Answer:
The length of one side of the hot tub is 4.8ft
Step-by-step explanation:
Given
Shape: Square
[tex]k = 5[/tex] -- scale factor
[tex]B'C' = 24[/tex]
Required
Side length of ABCD (the hot tub)
From the question, we understand that
[tex]ABCD \to D_5 \to A'B'C'D[/tex] ABCD dilated by 5 to A'B'C'D
This implies that:
[tex]BC * 5 = B'C'[/tex] i.e. the sides of ABCD is multiplied by 5 to get A'B'C'D
So, we have:
[tex]BC * 5 = 24[/tex]
Divide by 5
[tex]BC = 4.8[/tex]
What is the second integral of
[tex] \frac{1}{x} [/tex]
?
Answer:
[tex]\displaystyle \int {\int {\frac{1}{x}} \, dx} \, dx = xln|x| - x + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationLogarithmic Differentiation
Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Logarithmic Integration
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {\int {\frac{1}{x}} \, dx} \, dx[/tex]
Step 2: Integrate Pt. 1
[Inner Integral] Logarithmic Integration: [tex]\displaystyle \int {ln|x|} \, dx[/tex]Step 3: Integrate Pt. 2
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = ln|x|[/tex][u] Differentiate: [tex]\displaystyle du = \frac{1}{x} \ dx[/tex]Set dv: [tex]\displaystyle dv = dx[/tex][dv] Integrate: [tex]\displaystyle v = x[/tex]Step 4: Integrate Pt. 3
[Integral] Integration by Parts: [tex]\displaystyle \int {ln|x|} \, dx = xln|x| - \int {(x \cdot \frac{1}{x})} \, dx[/tex][Right Integral] Simplify: [tex]\displaystyle \int {ln|x|} \, dx = xln|x| - \int {} \, dx[/tex][Right Integral] Reverse Power Rule: [tex]\displaystyle \int {ln|x|} \, dx = xln|x| - x + C[/tex]Redefine: [tex]\displaystyle \int {\int {\frac{1}{x}} \, dx} \, dx = xln|x| - x + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Help Needed Please!!!
First the volume of the sphere
Answer:
1766 using 3.14 for pi
1767 using the pi button
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
we need to know the radius
r =d/2 = 15/2 = 7.5
V = 4/3 (pi)( 7.5)^3
V =562.5 pi
Approximating pi by 3.14
V = 562.5 (3.14)
V =1766.25
To the nearest whole number
V = 1766
If you use the pi button
1767.14586
To the nearest whole number
1767
Answer:
[tex]V=1767[/tex]
Step-by-step explanation:
Step 1: Find the volume of the sphere
Volume of a Sphere: [tex]V=\frac{4}{3}\pi r^{3}[/tex]
Find the radius
[tex]Radius = Diameter / 2[/tex]
[tex]Radius = 15 / 2[/tex]
Plug in the values and solve
[tex]V=\frac{4}{3}\pi * \frac{15}{2}^{3}[/tex]
[tex]V=\frac{4}{3}\pi * \frac{3375}{8}[/tex]
[tex]V=\frac{1125}{2}\pi[/tex]
[tex]V=1767[/tex]
Answer: [tex]V=1767[/tex]
please help asap
6. Solve for x
Answer:
D. -2
Step-by-step explanation:
19 = x + 12 + 11 + x
Solve for x
Combine like terms
x + x = 2x
12 + 11 = 23
We now have
19 = 23 + 2x
Subtract 23 from both sides
19 - 23 = -4
23 - 23 cancels out
We now have -4 = 2x
Divide both sides by 2.
-4/2 = -2
2x/2 = x
x = -2
simplify m√p + n√p - √p
Answer:
[tex]{ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p}(m + n - 1) }}[/tex]
Calculate the answer without using a calculator
g) cos 180° + 2 fan 30 sin 60
Answer:
0
Step-by-step explanation:
Tan 30 and Sin 60 are in first quadrant and so their values will be positive.
Cos 180 is in Second quadrant. In second quadrant , value of cos is negative.
Cos 180 = -1 ; Tan 30 = 1/√3 & Sin 60 = √3/2.
