round it to the nearest hundredths.
Therefore, a pair of socks cost around $1.11 excluding taxes.
A student winds a strip of paper eight times round a cylinderical pencil of diameter 7mm. Use the value 22/7 for the to find the length of the paper( ignore the thickness of the paper)
As per the circumference of a circle, the length of the paper is 176 mm.
What is the circumference of a circle?The circumference of a circle is the total arc length of it.
The diameter of the pencil is(d) 7 mm
Therefore, the radius of the pencil is(r)
[tex]= \frac{d}{2} \\= 7/2 mm\\= 3.5 mm[/tex]
Now, the circumference of the cross-section of the pencil is
[tex]= 2[/tex](π)r units
[tex]= (2) (22/7) (3.5) mm\\= 22 mm[/tex]
Therefore, the length of the paper is
= (circumference of the cross-section of the pencil) × 8 units
[tex]= (22) (8) mm\\= 176 mm[/tex]
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write the sentence as a equations
the product of 248 and a is 391
Answer:
248*a=391
Step-by-step explanation:
Write the point-slope form of the equation of the line through (4,-2) with slope of -1/2.
Answer:
Step-by-step explanation:
y + 2 = -1/2(x - 4)
y + 2 = -1/2x + 2
y = -1/2x
Can somebody please solve these thank you!
Answer:
1/2(-1/3)=-1/6
-2/5(-5/9)=2/9
-3/4(8/9)=-2/3
Answer:
1/2 multiplied by (-1/3)=-1/6 or 0.166666667
-2/5 multiplied by (-5/9)=2/9 or 0.222222222
-3/4 multiplied by 8/9=2/3 or 0.666666667
you just multiply.
Miss Lawrence buys 8 ounces of smoked salmon at $17.98 per pound. How much money
does Miss Lawrence spend on the smoked salmon?
Answer:
1 pound = 16 ounces
She bought 8 ounces, which is 0.5 pounds. Just multiply the number of pounds she bought by the price per pound.
(0.5 pounds)($17.98 per pound) = $8.99
Step-by-step explanation:
Answer: 8.99
Step-by-step explanation:
A can factory requires 2 sheets of metal to make 36 cans and 10 sheets of metal to make 180 cans. The proportionality constant between the number of cans made and the number of sheets of metal used is 36 18 288 5
Answer:From the statement above, we can say that there is a direct relationship between the number of sheets used to the number of cans that can be made. That is, # of sheets is directly proportional to # of cans. We make an equation as follows:
let y = # of sheets
x = # of cans
y = kx where k is the proportionality constant
Assuming linear relationship of the two, we can use either data point as follows:
y = kx
2 = k(36)
k = 1/18
Therefore, the proportionality constant is 1/18.
Step-by-step explanation:
7.08x10^-4 in standard notation
Answer:
It's supposed to be 7.0800.
Step-by-step explanation:
Since it's 10 to the power minus 4 you'll have to count 4 places after the decimal point, so it'll be 7.0800
Answer:
0.000708
Step-by-step explanation:
you move the decimal 4 times to the left since the notation is negative. If the notation was positive, you would move it to the right.
Can i have the brainliest, please?
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answer:
1.3
Step-by-step explanation:
divide the 20 cupcakes and the 15 students
20 divided by 15 = 1.3
Gena and her friends each estimated the quotient of –137.56 divided by –6.12 using compatible numbers. Which shows the best estimate using compatible numbers?
Answer:
i think it would be a.
Step-by-step explanation:
Answer:Gena and her friends each estimated the quotient of –137.56 divided by –6.12 using compatible numbers. Which shows the best estimate using compatible numbers?
Negative 140 divided by negative 7 = 20
Negative 140 divided by 6 = 23.ModifyingAbove 3 with bar
Negative 135 divided by negative 7 = 22.5
Negative 135 divided by negative 5 = 27
Step-by-step explanation: The answer is A because it is showing the right way to do the step
The number of hours a group of 12 children in Mrs. Smith's kindergarten class read in a day.
Answer:
30 minuetes because their brain can take so many
Step-by-step explanation:
2.) 4 – бу = 28
Solve for the variable
Answer:
y = -4
Step-by-step explanation:
4 - 6y = 28
Group like terms
-6y = 28 - 4
-6y = 24
divide through by -6
-6y/-6 = 24/-6
y = -4
How is making a ten to add the same as making a ten to subtract? How is it different?
Answer:
when adding a ten the number goes higher but when subtracting ten the number is lower than the original number
Step-by-step explanation:
for example :
20+10= 30 ( its greater )
90-10=80( is lower )
PLZ HELP ASAP! ANSWER ALL FOR BRAINLIEST
Answer:
4.
