The volume of the solid with base x^2 + y^2 = 1 and perpendicular cross sections that are isoceles right triangles with leg on the xy-plane is 4/3 cubic units.
To find the volume of the solid, we need to integrate the area of each cross section perpendicular to the x-axis over the interval of x that makes up the base of the solid. Since the cross sections are isoceles right triangles with leg on the xy-plane, we know that the height of each cross section is equal to the length of the leg on the xy-plane, which is given by 2√(1-x^2).
So, the area of each cross section is (1/2) * base * height, where the base is also equal to 2√(1-x^2). Therefore, the volume of the solid can be calculated as follows:
V = ∫[a,b] (1/2) * base * height dx
V = ∫[-1,1] (1/2) * 2√(1-x^2) * 2√(1-x^2) dx
V = ∫[-1,1] (1-x^2) dx
V = [x - (1/3)x^3]_[-1,1]
V = 4/3
Therefore, the volume of the solid is 4/3 cubic units.
To know more about volume,
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Please help!!!!!!!
thank you for helpingggggg
Answer:
x = 9
Step-by-step explanation:
5x * 135 = 180
180 - 135 = 45
5x = 45
5 ÷ 5 = 0
45 ÷ 5 = 9
X = 9
The hypotenuse of a right angle triangle is 4 metres. If its other sides are equal find the length of each side.
Answer:
[tex] \sqrt{8} [/tex]
or
[tex]2 \sqrt{2} [/tex]
Step-by-step explanation:
Since the legs are equal this is a 45-45-90 triangle.
The ratio of side length for a 45 45 90 triangle
[tex](1)(1)( \sqrt{2} )[/tex]
where 1 is the legs length and sqr root of 2 is the length of the hypotenuse.
Since we are trying to find the length of the legs side we can set up a proportion.
We know the hypotenuse is 4 so our proportion looks like
[tex] \frac{1}{x} = \frac{1}{x} = \frac{ \sqrt{2} }{4} [/tex]
Let see how far sqr root of 2 goes into 4.
[tex] \sqrt{2} \times x = 4[/tex]
[tex] \sqrt{2} \times x = \sqrt{16} [/tex]
[tex]x = \sqrt{8} [/tex]
so that means the answer for the legs length is
[tex] \sqrt{8} [/tex]
or
[tex]2 \sqrt{2} [/tex]
Answer:
Step-by-step explanation:
hello :
use phtagor - rule: let x the length of each side
x² +x² =4²
2x² =16
x² = 8
x = √8
but : 8 = 4×2 = 2²×2
x = √(2²×2) = √2²× √2 =2√2 ...... √2² =2
x = 2√2 metres.
Philippe will read One-half of the number of pages that Rafael reads. How many pages will Rafael read?
Answer: I cannot answer it because it needs more details. For ex say how much day he/she needs and how much pages he/she will read.
Step-by-step explanation: Unknown
can someone help me
Step-by-step explanation:
40 ÷ 4 ( 4 sides) = 10
So each side measures 10inches
Answer:
10
Step-by-step explanation:
beacue 10x4
A grocery store is offering a sale on bread and soup. Kacey buys four cans of soup and three loaves of bread for $12.35. Fernando buys eight cans of soup and one loaf of bread for $13.05.
a. Write equations for both Kacey’s and Fernando’s purchases.
Answer:
Kacey
4x+3y=12.35
Fernando
8x+1y=13.05
Amanda bought 4 pairs of jeans for $71.40. How much would she need to pay for 8 pairs of jeans?
==========================================================
Explanation:
To get this answer, we double the 71.40 to get 142.80
You can think of it like an equation and we multiply both sides by 2
4 jeans = 71.40 dollars
2*(4 jeans) = 2*(71.40 dollars)
8 jeans = 142.80 dollars
------------
Or you could solve it like this
(4 jeans)/(71.40 dollars) = (8 jeans)/(x dollars)
4/71.40 = 8/x
4x = 71.40*8
4x = 571.2
x = 571.2/4
x = 142.80
------------
Yet another way to solve is to first find the unit rate
4 jeans cost 71.40, so that must mean 1 pair of jeans cost 71.40/4 = 17.85 dollars. This is the unit rate since "unit" means "one". It's the price per pair of jeans.
Multiply that by 8 to find out how much 8 pairs will cost, and we get 17.85*8 = 142.80
Della has $575.38 in her checking account. What is the balance after she makes a deposit of $50.00 and a withdrawal of $85.45?
