Answer:
The volume of the solid is 19.[tex]\overline{142857}[/tex] unit³
Step-by-step explanation:
The given function is y = x³
The solid is created by revolving R about the line y = 1
We have that when y = 1, x = 1
Taking the end point as x = 2, we have the volume given by the washer method as follows;
[tex]V = \pi \cdot \int\limits^a_b {\left( [f(x)]^2 - [g(x)]^2 \right)} \, dx[/tex]
Where;
a = 1, and b = 2, we have;
g(x) = 1
[tex]V = \pi \cdot \int\limits^{2}_1 {\left( [x^3]^2 - [1]^2 \right)} \, dx = \pi \cdot \left[\dfrac{x^7}{7} + x \right]_1^{2} = \pi \cdot \left[\dfrac{2^7}{7} +2 -\left( \dfrac{1^7}{7} + 1\right)\right] =19\dfrac{1}{7}[/tex]
The volume of the solid, V = [tex]19\dfrac{1}{7}[/tex] unit³ = 19.[tex]\overline{142857}[/tex] unit³
How many times must a fair coin be flipped in order to ensure that there is at least a 99% chance of
getting at least one tail?
Find the perimeter of the shaded region. Round your answer to the nearest hundredth.
Answer:
59.16 units
Step-by-step explanation:
Given that,
The length of rectangle, L = 13
The breadth of the rectangle, B = 6
The perimeter of the shaded region = perimeter of rectangle - 2(perimeter of semicircle)
[tex]P=13\times 6-[2\times \dfrac{2\pi r}{2}]\\\\=78-2\pi r\\\\=78-2\times 3.14\times 3\\\\=59.16[/tex]
So, the perimeter of the shaded region is 59.16 units.
The straight line y = 3x +2 intersects the curve y = 2x^2 + 7x-11 at two points. Find the coordinates of these two points Give your answers correct to 2 decimal places.
Given:
The equation are
[tex]y=3x+2[/tex]
[tex]y=2x^2+7x-11[/tex]
To find:
The coordinates of intersection points.
Solution:
We have,
[tex]y=3x+2[/tex] ...(i)
[tex]y=2x^2+7x-11[/tex] ...(ii)
From (i) and (ii), we get
[tex]3x+2=2x^2+7x-11[/tex]
[tex]0=2x^2+7x-11-3x-2[/tex]
[tex]0=2x^2+4x-13[/tex]
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then by quadratic formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
In the equation [tex]0=2x^2+4x-13[/tex], we have [tex]a=2,b=4,c=-13[/tex].
Using quadratic formula, we get
[tex]x=\dfrac{-4\pm \sqrt{4^2-4(2)(-13)}}{2(2)}[/tex]
[tex]x=\dfrac{-4\pm \sqrt{16+104}}{4}[/tex]
[tex]x=\dfrac{-4\pm \sqrt{120}}{4}[/tex]
Now,
[tex]x=\dfrac{-4+\sqrt{120}}{4}[/tex] and [tex]x=\dfrac{-4-\sqrt{120}}{4}[/tex]
[tex]x=1.7386[/tex] and [tex]x=-3.7386[/tex]
[tex]x\approx 1.74[/tex] and [tex]x\approx -3.74[/tex]
Putting x=1.74 in (i), we get
[tex]y=3(1.74)+2[/tex]
[tex]y=5.22+2[/tex]
[tex]y=7.22[/tex]
Putting x=-3.74 in (i), we get
[tex]y=3(-3.74)+2[/tex]
[tex]y=-11.22+2[/tex]
[tex]y=-9.22[/tex]
Therefore, the coordinates of the intersection points are (1.74, 7.22) and (-3.74,-9.22).
PLEASE HELP ME WITH THIS QUESTION! I haven’t got any answers for this question so please help!
Answer:
15 slices
5 slice more
Step-by-step explanation:
1 and 1/4 ÷ 1/12 = 15
5/6 ÷ 1/12 = 10
15 - 10 = 5
The value of Kensington's car decreases in value according to the exponential decay
function V
Pe-0.12t , where Vis the current value of the vehicle, t is the
number of years Kensington has owned the car and P is the purchase price of the car,
$20,000. To the nearest dollar, what will be the value of Kensington's car in 8 years?
The selling price of an item is $585. It is marked down by %20, but this sale price is still marked up from the cost of $360. Find the markup from cost to sale price.
