Answers
Answer:
1. x = 6 cm
2. The coordinates of the x-intercept are (-15.798879, 0) and (8.177004, 0)
b) The maximum value of is y is approximately 459.874
The value of 'x' for which the maximum occurs is x is -3.8109375
c) 'k' is approximately -15.63748 or 'k' is approximately 8.0156
Step-by-step explanation:
1. The area of rectangle ABCD - Area of triangle ABP = 114 cm²
Therefore, we have;
The area of rectangle ABCD = (2·x - 3)·(3·x + 1)
∴ The area of rectangle ABCD = 6·x² + 2·x - 9·x - 3 = 6·x² - 7·x - 3
The area of triangle ABP = 1/2 × (3·x + 1)·x = 3·x²/2 + x/2
The area of rectangle ABCD - Area of triangle ABP = 6·x² - 7·x - 3 - 3·x²/2 - x/2
6·x² - 7·x - 3 - 3·x²/2 + x/2 = 9·x²/2 - 13·x/2 - 3 = 114
9·x²/2 - 15·x/2 - 3 = 114
9·x² - 15·x - 6 - 228 = 0
9·x² - 15·x - 234 = 0
x = (15 ± √((-15)² - 4 × 9 × (-234)))/(2 × 9) = (15 ± 93)/18
∴ x = 6 or x = -13/3
Given that x is a natural number, we have that x = 6 cm
2. The given equation is 'y = -3.2·x² - 24.39·x + 413.4'
Therefore, we have;
The x-intercept are the values of 'x', where the value of 'y' is 0
Therefore, we have, at the x-intercept;
y = 0 = -3.2·x² - 24.39·x + 413.4
By the quadratic formula, we have;
x = (24.39 ± (√((-24.39)² - 4×(-3.2)×413.4)))/(2 × (-3.2))
x ≈ -15.798879 or x ≈ 8.177004
The coordinates of the x-intercept are;
(-15.798879, 0) and (8.177004, 0)
b) The maximum is given at dy/dx = 0
Therefore, at the maximum point, we have;
dy/dx = d(-3.2·x² - 24.39·x + 413.4)/dx = -6.4·x - 24.39 = 0
dy/dx = -6.4·x - 24.39 = 0
∴ x = 24.39/(-6.4) = -3.8109375
x = -3.8109375 at the maximum point
At the maximum point, we have;
y = -3.2·x² - 24.39·x + 413.4 = -3.2·(-3.8109375)² - 24.39·(-3.8109375) + 413.4 ≈ 459.874
y ≈ 459.874
Therefore, the maximum value of 'y' is given as follows
[tex]y_{max}[/tex] ≈ 459.874
The value of 'x' for which the maximum occurs is x = -3.8109375
c) The coordinate of the point is (12.3, k), therefore, we have;
y = -3.2·x² - 24.39·x + 413.4
When y = 12.3, therefore, -3.2·x² - 24.39·x + 413.4 = 12.3
-3.2·x² - 24.39·x + 413.4 = 12.3
-3.2·x² - 24.39·x + 413.4 - 12.3 = -3.2·x² - 24.39·x + 401.1 = 0
By the quadratic formula, we have;
x = (24.39 ± √((-24.39)² - 4×(-3.2)×401.1))/(2 × (-3.2))
x ≈ -15.63748 or x ≈ 8.015600
Therefore, k ≈ -15.63748 or k ≈ 8.015600
Related Questions
An archeologist has found a fossilized leg bone of some unknown mammal. Based on the size of the bone, she determines that it should have contained about 100 g of carbon-14 when the animal was alive. Knowing that the half-life of carbon-14 is 5730 years, write an equation that will model how much carbon-14 is left in the bone now after "t" years.
Answers
Answer:
Therefore, required equation is N = 100 x [tex]2^{- \frac{t}{5730 }[/tex]
Step-by-step explanation:
According to the question it is given that
Amount of carbon atom when animal was alive is [tex]N_0[/tex] = 100g
Half life of C-14 is 5730 years
Let 'N' be the amount of carbon atom present after 't' time
since the differential equation of decay process of radioactive atom is
[tex]\frac{dN}{dt} = \lambda N[/tex] where, λ is the decay constant
on solving this we get
[tex]N = N_0 e^{-\lambda t}[/tex]
on further solving and substituting [tex]\lambda = \frac{ln2}{T_{1/2}}[/tex] we get
[tex]N = N_0 2^{- \frac{t}{T_{1/2}} }[/tex]
on substituting the value of [tex]N_0[/tex] = 100g and [tex]T_{1/2}[/tex] = 5730 we get
N = 100 x [tex]2^{- \frac{t}{5730 }[/tex]
Which of the following numbers is irrational?
A)5/8
B)2/3
C) √12
D-√36
Answers
Answer:
A) 5/8
Step-by-step explanation:
5 and 8 are irrational as a fraction
Answer:
5/8 i TOOK THE EXAM REVIEW
Step-by-step explanation:
Why does no one answer my questions?
Answers
Answer:
Which one do you need help with
Eight people went to a movie and three of them purchased a drink. Write an expression you could use to solve for the total cost if the tickets are $12 each and the drinks are $2.50 each.
Answers
Answer:
The expression : 12x + 2.50y
Total cost = $103.5
Step-by-step explanation:
The number of people that went to the movie = x
Number of people that bought drinks = y
Total cost = 12x + 2.50y
Eight people went to a movie and three of them purchased a drink
Total cost = 12 × 8 + 2.50 × 3
Total cost = 96 + 7.5
Total cost = $103.5
1. Doug invested $2,500 into a Certificate of Deposit earning 6.5% interest. How long will it take to
double Doug's investment?
Answers
Answer:
Step-by-step explanation:
14.5 years
URGENT PLZ HELP!
Find the value of x so that the points
(x, 2) and (-5, 8) lie on a line with a slope
of -1.
Answers
9514 1404 393
Answer:
x = 1
Step-by-step explanation:
The slope formula can be useful here.
m = (y2 -y1)/(x2 -x1)
-1 = (8 -2)/(-5 -x)
5 + x = 6 . . . . . . . . multiply by (-5-x)
x = 1 . . . . . . . . subtract 5
Hi. I need help with these questions (see image)
Please show workings.
Answer a and b
Answers
Answer:
see explanation
Step-by-step explanation:
Using the chain rule along with standard derivatives
Given
y = f(g(x)) , then
[tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x)
[tex]\frac{d}{dx}[/tex] (sinx) = cosx , [tex]\frac{d}{dx}[/tex] (cosx) = - sinx
(a)
y = sin x²
[tex]\frac{dy}{dx}[/tex] = cos x² × [tex]\frac{d}{dx}[/tex] (x² )
= cos x² × 2x
= 2xcosx²
(b)
y = cos4x³
[tex]\frac{dy}{dx}[/tex] = - sin4x³ × [tex]\frac{d}{dx}[/tex] (4x³ )
= - sin4x³ × 12x²
= - 12x²sin4x³
A store pays $100 for a barbecue grill and marks the price up by 7%. What is the amount
of the mark-up?
Answers
Answer:
$7
multiply .07 times 100
The Paint Factory has 500 different colors of interior paint from which to choose. Generate an equivalent expression using prime factorization for the number 500.
a)2 x 2 x 5 x 25
b)4 x 5 x 25
c)2 x 2 x 5 x 5 x 5
please hurry
Answers
Answer:
The answer is C.
Step-by-step explanation:
The simplest form is C.
Answer:
c)2 x 2 x 5 x 5 x 5
[tex]500 \\ \frac{500}{5} = 100 \\ \frac{100}{5} = 20 \\ \frac{20}{2} = 10 \\ \frac{10}{2} = 5 \\ \frac{5}{5} = 1\\ [/tex]
Rewrite the denominators
2 x 2 x 5 x 5 x 5
A triangle has sides with lengths of 16 millimeters, 20 millimeters, and 25 millimeters. Is it a
right triangle?
Answers
Answer:
No
Step-by-step explanation:
If it is a right triangle, then the Pythagorean theorem must work.
a^2 + b^2 = c^2 (a and b are the shorter sides and c is the longest)
16^2 + 20^2 = 25^2
256 + 400 = 625
656 = 625
This is not true
Hope this helps!
if f(x)= x3 -7÷2 find f-1 (x)
Answers
Answer:
The inverse of given function is
[tex]f^{-1} ( x ) = (2x+7)^{\frac{1}{3} }[/tex]
Step-by-step explanation:
Explanation:-
Given function
[tex]f(x) = \frac{x^{3}-7 }{2}[/tex]
let y = f(x)
[tex]y = f(x) = \frac{x^{3}-7 }{2}[/tex]
⇒ 2 y = x³ - 7
⇒ 2y +7 = x³
⇒ [tex]x = ( 2 y +7 )^{\frac{1}{3} }[/tex]
⇒[tex]f^{-1} ( y ) = (2y+7)^{\frac{1}{3} }[/tex]
The inverse of given function is
[tex]f^{-1} ( x ) = (2x+7)^{\frac{1}{3} }[/tex]
Use the equation below to find v, if u =21, a= 12, and t = 2.
v=utat
Answers
Step-by-step explanation:
We have v = u + at = (21) + (12)(2) = 45.
Answer:
v= 1008
v=21*2*12*2
Step-by-step explanation:
Which expression is equivalent to 5(4x + 5)
Answers
Answer:
5(4x+5)=20x+25
Step-by-step explanation:
A c ompany purchased 3,128 bottles of water.Each departments needs 55 bottles.Which compatible numbers provide a better estimate for the number of departments that can get the bottles needed 3,000 divided 60 or 3,000 divided 50? Explain.Then make the estimate.
Answers
Answer:
3,000 divided 60 are the compatible numbers, and the estimate is 50.
Step-by-step explanation:
Compatible numbers can be described as numbers which are close in value to the actual numbers and can easily be added, subtracted, multiplied, or divided mentally.
From the question, 3,000 divided 60 are the compatible numbers that provide a better estimate for the number of departments that can get the bottles because 55 can be rounded up to 60.
The estimate will therefore be as follows:
Estimate = 3,000 / 60 = 50
PLEASE HELP!!! i will give 5 stars and a thanks
Answers
Answer:
i DONT KNOW HOPEFULLY U DO GOOD
Step-by-step explanation:
I need some help please
Answers
Answer:
a) -10
b) 7
Step-by-step explanation:
a) [tex]2(x + 3) = x - 4[/tex]
[tex] = > 2x + 6 = x - 4[/tex]
[tex] = > 2x - x = - 4 - 6[/tex]
[tex] = > x = - 10[/tex]
b) [tex]4(5x - 2) = 2(9x + 3)[/tex]
[tex] = > 20x -8 = 18x + 6[/tex]
[tex] = > 20x - 18x = 8 + 6[/tex]
[tex] = > 2x = 14[/tex]
[tex] = > x = \frac{14}{2} = 7[/tex]
Answer:
a)-10 b)7
Step-by-step explanation:
a)2 ( x + 3 ) = x - 4
2x+6=x-4
2x+6-x=-4
x+6=-4
x=-4-6
x=-10
b)4 ( 5 x - 2 ) = 2 ( 9 x + 3 )
20x-8=2(9x+3)
20x-8=18x+6
20x-8-18x=6
2x-8=6
2x=6+8
2x=14
x=14/2
x=7
A single card is drawn at random from a standard 52 card deck.
Work out the following probabilities in their simplest form:
P(8)
=
P(not 8)
=
Answers
Answer:
Step-by-step explanation:
P(8)
There are 4 eights in a standard deck (no jokers) So the probability is 4/52 = 1/13 = 0.0769
P( ~ 8)
48 cards in a standard deck are not 8
P( ~8) = 12/13 = 0.9231
What is the solution of the system of equations?
{3x−12y=−72x+2y=1
Answers
Answer:
i think 9
Step-by-step explanation:
i not surecalculate the cost of 15 articles at 1.95 each
Answers
Answer:
29.25
Step-by-step explanation:
15x1.95= 29.25
Hope this helps :)
if 1 article = 1.95
then if u want to find how much 15 articles = to
you just have to multiply 1.95 * 15 which is equal to 29.25
hope this helps
:)
PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!V
Answers
Answer:
12+12+14+15+16+18+20+23=130
130÷8=16.25
aanswer=16
you move 89 as its anomalous
too higher than the other numbers
What is the equation of the line whose y-intercept is 3 and slope is 1?
O y=x-3
O y=x+3
O y= 3x+1
Answers
Answer:
y = x + 3
Step-by-step explanation:
y = mx + b
m is the slope
b is the y intercept
if m = 1 and b = 3 then
y = x + 3
Word problem:
(I only need the answer and explanation no need statements PLS HELP )
The weight of Jack is 30kg 500g. The weight of Dereck is 28kg 700g. What is their total weight? Also, find the difference of their weight?
Answers
Answer:
Below.
Step-by-step explanation:
30 kg 500g + 28kg 700g
= 58kg + 1200g
= 59kg 200g.
Difference
= 30 kg 500g - 28kg 700g
= 2kg + 500 - 700
= 2kg - 200g
= 1kg 800g.
Javier wants to put in a home theater. The area of the space for the screen is 20 ft. by 16 ft. What is the largest home theater screen he can purchase if the size is determined by the length of the diagonal?
Group of answer choices
15 feet
20 feet
25 feet
30 feet
Answers
Answer:
25
Step-by-step explanation:
34.7 divided by 4 HELP ME PLZZZZZ
Answers
Answer:
347/40
Step-by-step explanation:
34.7/4 = 34 7/10 / 4
= 347/10 / 4
= 347/40
Kareem heats a beaker of water to a boil. Then he records that the water temperature decreases from 100°C to 19°C in 5 and 2/5 minutes.