A)
$539.93
B)
$558.45
C)
$561.63
D)
$603.73
Answer:
A) 539.93
Step-by-step explanation:
575.38 + 50 - 85.45 = 539.93
Answer: A
$539.93
Step-by-step explanation:
Balance is $575.38 so add (+) $50 for her deposit and subtract (-) $85.45 to get the answer
Factor: k^2 + 7x + 10
A:(k+10)(k+4)
B:(k+2)(k+5)
C:(k+2)(k-5)
D:(k-2)(k-5)
Answer:
the answer is B. (k+2)(k+5)
Answer:
a
Step-by-step explanation:
1f (-2, y) lies on the graph of y = 3, then y =
Answer:
y = 3
Step-by-step explanation:
the y-value of any ordered pair that lies on the line 'y = 3' will be equal to 3.
math is so hard man but can someone help me
Answer:
a
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
No, because
the first function if you further calculate you have
y= 3(x +5) is y = 3x+15 ; since you have to distribute
the second function if you have to translate is y=3x+5 because if you read it out loud the equation now you will say y equals 3 times x plus 5 like was given
IMPORTANT!! in a unit circle, what is the relationship between arc length and central angle?
The measure of an arc refers to the arc length divided by the radius of the circle. The arc measure equals the corresponding central angle measure, in radians. That's why radians are natural: a central angle of one radian will span an arc exactly one radius long.
What are 3 of the 6 essential principles in Jefferson's Inaugural Address?
GIVE ME 3 OF THEM PLEASEEE
Answer:
He said that the nation had "room enough for our descendants to the thousandth and thousandth generation" and that his administration would pursue "honest friendship with all nations, entangling alliances with none." He affirmed that America's future depended upon "the preservation of the General government
Step-by-step explanation:
A light house worker is tracking a boat that is 5 km south of her. She is also tracking a boat
that is 6 km from the tower located 70° east of north. To the nearest kilometer, how
far apart are the two boats?
A. 7 km
B. 9 km
C. 8 km
D. 16 kM
Answer:
cccccccccccccccccccccccccccccc c
Describe the steps necessary to solve the following system equations:
-3x - 4y = 2 and 3x + 3y = -3
Answer:
(- 2, 1 )
Step-by-step explanation:
Given the 2 equations
- 3x - 4y = 2 → (1)
3x + 3y = - 3 → (2)
Adding the 2 equations term by term will eliminate the x- term, that is
0 - y = - 1
- y = - 1 ( multiply both sides by - 1 )
y = 1
Substitute y = 1 into either of the 2 equations and solve for x
Substituting into (2)
3x + 3(1) = - 3
3x + 3 = - 3 ( subtract 3 from both sides )
3x = - 6 ( divide both sides by 3 )
x = - 2
solution is (- 2, 1 )
Answer:
x = -2 and y = 1
Step-by-step explanation:
3x + 3y = -3, x + y = -1, x = -y -1
-3(-y-1) - 4y = 2, 3y + 3 - 4y - 2 = 0
-y +1 = 0, y = 1
x + y = -1, x + 1 = -1, x = -2
Write the equation of the line in slope-intercept form that goes through the points (4, -2) and (8, -9)
Answer:
y = 17/6 x - 40/3
Step-by-step explanation:
Slope-intercept form: y = mx + b
First, let's find the slope:
slope formula: (y2-y1) divded by (x2-x1)
(4, -2) and (8, -9)
(-9 - 8) divded by (-2 - 4) = 17/6
We found m, now we have to find b.
The new equation: y = 17/6 x + b
Insert any of the two points, in this case, I'll insert (4, -2)
-2 = 17/6 (4) + b
-2 = 68/6 + b
b = -2 - 68/6
b = -40/3
Overall equation: y = 17/6 x - 40/3
Kirk is getting a raise of 5% due to inflation. His normal salary is $56,000 per year. Which of the following calculations gives Kirk's new salary, in dollars? A. 56,000 +5 B. 56,000 + 56,000(0.05) C. 56,000 + 56,000(0.50) D. 56,000 + 56,000(5) E. 56,000(.05)
Answer:
The answer is B. 56,000 + 56,000(0.05) because 5% or expressed in decimals 0.05 multiplied by the quantity 56,000 gives us 5% of Kirk's normal salary and added to his normal salary will give us his new salary.
(His new salary is 58,800 and 5% of his normal salary is 2,800)
Find the length of the third side. If necessary, write in simplest radical form
Answer:
4^2 + 6^2 = x^2
Step-by-step explanation:
Pythagorean theorem is used. Solve for x.
Find the slope .
What does this mean?
Find the y intercept.
What does this mean?
Suppose ABC and DEF are complementary angles. If ABC = (5x + 7)º
and ABC = (3x + 3)', What are the measures of the two angles?
Answer:
The first will be 16.6
The second will be 29
Step-by-step explanation:
Hope this Helped
[tex]5x + 7 = 90[/tex]
[tex]3x + 3 = 90[/tex]
A rectangle is covered by 24 unit squares. There are no gaps or overlap.
How can the area of the rectangle be found?
The area of the rectangle is equal to the number of unit squares that cover the rectangle. The area of the rectangle is 24 square units.
The area of the rectangle is half the number of unit squares that cover the rectangle. The area of the rectangle is 12 square units.
The area of the rectangle is double the number of unit squares that cover the rectangle. The area of the rectangle is 48 square units.
Answer: Choice A
The area of the rectangle is equal to the number of unit squares that cover the rectangle. The area of the rectangle is 24 square units.
=====================================================
Explanation:
Imagine drawing equally spaced grid lines to subdivide the rectangle. This splits the rectangle into smaller squares. In this case, each little square is 1 square unit. Having 24 of these squares leads to a total area of 24 square units.
We could have 8 rows and 3 columns of these squares to get 8*3 = 24 total. Or we could have 6 rows and 4 columns to get 6*4 = 24. Another configuration is 12 rows and 2 columns which leads to 12*2 = 24.
hola me ayudan pliss como saco el resultado de 584 × (?) =179288 y (?) ÷ 143 = 572
Answer:
1)307
2)81796
Step-by-step explanation:
584 × (?) =179288
[tex]\frac{179288}{584}[/tex] =307
(?) ÷ 143 = 572
572x143 =81796
¡Espero que esto sea de ayuda! :)
Graph the function y = 4x4 – 8x2 + 4. Which lists all of the turning points of the graph?
(0, 4)
(–1, 0) and (1, 0)
(–1, 0), (0, 4), and (1, 0)
(–4, 0), (–1, 0), (0, 4), and (1, 0)
in case you are wondering, there is no graph.
Answer:
[tex]4(x + 1)^{2}(x - 1)^{2}[/tex]
Step-by-step explanation:
STEP 1:
The equation at the end of step 1
[tex]((4 (x^4)) - 2^3x^2) + 4[/tex]
STEP 2:
The equation at the end of step 2:
[tex](2^2x^4 - 2^3x^2) + 4[/tex]
STEP 3:
STEP 4: Pulling out like terms
4.1 Pull out like factors:
[tex]4x^4 - 8x^2 + 4 = 4(x^4 - 2x^2 + 1)[/tex]
Trying to factor by splitting the middle term
4.2 Factoring [tex]x^4 - 2x^2 + 1[/tex]
The first term is, [tex]x^4[/tex] its coefficient is 1.
The middle term is, [tex]-2x^2[/tex] its coefficient is -2.
The last term, "the constant", is +1.
Step-1: Multiply the coefficient of the first term by the constant 1 • 1 = 1
Step-2: Find two factors of 1 whose sum equals the coefficient of the middle term, which is -2.
-1 + -1 = -2 That's it
Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and -1
x4 - 1x2 - 1x2 - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
x2 • (x2-1)
Add up the last 2 terms, pulling out common factors :
1 • (x2-1)
Step-5 : Add up the four terms of step 4 :
(x2-1) • (x2-1)
Which is the desired factorization
Trying to factor as a Difference of Squares:
4.3 Factoring: x2-1
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (x + 1) • (x - 1)
Trying to factor as a Difference of Squares:
4.4 Factoring: x2 - 1
Check : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (x + 1) • (x - 1)
Multiplying Exponential Expressions:
4.5 Multiply (x + 1) by (x + 1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+1) and the exponents are :
1 , as (x+1) is the same number as (x+1)1
and 1 , as (x+1) is the same number as (x+1)1
The product is therefore, (x+1)(1+1) = (x+1)2
Multiplying Exponential Expressions:
4.6 Multiply (x-1) by (x-1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x-1) and the exponents are :
1 , as (x-1) is the same number as (x-1)1
and 1 , as (x-1) is the same number as (x-1)1
The product is therefore, (x-1)(1+1) = (x-1)2
Final result :
4 • (x + 1)2 • (x - 1)2
4d = 30 the answer would be c=7.5 right if not plz correct me if im wrong
Answer:
Correct!
Step-by-step explanation:
You did it the correct mathematical way, where you divide 4 by 30. Some people get confused and multiply 30 and 4, so good job!
Answer:
Step-by-step explanation: 4÷30=7.5 D = 7.5
Find the distance between the points A and B given below.
Answer:
use formula
Step-by-step explanation:
distance between the points A and B=
√((x2-x1)²+(y2-y1)²)
BRO PLS HELP ME I NEED TO TURN IT IN AN HOUR
Answer:
A
Step-by-step explanation:
Multiply all the points by 2.
Who tryna help me with my work? 10th Grade work btw.....
Answer:
Thanks for the points- but im a duma$s
Step-by-step explanation:
Is (-1,3) a solution for y < 2x + 5?
What is the measure of
Angles are not necessarily drawn to scale.
Answer: 58
Step-by-step explanation:
180-114= 66
66+56=122
180-122= 58
Pls help me ASAP pls
Jessica is bringing cupcakes to school for her birthday. She is placing them in a rectangular box that can fit 4 more cupcakes long that it can wide. They will not all fit in the box, so she is also bringing a bag that can hold 12 cupcakes. The amount of cupcakes she is bringing can be represented as x(x + 4) + 12. Solve for the number of cupcakes wide and long the box will hold. Part A) What does x represent?
Answer:
the amount of cupcakes
Step-by-step explanation:
you said the amount of cupcakes can be represented by