Answer:
Gradient or slope at x=1 is -3
Step-by-step explanation:
[tex]y=x^2-5x+6\\\frac{dy}{dx} =2x-5\\at ~x=1\\\frac{dy}{dx} =2(1)-5=-3[/tex]
Given that line AB is the angle bisector or
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
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 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!
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 )
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
Evaluate+the+expression
12-3y/2+v(2y-4/v) for y=3
Answer:
Y=3 but V=??????????????!!How do you solve this step-by-step?
Answer:
7 1/20OAmalOHopeO
its given that s=n(a+c)/2
Express c in terms of s, n and a
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
Can someone help me with this math homework please!
Explanation:
Choice A has the f(x) values going down on the interval -1 < x < 1 only.
Choice B appears to be decreasing over its entire domain, so we can rule this out (since we want -1 < x < 1 to be the only decreasing interval).
Choice C's table isn't decreasing when -1 < x < 1 since y = -3 increases to y = 0 (from x = -1 to x = 0). So we can rule it out.
A similar situation happens with choice D as well, so we can rule this out. The function isn't decreasing when we go from f(-1) to f(0).
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
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]
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]
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
Use the distributive property to write equivalent expressions.
Someone please help ty!
Answer:
12+27k
Step-by-step explanation:
distribute the 3
at a post office always charges a flat one-time fee for any order. One time, Michael sent 35 letters and paid 26 dollars. The next time, he send 18 letters and paid $14.10. How much does the post office charge to send one letter? What is the flat fee?
Answer:
The post office charges $0.7cents to send one letter, and the fee is $1.5
Step-by-step explanation:
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)
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]
need help asap plz
A rectangle ABCD has a width of 3 inches and a length of 7 inches.
Answer the following questions:
a) What is the Perimeter of the rectangle?
b) What is the Perimeter of the new rectangle if you double the width of rectangle ABCD? How did you find it? How many times bigger or smaller did the new Perimeter get? (You can divide the new Perimeter over the old one to find the times of increase/decrease)
c) What is the Perimeter of the new rectangle if you double the width and length of rectangle ABCD? How did you find it? How many times bigger or smaller did the new Perimeter get compared to the perimeter of rectangle ABCD?
d) Now choose a different shape of your liking and give it your own dimensions. Answer questions a), b), c) and d) for the shape you chose.
e) Can you generalize what happens to the Perimeter if you change one of the dimensions of a shape and what happens when you change both dimensions of the shape?
Answer:
I'm sorry but i only know a) so yeah
anyway a) is 20 in.
Step-by-step explanation:
Hope it helps!
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
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 ?
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.
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]
{(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}
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).
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
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
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
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