Answer:
$108
Step-by-step explanation:
The selling price being marked down by 20% means that $585 was reduced by 20%
Selling price = $585 - ( 20% x $585)
$585 - (0.2 x $585) = $468
Markup from cost = selling price - cost price
$468 - $360 = $108
The value of 3° is
its from the chapter exponenets
Answer:
1
Step-by-step explanation:
=>. the value of 3° = 1
=> it is known to us that any number to the
power zero is equals to 1
hope it helps
Solve the equation -25p – 2 = 48 for p.
A. -2
B. 1
C. 3
D. 8
Answer:
A. -2
Step-by-step explanation:
-25p - 2 = 48
First, add 2 to both sides
That gives you
-25p = 50
Then, divide both sides by -25. Then that leaves the answer.. p = -2
Help please its geometry
Answer:
b
Step-by-step explanation:
Opposite angles are equal in a parallelogram. Therefore 2 angles are 112°. Angles in a parallelogram or any quadrilateral are equal to 360°. To find the remaining sides: 360-(112×2) and divide your answer by 2.
HELP please I don’t know what to do
Answer:
47 degrees
Step-by-step explanation:
180-133=47
Answer:
∠Q = 44°
Step-by-step explanation:
∠R = 180° - 133° = 47°
∠Q = 180° - 89° - 47° = 44°
find the unknown value in the pair of equivalent fractions.
5/? = 15/45
The square root of 5 , has a decimal expansion that does not end or repeat. To which set of numbers does it belong?
A. rational
B. Natural
C. Integer
D. Irrational
Answer:
Irrational numbers is correct.
The required square root of 5 is an irrational number.
Given that,
The square root of 5, has a decimal expansion that does not end or repeat. To which set of numbers does it belong is to be determined.
In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.
What are irrational numbers?An irrational number is a type of real number which cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.
Here,
√5 = 2.2360679775..
Which is an irrational number.
Thus, the required square root of 5 is an irrational number.
Learn more about rational numbers here:
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How would you solve this?
Answer:
The equation has three solutions:
x= [tex]\frac{1}{2} + \frac{1}{2} log_{2} (3)[/tex]
x=1
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
||[tex]4^{x} - 3[/tex]|[tex]-2[/tex]| = 1
|[tex]4^{x} - 3[/tex]|[tex]-2[/tex] = 1 |[tex]4^{x} - 3[/tex]|[tex]-2[/tex] = - 1
|[tex]4^{x} - 3[/tex]| = 1+2 |[tex]4^{x} - 3[/tex]| = -1+2
|[tex]4^{x} - 3[/tex]|=3 |[tex]4^{x} - 3[/tex]| = 1
[tex]4^{x} - 3[/tex] =3 [tex]4^{x} - 3[/tex] = - 3 [tex]4^{x} - 3[/tex] = 1 [tex]4^{x} - 3[/tex] = - 1
x= [tex]\frac{1}{2} + \frac{1}{2} log_{2} (3)[/tex] x∉∅ x=1 [tex]x = \frac{1}{2}[/tex]
The union of these four solutions is: [tex]\frac{1}{2} , 1,[/tex] [tex]\frac{1}{2} + \frac{1}{2} log_{2} (3)[/tex]
I hope this is clearly and understandably written to you :)
2 24-5what is 24 - 2x wanted to 24 - 5 exponent
Answer:
24-5:x2
Step-by-step explanation:
im not sure
mark brainliest if it helps
What is 4 5/13 as a decimal rounded to the nearest tenth
Answer:
4.4
Step-by-step explanation:
4 5/13 = 4 + 5/13 = 4 + 0.384615... = 4.384615...
Answer: 4.4
Answer:
4.4
Step-by-step explanation:
Evaluate -4x^2 + 2x - 6 when x = -2.
Answer:
-26
Step-by-step explanation:
-4(-2)^2 + 2(-2) - 6
-4(4) + -4 - 6
-16 -10
-26
The value of equation [tex]-4x^{2}+2x-6[/tex] is -26 when x = -2
What is equation?"An equation is a statement of equality between two expressions consisting of variables and/or numbers."
Substitute the value x = -2 in the given equation
[tex]=-4(-2)^{2}+2(-2)-6 \\=-4(4)-4-6\\=-16-4-6\\=-16-10\\=-26[/tex]
Hence, the value of the given equation is -26
To learn more about equation here
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what is the table rule
Answer:
x+4 = y
Step-by-step explanation:
Pretty simple
Lana sells lampshades for $8 each and paper lanterns for $5 each at a one-day craft fair. She sells k lampshades and (k+5) paper lanterns. The expression 8k + 5(k+5) represents Lana's total sales. Select all the equivalent expressions for Lana's total sales at the fair
Answer:
8k + 5k + 25
Or
13k + 25
Step-by-step explanation:
Lana's total sales = 8k + 5(k+5)
Since the expressions are not given in the question;
The equivalent expression could be
= 8k + 5k + 25
Equivalent to
= 13k + 25
According to the diagram below, which similarity statements are true?
Check all that apply.
P
S
R
A. APQR - APRS
B. APQR ~ APSQ
O C. APQR ~ AQSR
D. APQS ~ AQRS
The required triangle PQS and triangle QRS are similar triangles. Option D is correct.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
According to the diagram,
It can be inferred that triangle PQS and triangle QRS are similar to each other. The term "similar" implies that these two triangles have the same shape but can be different in size. Specifically, the corresponding angles of these triangles are equal, and the corresponding sides are in proportion.
Consider triangle, PQS, and triangle QRS
Angle S is the common angle in both the triangles
And angle Q is similar to angle R
So both the triangle are similar by AA similarity postulate
Therefore, option D is correct.
Learn more about triangle similarities here:
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plz help find perimeter and area
Rewrite using a single positive exponent.
8
.8
-3
Find the simple interest paid on a loan of $4,750 at a rate of 19.5% for 30 months.
Answer:
Monthly Payment $201.31
Total Interest Paid $1,289.26
Total Paid $6,039.26
Step-by-step explanation:
2+5.67890654321678-5432
if b = -3, what is the value of b³?
Answer:
-27
Step-by-step explanation:
b³=(-3)³
b³=(-3×-3×-3)
b³=-27
Simplify the expression. 9.6r - 6.3r =
3.0 r is the answer
Step-by-step explanation: I help ;)
In XYZ, X = 57 cm, z = 54 cm and ZZ=112°. Find all possible values of ZX, to the
nearest degree
Answer:
No Possible Triangles
Step-by-step explanation:
Deltamath
Answer:
102
Step-by-step explanation:
sinA/a = sinB/b
sin x /57=sin 112/54
0.9786941
sin ^ -1 (0.786941)=78
180- 78=102
Anna makes a quilt by sewing together green, white, and yellow fabric. When she finishes, 2/6 of the quilt is green, and 3/6 is yellow. The rest is white. What fraction of the quilt is white? Show your work.
Answer:fraction of the quilt is white = 1/6
Step-by-step explanation:
Let the total quilt be = 1 ( since we are dealing with fraction)
The portion of quilt that is green 2/6
The portion of quilt that is yellow 3/6
The portion that is white = Total quilt −( portion of quilt that is green and yellow)
=1−( 2/6 + 3/6 )
=1 −5/6
=1/6
What is the value of the expression of 1.623/100
Step-by-step explanation:
1.623/100
=1.623×10^-2
or
=0.01623
Hope it helps
use the following values for x {-1 ,0 , 1 , 2 } for the function f{x} = 4x+3 to make a function table
please help me , and thanks
Answer:
f(x)= -1
f(x)= 3
f(x)= 7
f(x)= 11
Step-by-step explanation:
You need to add the values of x into the function
f(x)= 4(-1) + 3
f(x)= 4(0) + 3
f(x)= 4(1) + 3
f(x)= 4(2) + 3
Mary has a budget for groceries fuel, and utilities. She spent 30% of her budget in groceries if mary spent 42$ on groceries than how much is her budget
Given:
Mary spent 30% of her budget in groceries.
She spent 42$ on groceries.
To find:
The total amount of her budget.
Solution:
Let x be the total amount of the budget.
Then, the amount spent on groceries is 30% of x.
[tex]\dfrac{30}{100}x=0.3x[/tex]
She spent 42$ on groceries.
[tex]0.3x=42[/tex]
Divide both sides by 0.3.
[tex]x=\dfrac{42}{0.3}[/tex]
[tex]x=140[/tex]
Therefore, the total amount of the budget is 140$.