-building
-artisting
-selling
-making good
-trading
-farming
5. "Being settled meant being tied to land and possessions; being nomadic meant having a mobile community with a mobile food supply. This allowed nomads to attack and plunder resources. They could gain access to agricultural products without having to farm or trade."
6. " They were also trained in riding and archery, as they sometimes had to defend their communities from outsiders. Women’s graves sometimes contained weapons, suggesting they had a role in military life as well."
Step-by-step explanation:
solve the given triangle by finding the missing angle and other side lengths.
Answer: The missing angle (B) is 22 degrees
Step-by-step explanation:
a triangle in general is 180 degrees. You take the angles given
A(18) + B + C(140) = 180
Subtract A and C from each side and end up with B = 22 degrees.
The traditional way of writing a number.
Step-by-step explanation:
In legal prose it is traditional to write every number twice, first in words, followed by the same number written in digits enclosed in brackets: That sentence contained twenty-five (25) words. Easy as one (1), two (2), three (3).
The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x – 72.5| = 4. What are the minimum and maximum temperatures in the house? 72.5°F and 76.5°F 68.5°F and 76.5°F 70.5°F and 74.5°F 72.5°F and 74.5°F
Answer:
The minimum and maximum temperatures in the house are 68.5°F and 76.5°.
To keep the house in heat, the minimum and maximum temperature is set to option 68.5°F and 76.5°F.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The equation |x – 72.5| = 4.
The minimum and maximum temperatures can be found by substituting +4 and -4 in x.
Minimum temperature,
⇒ [tex]|+4-72.5|=|-68.5|[/tex]
⇒ [tex]68.5[/tex]
Maximum temperature,
⇒ [tex]|-4-72.5|=|-76.5|[/tex]
⇒ [tex]76.5[/tex]
Hence we can conclude that to keep the house in heat, the minimum and maximum temperature is set to option 68.5°F and 76.5°F.
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convert 35 kg into lb, then round it to two decimal places
Answer:
77.16 lbs
:)))))))))))))
What is 2.5 × 15.625
Answer:
39.0625
Step-by-step explanation:
Answer:
39.0625
Step-by-step explanation:
Write a corresponding real-world problem for each equation.
1. 0.55x + 4.50 = 0.65x + 3.50
2. 8x + 80 = 4x + 120
Answer:
It is 2 because it is a math question with the factors on the multipulcation
Step-by-step explanation:
Kelly works 8 hours less than three times as much as Marcy works for the week. Which expression represent
the number of hours Kelly works in relation to Marcy.
Answer:
X= 3y-8
Where
X represent hours worked by Kelly
Y represent hours worked by Marcy
Step-by-step explanation:
Kelly works 8 hours less than three times as much as Marcy works for the week.
Let the number of hours worked by Kelly= x
Let the number of hours worked by Marcy= y
X= 3y-8
The circle graph shows the most important problems for the
14,158,428 high school teenagers in a country. Without using a
calculator, estimate the number of high school teenagers for whom
drugs is the most important problem.
Drugs is the most important problem for approximately how many of the high school teenagers?
A 11.200.000
B. 1.400.000
C. 2.800.000
D. 8,400,000
Answer:
Option (C)
Step-by-step explanation:
From the circle graph attached,
14158428 students have been divided into the sectors of a circle which represent the most important problems for the high school teenagers.
Each sector corresponds the percent of different problem.
Red sector (22% of the total students) represents the most important problem of drugs.
14158428 students ≈ 14000000
22% ≈ 20%
Now 20% of 14000000 high school students = 14000000×[tex]\frac{20}{100}[/tex]
= 2800000
Therefore, Option (C) will be the answer.
How many subsets does the set A= {1, 2 3, 4} have? *
2 points
8
16
4
12
Answer:
[tex]\huge\boxed{\mathrm{Subsets = 16\ }}[/tex]
Step-by-step explanation:
A = {1,2,3,4}
Subset = [tex]\sf 2^n[/tex]
Where n is the number of elements in the set
There are 4 elements in the set
Subset = [tex]\sf 2^4[/tex]
Subsets = 16
Find a general solution. Show the steps of derivation. xy'=y+2x³sin²y/x (Set y/x=u)
Answer:
y = 2 tan(2x + c) - 4x
Step-by-step explanation:
See the attachment for the derivation and integration
Simplify -4 1/6 - -6 1/3 Which of the following is correct?
Answer:
its 2 1/6 (B)
Step-by-step explanation: