The equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
What do we mean by equations?An equation is a mathematical declaration composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.To find the equation:
When we differentiate the function [tex]y=6 \sec (x)-12 \cos (x)[/tex], we get:
[tex]\begin{aligned}y^{\prime} &=\frac{d}{d x}(6 \sec (x)-12 \cos (x)) \\&=6 \frac{d}{d x}(\sec (x))-12 \frac{d}{d x}(\cos (x)) \\&=6 \sec (x) \tan (x)+12 \sin (x)\end{aligned}[/tex]
The slope of the tangent line is given by this derivative at the point [tex]x=\frac{\pi}{3}[/tex]:
[tex]y^{\prime}\left(\frac{\pi}{3}\right)=6 \sec \left(\frac{\pi}{3}\right) \tan \left(\frac{\pi}{3}\right)+12 \sin \left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex]The general equation y applies to the tangent line passing through the point [tex](a, y(a))[/tex] on the curve [tex]y(x)-y(a)=y^{\prime}(a)(x-a)[/tex].The tangent line in this case passes through the point [tex]\left(\frac{\pi}{3}, y\left(\frac{\pi}{3}\right)\right)=\left(\frac{\pi}{3}, 6\right)[/tex] and has the slope [tex]y^{\prime}\left(\frac{\pi}{3}\right)=18 \sqrt{3}[/tex].As a result, this tangent line has the equation: [tex]y-6=18 \sqrt{3}\left(x-\frac{\pi}{3}\right)[/tex]
Therefore, the equation can be simplified and written in a slope-intercept form as: [tex]y=18 \sqrt{3} x-6(\sqrt{3} \pi-1)[/tex]
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The correct question is given below:
Find the equation of the tangent line to the curve y = 6 sec (x) at the point ([tex]\pi[/tex]/3, 6). Give your answer in the form y = mx + b where m is the slope and b is the y--intercept.
Lowest term for 6/32
Answer:3/16
Step-by-step explanation:
Simplify 6/32 in Lowest Terms
6/32 = (?)
6/32 = (2 x 3)/(2 x 2 x 2 x 2 x 2)
= 3/16
6/32 = 3/16
A plot of land is in the shape of a triangle
If one side is x meters, a second side is
(2x - 4) meters and a third side is
(4x - 5) meters, express the perimeter of
the lot as a simplified expression in x.
Answer:
7x-9
Step-by-step explanation:
P=x+(2x-4)+(4x-5)
P= x+2x-4+4x-5
P =x+6x-9
P =7x-9
P is perimeter
The part of the drawing that shows information about scale, the date of the last revision, and the drawing number is the _____.
The part of the drawing that shows information about scale, the date of the last revision, and the drawing number is the balloon framing.
Where is a drawing's scale often indicated?
Here, the scale may be shown on the drawing's axes or real distances may be displayed on the axes. In other situations, a scale could employ multiple measuring units. The air velocity, for instance, might be represented by the length of an arrow on an air flow diagram, where 1 cm = 0.1 m/s.What does balloon framing mean?
In contrast to platform framing, where each floor is framed independently, balloon framing uses studs (vertical members) that stretch the entire height of the building (often two storeys) from the foundation plate to the rafter plate.
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Simon invested $2600 into a simple interest account for 2 years if account yielded $234 at the end of two year what was the interest rate write your answer as a percent
Answer:
4.5%
Step-by-step explanation:
I = prt
234 = 2600 × r × 2
r = 234/5200
r = 0.045
r = 4.5%
Answer:
4.5%
Step-by-step explanation:
$234 is interest for 2 years
interest for 1 year will be 234/2 = 117
117/2600 = 0.045 which is 4.5%
Need help ASAP please !!!!
Answer:
The answer is D.
Step-by-step explanation:
You have $175.29 in a savings account. You deposit an additional $48.75. How much more do you need to save to buy the cell phone?
Price: $249.99
Include the steps
Answer:
Step-by-step explanation:
So in your account you got $175.29
Then you deposit mean increase the amount of money in your account by $48.75
So: 175.29+48.75 = 224.04
The price is $249.99
So: 249.99 - 224.04 = $25.95
You need to save $25.95 in order to buy your cell phone
To buy the cellphone of worth $249.99, additional $25.95 are required.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
Given that,
The price of cellphone = $249.99
The amount in saving account = $175.29
Additional amount deposit in account = $48.75
Total amount in account after deposit = 175.29 + 48.75 = 224.04
Since, the price of cellphone is $249.99
And the amount in account = 224.04
So the more amount required = 249.99 - 224.04 = 25.95
To buy the cell phone $25.95 are required.
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in 5-8, find each reciprocal. 5/9 8 7/3 1/12
the answer
155
324
5/9 (87/3(1/12)= 155/324
28. RS = 7a, ST= 12a, RT=76
Answer:
a=4
ST=48
As we know ,
RT=RS+ST=7a+12a=19a
And RT=76
That’s why RT=19a=76 => a = 76/19=4
ST=12a=12*4=48
then we find ,
a=4
ST=48
In geometry, variables often appear in problems related to perimeter, area and volume. Typical problems provide you with some precise measurements and ask you to find out an unknown measurement, or variable.
Determine which formula you need. For example, if you're working with the area of a triangle, you need to know that area equals one half the base times the height, or A=1/2bh.
Plug the known values into the formula. Using the area of the triangle example, assume you know that the area is 100 square inches and the base is 20 inches. When you plug these values into the formula, you get 100=1/2 (20h). The height of the triangle is the variable.
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Joe moves a 10 kg weight 5 meters with a force of 50 N in 10 seconds. Leroy uses the same force to move the same weight the same distance in 7.5 seconds? Who has more power and why
Answer:
10 sec
Step-by-step explanation:
Tutorial D
If x = 0 and y < 0, where is the point (x, y)
located?
◄))
on the x-axis
on the y-axis
What’s the measure of QS?
A ) 6.2 mm
B) 9.5 mm
C)21.9 mm
D)22.4 mm
Please show work because I need to understand
Which of the following shows double the sum of 8 and 4?
a. 2 *8 +4
b. 2(8 + 4)
C. 2*8-4
d. 2(8-4)
Answer:
C
Step-by-step explanation:
URGENT PLS IM DESPERATE!!! IT'S DUE IN 35 MINUTES!!! Write an equation for each table, graph, and verbal description. (A) Table of X and Y values. When X is 1, Y is 9. When X is 2, Y is eighteen. When X is 3, Y is twenty-seven. When X is 4, Y is thirty-six. y = x (B) First quadrant of a coordinate plane. The points 0 comma 0, 2 comma 5, 4 comma ten, 6 comma fifteen, 8 comma twenty, and ten comma twenty-five are graphed and connected with a line. y = x (C) Each hour, Milo reads 24 pages. y = x
Your answer will be:
y = 9x
y = 2.5x
y = 24x
I hope this helps!
Need answers now...................
Answer:
[tex]\sqrt{17}[/tex]
Writing Numerical Expressions
A numerical expression is a mathematical phrase that contains only numbers and mathematical operations. For example, 6+2+1 is a numerical
expression.
Some numerical expressions contain multiplication. Multiplication can be represented in several ways, including a raised dot or parentheses. Here are
some ways to represent the product of 2 and 3.
2.3
2(3)
Think About It!
Identify the factors of the numerical expression 6(11).
(2)3 (2)(3)
MO
6(11) = 2 x 3 x 11
Its factors are =1 ,2 ,3 , 6, 11, 22, 33 66
2.3 = 2 x 3
Its factors are = 1, 2, 3, 6
2( 3) = 2 x 3
Its factors are = 1, 2,3, 6
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Which number below is more than 15 but less than 16?
O√225
O√247
O √256
O √265
Answer: √247
Step-by-step explanation:
15^2=225. 16^2=256. n=number
n^2>225 and n^2<256
√225=15.
√247=15.7 ==> 2nd option. 247>225 and 247<256. 15.7>15 and 15.7<16
√256=16
√265=16.3
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed
2(multiplicity 2) 5+i (multiplicity 1)
The polynomial function will be y = (x⁴-14x³+70x²-144x+104)
2 and 5+i are the roots of the given polynomial and the multiplicity of 2 and 5+i are 2 and 1 respectively.
Thus, the general form of the polynomial will be given as:
y = (x-2)² (x-(5+i)) (x-(5-i)) [as (5-i) is conjugate of (5+i)]
y = (x²+4-4x) (x-5-i) (x-5+i)
y = (x²-4x+4) (x²-5x+xi-5x+25-5i-xi+5i-i²)
y = (x²-4x+4) (x²-10x+25+1) [as i²= -1]
y = (x²-4x+4) (x²-10x+26)
y = (x⁴-10x³+26x²-4x³+40x²-104x+4x²-40x+104)
y = (x⁴-14x³+70x²-144x+104)
Thus, the polynomial is y = (x⁴-14x³+70x²-144x+104)
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1/3 x =5 solved, please help me if anyone can! :)
EASY POINTS PLEASE HELP if you can answer bother that would be nice but u can answer one if u want
Answer:
#9: B
#10: D
Step-by-step explanation:
#9 had biggest scientific notaiton
#10 had smallet scientific notaiton and numbeer
Answer:
9. B
10. D
Step-by-step explanation:
a. 5406000000
b. 56040000000
c. 550400000
d. 6503000000
a. 900000
b. 120000
c. 3010000000
d. 19010
HELP PLS TEACHER GONNA FAIL ME
Answer:
B and D
Step-by-step explanation:
Michael is planning a trip to Hooperville. On the map, it is 3.5 inches from his home town. The map’s scale is 1.5 inches : 50 miles. How far away is Hooperville from his home town?
The real distance between Hooperville and Michael's home town is 116.667 miles.
How to use scales to estimate distancesScales are ratios commonly used to contain great extensions of land in images and maps and offer a quick though efficient manner to estimate distances. The real distance between Hoopersville and Michael's home town can be found thorugh this formula:
d' = d / r
Where:
r - Scale, in inches per miled - Reduced distance, in inchesd' - Real distance, in milesIf we know that d = 3.5 in and r = 1.5 in / 50 mi, then the real distance between Hooperville and Michael's hown town is:
d' = 3.5 in / (1.5 in / 50 mi)
d' = 116.667 mi
The real distance between Hooperville and Michael's home town is 116.667 miles.
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Rearrange the formula c=4/a-b to make a the subject
Answer:
[tex] a = \dfrac{4 - bc}{c} [/tex]
Step-by-step explanation:
c = 4/(a - b)
Multiply both sides by a - b.
c(a - b) = 4
ac + bc = 4
ac = 4 - bc
a = (4 - bc)/c
[tex] a = \dfrac{4 - bc}{c} [/tex]
Solve (8×5)÷4×5 step by step
Answer:
50
Step-by-step explanation:
Apply PEMDAS to this problem
8 × 5 = 40
Now you are left with: 40÷4×5
You then use PEMDAS from left to right from here
So 40 ÷ 4 would be 10, and now you are left with 10 × 5, which would be 50.
Need help ASAP
logx = 7
logy = 2
logz = 5
Find log[tex]\frac{x^2\sqrt{z} }{y^3}[/tex]
Using some logarithmic properties, we will see that the solution of the logarithmic equation is 10.5
How to find the value of the logarithm?
Here we have some properties that you need to remember.
log(A*B) = log(A) + log(B)
log(A/B) = log(A) - log(B)
log(Aⁿ) = n*log(A)
Then we can rewrite our equation as:
[log(x²) + log(√z)] - log(y³)
Now, remember that a square root is equal to an exponent of 0.5, then:
[log(x²) + log(√z)] - log(y³) = 2*log(x) + 0.5*log(z) - 3*log(y)
Now we can replace the logarithms by the given values:
2*log(x) + 0.5*log(z) - 3*log(y)
2*7 + 0.5*5 - 3*2 = 10.5
The solution of the logarithmic equation is 10.5
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Write an equation in standard form of a line that is parallel to y=4x-3 and passes through the point (7, 10).
The equation of a line that is parallel to y=4x-3 and passes through the point (7, 10) is 4x - y = 18.
What is the equation of a line that is parallel to y=4x-3 and passes through the point (7, 10)?Given that;
Equation of line: y = 4x - 3Point: ( 7,10 )First, we determine the slope of the line using the slope intercept form.
y = mx + b
m is slope and b is y-intercept.
y = 4x - 3
Comparing with the slope intercept form equation,
Slope m = 4
Now, to determine the the equation of line parallel, the slopes must equal.
We find the line using the point slope formula.
y - y₁ = m(x - x₁)
Plug in m = 4, x₁ = 7, y₁ = 10 and simplify.
y - 10 = 4(x - 7)
y - 10 = 4x - 28
-10 + 28 = 4x - y
4x - y = -10 + 28
4x - y = 18
Therefore, the equation of a line that is parallel to y=4x-3 and passes through the point (7, 10) is 4x - y = 18.
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50 POINTS!!! Solve all!
Answer:
3. My first guess would be that Salva looked away quickly, turning their head away from the woman quickly.
4. Make a quick, nervous movement as an instinctive reaction to fear, pain, or surprise. [Provided by Oxford Languages Dictionary]
5. My first guess would be that Salva was performing a "squat" with her lower body, which would be the haunches.
uwu hello 2019 its me future with the better memes, dat me up,hoiyah,and OH NO.... OUR TABLE!!!!! ISH BROKEN!!!!!!
Use the following information to find x. Write the value of the variable.
B is between A and C;
AB=3x+6;
BC=15x – 2; and
AB≅BC .
Answer:
2/3
Step-by-step explanation:
[tex]AB \cong BC \implies AB=BC \\ \\ 3x+6=15x-2 \\ \\ 6=12x-2 \\ \\ 8=12x \\ \\ x=\frac{2}{3}[/tex]
ASSOCIATIVE PROPERTIES
COMMON CORE ALGEBRA I HOMEWORK
FLUENCY
Combine the expressions below. Replace subtraction by addition of opposites, if needed.
(a) 7x+3+6x+11
(b) 12x+10+3+8x
(c) 10y+12-7y-8-3y
What is an associative property?
According to the associative property, if three or more integers are classified differently, the total or product does not change. It is possible to apply this associative characteristic to addition and multiplication. Both (A + B) + C = A + (B + C) and (A + B) C = A + (B C) are used to represent it.In accordance with the associative property, it is irrelevant how the integers are grouped when adding or multiplying them, i.e., where the parenthesis are placed.Given expressions with rearrangement as per associative property are:
(a) 7x+3+6x+11
=(7x+6x)+(3+11)
(b) 12x+10+3+8x
=(12x+8x)+10+3
(c) 10y+12-7y-8-3y
=(10y-7y-3y)-(-12+8)
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the perimeter of a rectangle is 260cm the length is 50 less than its width. find its dimensions
The dimensions of the rectangle is found as: (b = 90 cm) and (l = 40 cm
).
What is defined as the perimeter of the rectangle?The perimeter (P) of such a rectangle has been the total length of all of its sides. A rectangle does have two equal lengths as well as two equal widths because its opposite sides are equal. The perimeter of a rectangle is calculated as follows: perimeter = length + length + width + widthLet 'l' be the length of the rectangle.
Let 'b' be the width of the rectangle.
then,
Perimeter = 2(l + b)
The given value of the perimeter = 260 cm.
The length is 50 less than the width.
Thus, l = b - 50.
Put the values in the formula;
260 = 2( b - 50 + b)
Simplify the equation;
260 = 4b - 100
4b = 360
b = 90 cm
Put the value of b in the length;
l = b - 50
l = 90 - 50
l = 40 cm
The dimension are estimated as; (l = 40 cm) and (b = 90 cm).
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"
Question
Normal
Shane earns $8 per hour babysitting and $6 per hour walking dogs. He also earns tips for each job. Last week Shane spent 2 more hours walking dogs than babysitting. He received $12 in tips for babysitting and
$10 in tips for dog-walking. Shane earned the same total amount for each job.
Write an equation to represent the situation. Use the variable h to represent the number of hours Shane spent babysitting
The equation to represent the situation is given as $2h -$10 = 0
We have been given that
Money earned by Shane for babysitting = $8 per hour
Money earned by Shane for walking dogs = $6 per hour
Let the number of hours spent by Shane be h hours
Tips she received for babysitting = $12
Tip she received for walking dogs = $10
Total amount earned by Shane for babysitting = $8*h + $12
Also Shane worked two more hours for walking dogs then the amount will be = 2*$6 = $12
Total amount earned by Shane for walking dogs = $6*h + $12 + $10
= $6h + $22
As she earned the same total amount of job the equation will be given as
$8h + $12 = $6h + $22
$2h -$10 = 0
Which is the required equation
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