$\sf\underline\bold\blue{Information\:given\:in\:the\:question:}$
π =[tex]\sf{ 3.1415}[/tex]$\sf{Diameter = 20inches}$$\space$
$\sf\underline\bold\blue{What\:we\:have\:to\:find?}$
$\sf{Area\:of\:the\:circle.}$$\space$
$\sf\underline\bold\blue{Answer:}$
$\sf\small{Area\:of\:the\:circle\:is : 314.15}$$\space$
$\sf\underline\bold\blue{Calculations:}$
Here we have the value of the circle's diameter that is 20inches. So, first we have to calculate the radius of the circle using the formula :
$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{Diameter}{2}$
$\space$
$\sf\underline\bold\blue{Calculating\:the\:required\:values:}$
$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{20}{2}$
$\sf{Convert \: to \: the\:lowest\:term(Divide),}$
$\mapsto$ $\sf\underline\bold{Radius=10}$
☆Now we know the value of the radius . So now let's calculate the area of the circle.
$\space$
$\sf\bold{Area\:of\:circle:}$ π$\sf{ r \: ^{2} }$
$\sf\bold{Evaluating \: the\:required\:values:}$
$\sf\bold{Area\:of\:circle=3.1415(10)^2}$
$\space$
$\sf\bold{Area\:of\:the\:circle=3.1415\times10\times10}$
$\sf\bold{Now,}$
$\sf\bold{Area\:of\:the\:circle:3.1415\times100}$
$\space$
$\sf\underline\bold\green{Thus,Area\:of\:the\:circle\: is \: 314.15}$
____________________________
I will mark you the brainiest for the correct answer, please be correct, Have a good day and take care, thanks. ( VIEW THE IMAGE TO ANSWER)
If f(x)f(x) is an exponential function where f(1.5)=5f(1.5)=5 and f(7.5)=79f(7.5)=79, then find the value of f(3)f(3), to the nearest hundredth.
Answer: [tex]7.93[/tex]
Step-by-step explanation:
Given
[tex]f(x)[/tex] is an exponential function. Suppose [tex]f(x)[/tex] is [tex]ae^{bx}[/tex]
[tex]f(1.5)=5\ \text{and}\ f(7.5)=79[/tex]
[tex]\Rightarrow 5=ae^{1.5b}\\\Rightarrow \ln 5=\ln a-1.5b\quad \ldots(i)[/tex]
Similarly,
[tex]\Rightarrow 79=ae^{7.5b}\\\Rightarrow \ln(79)=\ln a+7.5b\quad \ldots(ii)[/tex]
Subtract (i) and (ii)
[tex]\Rightarrow \ln (79)-\ln (5)=9b\\\Rightarrow \ln (\frac{79}{5})=9b\\\\\Rightarrow b=\dfrac{\ln (\frac{79}{5})}{9}\\\\\Rightarrow b=0.3066[/tex]
Insert the value of [tex]b[/tex]
[tex]\Rightarrow 5=ae^{0.46}\\\Rightarrow a=5\times 0.6312\\\Rightarrow a=3.156\approx 3.16[/tex]
So, the function becomes
[tex]\Rightarrow f(x)=3.16e^{0.3066b}[/tex]
[tex]\Rightarrow f(3)=3.16e^{0.3066\times 3}\\\Rightarrow f(3)=7.927\approx 7.93[/tex]
Answer:
7.93
General Exponential Form: y=ab^x
Plug in both points
divide the equations
cancel out a, subtract exponent of b
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
If y=-12 when x=9, find y when x=-4
please answer quickly
Answer: x=3
Step-by-step explanation:
to make y=-4 from -12 you have to divide by 3. so divide the 9 by 3 to get 3 which is your answer
{(5,2), (-2,4), (2, -7)}
Domain:
Range:
Answer:
Step-by-step explanation:
The domain are all the x values in order, no repeats allowed:
D = {-2, 2, 5}
Same thing for the range, except these are the y values:
R = {-7, 2, 4}
The coordinates stated this way don't match up to what they are in coordinate form, but they don't have to.
Answer:
Domain : {-2,2,5}
Range:{ -7,2,4}
Step-by-step explanation:
The domain is the inputs
Domain : {-2,2,5}
The range is the outputs
Range:{ -7,2,4}
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).
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 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]
Which shows the following expression after the negative exponents have been eliminated?
Answer:
Option A
Step-by-step explanation:
[tex]\frac{1}{a^{-m}}=a^{m}\\[/tex]
[tex]\frac{m^{7}n^{3}}{mn^{-1}}=\frac{m^{7}n^{3}n^{1}}{m}=\frac{m^{7}n^{3}n}{m}[/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 )
its given that s=n(a+c)/2
Express c in terms of s, n and a
When the polynomial is written in standard form, what are the values of the leading coefficient and the constant?
5x + 2 – 3x2
Answer:
leading coefficient -3
constant 2
Step-by-step explanation:
Standard from is from largest power to smallest power
-3x^2 +5x +2
The leading coefficient is the number in front of the largest power of x
-3
The constant is the number without a power of x ( or x^0)
2
Use the distributive property to write equivalent expressions.
Someone please help ty!
Answer:
12+27k
Step-by-step explanation:
distribute the 3
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.
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
THIS QS with explanation sum
Answer:
X = 276°
Step-by-step explanation:
Divide X into x1 and x2
then then using the trick of co-interior angles, find the answer of x1 and x2 . then add x1 and x2
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]
A boy spent 2/7 of his pocket money on transport and 1/5 on sweet. if he left with 20. what is the amount of money in the boys pocket
Answer:
x = 350
Step-by-step explanation:
x - starting amount
[tex]\frac{2}{7} x[/tex] = after transport
[tex]\frac{1}{5} (\frac{2}{7} x)[/tex] = after sweets
[tex]\frac{1}{5} (\frac{2}{7} x)[/tex] = 20
[tex](\frac{2}{35} x)[/tex] = 20
2x = 700
x = 350
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
#SPJ2
Evaluate+the+expression
12-3y/2+v(2y-4/v) for y=3
Answer:
Y=3 but V=??????????????!!Instructions: Find the measure of the indicated angle to the nearest degree.
29 and 17
Answer:
30º
Step-by-step explanation:
because it is a right triangle, we can use trig functions to solve
tan^{-1}=17/29=30.379
Solve the system of equations using substitution.
y = x + 6
y = –2x – 3
Answer:
x = -3
y= 3
Step-by-step explanation:
y = x + 6 -----------------------(I)
y = -2x - 3 ---------------------(II)
Substitute y =x +6 in equation (II)
x + 6 = -2x - 3
Add 2x to both sides
x + 2x +6 = -3
Combine like terms
3x + 6 = - 3
Subtract 6 from both sides
3x = - 3 - 6
3x = -9
Divide both sides by 3
x = -9/3
x = -3
Plug in s = -3 in equation (I)
y = -3 + 6
y = 3
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
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
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
:)
Omg who can help me? Its due tomorrow
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 7+21?
please help please helppp
Answer:
=28
Step-by-step explanation:
21
+ 7
___________
28
Hope this helps! If it is a simple addition ?