Cos 180 + 2 tan 30 + Sin 60 = [tex]-1 + 2* \frac{1}{\sqrt{3}}*\frac{\sqrt{3}}{2}[/tex]
= [tex]-1 + 1 = 0[/tex]
Find the length of the arc round your answer to the nearest 10th
Answer:
i think its 30
Step-by-step explanation:
Answer:
length ≈ 2.6 ft
Step-by-step explanation:
arc length is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{30}{360}[/tex]
= 2π × 5 × [tex]\frac{1}{12}[/tex]
= 10π × [tex]\frac{1}{12}[/tex]
= [tex]\frac{10\pi }{12}[/tex]
≈ 2.6 ft ( to the nearest tenth )
Will it matter if I don’t get accelerated pre algebra in 7th grade and get into normal pre algebra? Will it make me less likely to get into top colleges?
Answer:
Maybe, there is a chance, but I don't know for sure.
It might matter, but I wouldn't worry or stress about it too much.
My only advice to you is do not procrastinate and if you need help don't be afraid to ask.
Answer:
It matters but not like you think.
GPA, extracurricular activities, and SAT/ACT are the biggies. Truthfully it won't change a thing if you took accelerated pre-algebra versus normal. In fact, spoiler alert, the SAT/ACT (I'm assuming your american) will matter more than your courses ever did. I took two years of college physics in highschool and i made more off my SAT. Not only that, but an A in an easy class looks better than a C in a hard one on transcripts.
My advise is slow down, relax, and learn it well. Better to learn the concept fully in normal so that you can apply it, than half learn it in advance and struggle in future applications. After all, math ALWAYS builds. Take it slow, take it easy.
I would recommend talking to a school guidance counselor about your academic stress. Im sure their professional insight will help put you at ease. It may also help to get you going in the right direction so that you achieve your goals.
Good luck. Enjoy life
would appreciate the help please!
Answer:
I think SAS is the correct Ans
Sue, Jane, and Alice share 213 paper clips equally among themselves. if Alice gives 24 paper clips to Sue, how many paper clips does Sue have altogether?
Please Solve:
x^2-4x-5=0
HELP PLEASEEE!!!! ASAP!!!!!
To find the inverse of a function, switch the x's and y's, then solve for y again.
y = 2/3x - 17
SWITCH
x = 2/3y - 17
2/3y = x + 17
y = 3(x + 17) / 2
y = x - 10
SWITCH
x = y - 10
y = x + 10
y = cuberoot(2x)
SWITCH
x = cuberoot(2y)
x^3 = 2y
y = x^3 / 2
y = x/5
SWITCH
x = y/5
y = 5x
Hope this helps!
What is the vertex of the function f(x) = -|x + 7| − 4?
A.
(-7,-4)
B.
(7,4)
C.
(-7,4)
D.
(7,-4)
Answer:
it would be
D.
(7,-4)
Mark me as brainliest pleases
Answer:
it would be A (-7,-4)
Step-by-step explanation:
Omg who can help me? Its due tomorrow
Sara has a rectangular garden in her backyard that measures 12 m by 15 m. She wants to put a rock walkway on the diagonal. How long will the walkway be? Round to the nearest tenth of a meter
Answer:
19.2 m
Step-by-step explanation:
Since this is a right triangle, we can use the pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
12^2 + 15^2 = c^2
144 + 225 = c^2
369 = c^2
Taking the square root of each side
sqrt(369) =sqrt(c^2)
19.20937271=c
To the nearest tenth
19.2 = c
Answer:
Diagonal of rectangle walk = 19.2 meter (Approx.)
Step-by-step explanation:
Given:
Length of rectangle = 12 meter
Width of rectangle = 15 meter
Find:
Diagonal of rectangle walk
Computation:
Diagonal of rectangle = √l² + b²
Diagonal of rectangle walk = √Length of rectangle² + Width of rectangle²
Diagonal of rectangle walk = √12² + 15²
Diagonal of rectangle walk = √144 + 225
Diagonal of rectangle walk = √369
Diagonal of rectangle walk = 19.2093
Diagonal of rectangle walk = 19.2 meter (Approx.)
In the same amount of time, James drove twice as far as Roger. Altogether, James and Roger drove 90km. Find the number of kilometres driven by each person.
Answer:
james drove 60 and roger drove 30
Step-by-step explanation:
90/3= 30= roger
90/3=30x2=60= james
james(60)+roger(30)= 90
5. Find the area of the shaded part in this figure.
(12) In a relay race, Mia ran 1.43 kilometers. Then she passed the baton to Gerald, who ran an
additional 2.7 kilometers. How many kilometers did they run in all?
a. 4.13 Kilometers
b. 3.36 kilometers
G. 3.50 Kilometers
d. 1.70 kilometers
Answer:
4.13
Step-by-step explanation:
To find out how many kilometres they ran in all you have to do 1.43+2.7 =4.13
Answer:
a
Step-by-step explanation:
Mai running=1•43km
Gerald=2•7km
Mai+Gerald=they run in all
1.43+2.7 = 4.13km
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
Answer:
(x-9)^2 +(y-12)^2 = 225
Step-by-step explanation:
First find the length of the radius
If is the distance from the center to the point
d = sqrt( (x2-x1)^2 + (y2-y1)^2 )
= sqrt( (0-9)^2 + (0-12)^2)
= sqrt ( 81+144)
= sqrt(225)
= 15
The equation for a circle is
( x-h) ^2+ (y-k)^2 = r^2
(x-9)^2 +(y-12)^2 = 15^2
(x-9)^2 +(y-12)^2 = 225
Which expression is equivalent to
Answer:
[tex]\frac{(x+2)}{(x-1)}[/tex]
Step-by-step explanation:
[tex]\frac{x^2 + x -2}{x^2 -2x+1}[/tex] =
[tex]\frac{(x+2)(x-1)}{(x-2)(x-1)}[/tex] =
[tex]\frac{(x+2)}{(x-1)}[/tex]
A particular strain of bacteria triples in population every 45 minutes Assuming you start with 50 bacteria in a Petri dish how many bacteria will there be in 4.5 hours
Answer:
4.5 hours in minutes = 270
Every 45 minutes, bacteria triples
You start with 50
Divide 270 (total time) by 45 (every time bacteria triples)
270/45 = 6
36,450 bacteria
arrange the resistance r1 r2 and r3 in increasing order.
Answer:
[tex]R_1>R_2>R_3[/tex]
Step-by-step explanation:
As per Ohm's law,
V = IR
I = Current
R = Resistance
V = Voltage
This law states → R = [tex]\frac{V}{I}[/tex]
If we graph the relation between Voltage and Current, linear graph represents the Resistance.
Greater the slope of the line will represent greater resistance.
Therefore, [tex]R_1>R_2>R_3[/tex]
Integrate the following.[tex]\int\limits^a_b {sin(x)} \, dx[/tex]
Answer: -cos(a)+cos(b)
Step-by-step explanation:
To integrate is the same as saying to find the antiderivative.
[tex]\int\limits^a_b {sin(x)} \, dx[/tex] [antiderivative of sinx is -cosx]
[tex]-cos(x)|_b^a[/tex] [include boundaries]
[tex]-cos(a)+cos(b)[/tex]
Therefore, the integral would be -cos(a)+cos(b).
What is the sum of the polynomials? (6x+7+x^2)+(2x^2-3)
a.-x^2+6x+4
b.3x^2+6x+4
c.9x + 4
d.9x^2+4
Answer:
b.
[tex]{ \tt{(6x + 7 + {x}^{2})(2 {x}^{2} - 3) }} \\ = { \tt{(2 + 1) {x}^{2} + 6x + (7 - 3) }} \\ = { \tt{3 {x}^{2} + 6x + 4 }}[/tex]
find the scale factor
Answer:
I think its 1.4
Step-by-step explanation:
if you divide 42 by 1.4 it makes 30 and if u multiply 30 by 1.4 it makes 42
Answer:
the scale factor is 7/5
Step-by-step explanation:
42/30=
42/30=
then you find a common factor between the two is 6, so you divide both sides of the fraction by 6 to get 7/5. and because they both are the same you know that they both have the same scale factor. Which is 7/5. I am not quite sure if you need to find the missing side length but in case you do multiply 40 by 7/5 so it looks like 40/1 x 7/5. 40 x 7 = 280. 280/5 = 56. so your side length is 56.
7. If the supplement of an angle is 69, then find its complement.
Answer:
no solution
Step-by-step explanation:
Supplementary angles add to 180
Let x be the supplement
x+69 = 180
x = 180-69
x =111
The complement of an angle means they add to 90
111+y = 90
y = 90-111
y =-21
But an angle cannot be negative so there is no solution
Answer:
21 degrees.
Step-by-step explanation:
To find the complementary angle you have to subtract the given angle from 90.
so,
90 - 69 = 21.
Extra info: if you need to find the supplementary angle you need to subtract the given angle from 180.
What is the exponential form of log3 2187 = 7?
Answer:
2187 = [tex]3^{7}[/tex]
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n , then x = [tex]b^{n}[/tex] , then
[tex]log_{3}[/tex] 2187 = 7
2187 = [tex]3^{7}[/tex]
Answer:
3 ^7 = 2187
Step-by-step explanation:
log3 2187 = 7
log a (b) = c
a^c = b
3 ^7 = 2187
Please help 50 points!
d=10
Answer:
Solution given:
[tex]\sqrt{25+3x}=d+2x[/tex]
squaring both side
25+3x=(d+2x)²
when x=-3
25+3*-3=(d+2*-3)²
25-9=(d-6)²
16=(d-6)²
[tex]\sqrt{16}=d-6[/tex]
4=d-6
d=4-6
d=10
Answer:
d = 6
Step-by-step explanation:
[tex] \sqrt{25 + 3( - 3)} = d + 2( - 3) \\ 4 = d - 6 \\ d = 10[/tex]
hopefully this makes sense
:)
Please help me with this (geometry)
Answer:
∠ 6 = 55°
Step-by-step explanation:
∠ 6 and 125° are same- side interior angles and sum to 180° , then
∠ 6 = 180° - 125° = 55°
Which of the following is the number of sides for a regular polygon that will
not form a regular tessellation?
A. 6
B. 4
C. 7
D. 3
Answer:
A
Step-by-step explanation:
A
The number of sides for a regular polygon that will not form a regular tessellation is 7. The correct option is C.
What is a polygon?A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
A tessellation or tiling is the seamless covering of a surface, frequently a plane, with one or more geometric shapes, known as tiles. One regular polygon can be used to create a single regular tessellation. Two or more regular polygons are used in a semi-regular tessellation.
Triangles, squares, and hexagons are the only three regular tessellations.
Now, the name of the polygon having 3, 4, and 6 sides is triangle, square, and Hexagon. Therefore, the only regular polygon that will not form a regular tessellation is heptagon, which has 7 sides.
Hence, the number of sides for a regular polygon that will not form a regular tessellation is 7.
Learn more about Polygon here:
https://brainly.com/question/10441863
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Noelle has containers that each hold one gallon of liquid. She used these containers to dispose of waste from the chemistry laboratory. She collected 3 quarts 1 pint of liquid from the first table, 4 quarts from the second table, 2 quarts from the third table , and 3 quarts 1 pint from the fourth table. What is the least number of containers Alyssa needed to collect the waste ? ( 4 quarts = 1 gallon , 2 pints = 1 quart )
Answer:
4 containers.
Step-by-step explanation:
Since Noelle collected 3 quarts 1 pint of liquid from the first table, the amount of liquid collected in quarts is 3 quarts + 1 pint = 3 quarts + 1 pint × 1 quarts/2 pints = 3 quarts + 0.5 quarts = 3.5 quarts.
She also collected 4 quarts from the second table, 2 quarts from the third table.
Finally, she collected collected 3 quarts 1 pint of liquid from the fourth table, the amount of liquid collected in quarts is 3 quarts + 1 pint = 3 quarts + 1 pint × 1 quarts/2 pints = 3 quarts + 0.5 quarts = 3.5 quarts.
So, the total amount of liquid she collected in quarts is V = 3.5 quarts + 4 quarts + 2 quarts + 3.5 quarts = 7.5 quarts + 5.5 quarts = 13 quarts
We now convert this value to gallons to know the amount of containers Noelle needs since she has one gallon containers.
13 quarts = 13 × 1 quarts = 13 quarts × 1 gallon/4 quarts = 13/4 gallons = 3.25 gallons
Since the total amount of liquid is 3.25 gallons = 3 gallons + 0.25 gallons, Noelle would need 4 containers since 3 containers would contain the first 3 gallons and the fourth container would contain the remaining 0.25 gallons.
So, Alyssa would need 4 containers.