What was the change in temperature each minute? Enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
2/5min=24 sec
5 min=300 sec
total=324 seconds
the water decreased 100-19=81 degrees
81/324=0.25 degrees/second
the change in temperature was 0.25 degrees per second
we will multiply by 60
15 degrees per minute
Aisha is spending a week at her family's cottage and wants to read her favourite book, which is 400 pages long. A) If she reads one page every 36 seconds, how many hours will it take her to read her book? B) Suppose Aisha only reads from 10:15 a.M. To 2:10 p.M., and from 7:20 p.M. To 9:00 p.M. Each day, starting on Monday. On what day and at what time will she finish reading her book? C) Aisha decides to read a second book that is 350 pages in length, starting right after finishing her first book. If she continues to read at the same speed, then when will she finish her second book?
Answers
Answer:
A) 4 hours
B) 7:25 PM on the same Monday.
C) 12:10 PM on Tuesday.
Step-by-step explanation:
Given that:
Number of pages in the first book = 400
A) Time taken to read each page = 36 seconds
To find the number of hours taken to finish reading the book, we need to first find the number of seconds taken to finish reading the book.
Time taken by Aisha to finish reading 400 pages = 400 [tex]\times[/tex] 36 = 14400 seconds
3600 seconds = 1 hour
14400 seconds = [tex]\frac{1}{3600}\times 14400[/tex] hours = 4 hours
B) Reading timings of Aisha :
1st time = 10:15 AM to 2:10 PM i.e. a duration of 3 hours and 55 minutes
2nd time = 7:20 PM to 09:00 PM i.e. a duration of 1 hour and 40 minutes
4 hours are taken to read this book.
So, it will require 5 more minutes after the 1st reading time.
Therefore, Aisha will finish reading at 07:25 PM on same Monday.
C) Second book has 350 pages.
Time taken to read 350 pages = [tex]\frac{350\times 36}{3600}[/tex] = 3.5 hours
She starts reading at 07:25 PM on Monday.
Up to, 9 PM, a duration of 1 hour and 35 minutes will be utilized for reading the second book.
A total of 1 hour and 55 minutes more will be required.
Therefore, the second book reading will be finished at 12:10 PM on Tuesday.
solve the linear equation
9x-2x+6=4x+3x+11-5
Answers
Answer:
Undefined
Step-by-step explanation:
0=0
Answer:
0
Step-by-step explanation:
Combine the like terms 9x-2x = 7x
Subtract the numbers 11-5 = 6
Combine the like terms again 4x+3x = 7x
Subtract 6 from both sides of the equation 6-6 = 0 6-6 = 0
Simplify 7x = 7x
Result 0
Questions related on indices. ( I need a full explanations of how the answer is found. )
Answers
Answer:
(a) m = 10
(b) n = 160
Step-by-step explanation:
To rewrite the expression in the manner indicated, write an equation that sets the given expression equal to the desired expression. Then solve for the variable value. The distributive property and the usual rules of exponents apply.
The rules of exponents you can use here are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^0 = 1
__
(a) 2^101 +2^103 = m×2^100
2^(101-100) +2^(103-100) = m × 2^(100-100) . . . . . . . multiply by 2^(-100)
2^1 +2^3 = m
2 + 8 = m
m = 10
__
(b) 2^101 +2^103 = n×4^48
2^101 +2^103 = n×(2^2)^48 . . . . . substitute 4 = 2^2
2^101 +2^103 = n×2^96 . . . . . . . . simplify
2^5 +2^7 = n . . . . . . . . . . . . . . . . . as above, multiply by 2^(-96)
32 +128 = n
n = 160
_____
Additional comment
The rules of exponents tell you that ...
(m × 2^100) × 2^-100 = m × 2^(100 -100) = m × 2^0 = m
This is effectively the same as dividing by 2^100. You're doing the same thing you would do to solve any linear equation: divide by the coefficient of the variable.
What classes should I take as a freshman in high school
math, science, social studies,elcteives, English,
Answers
Answer:
Depends on what you what to do in the future. But u should take math, science and english (those are the main important classes)
Step-by-step explanation:
work out (5 x 10^3) x (9 x 10^7)
Answers
Step-by-step explanation:
5×10³) × (9×10^7)
= 45 × 10^10
= 4.5 × 10¹¹
Answer:
(5*10^3)*(9*10^7)=4.5*10^11
Step-by-step explanation:
5*10^3=5*1000=5000
9*10^7=9*10000000=90000000
5000*90000000=5*1000*9*10000000=5*9*10000000000=45*10000000000=450000000000, or 45 with 10 0's, or 10^10
45*10^10 is not simplified, as we need a number less then 10, so we divide 10 from 45, and add 1 to the exponent, getting 4.5*10^11