Answer:
The equation of the tangent line
[tex]y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )[/tex]
Step-by-step explanation:
Step(i):-
Given function y = x cot (x) ....(i)
Differentiating equation (i) with respective to 'x' , we get
[tex]\frac{dy}{dx} = x (-Co sec^{2} (x)) +cot(x) (1)[/tex]
Step(ii):-
The slope of the tangent line
[tex]\frac{d y}{d x} = -x Co-sec^{2} (x) +cot x[/tex]
[tex](\frac{d y}{d x} )x_{=\frac{\pi }{4} } = -\frac{\pi }{4} Co-sec^{2} (\frac{\pi }{4} ) +cot \frac{\pi }{4}[/tex]
We will use trigonometry formulas
[tex]Cosec(\frac{\pi }{4} ) = \sqrt{2}[/tex]
[tex]sec(\frac{\pi }{4} ) = \sqrt{2}[/tex]
[tex]Cot(\frac{\pi }{4} ) = 1[/tex]
Now the slope of the tangent
[tex]\frac{dy}{dx} =-\frac{\pi }{4} (\sqrt{2})^{2} )+1[/tex]
[tex]\frac{dy}{dx} =-\frac{\pi }{2} +1[/tex]
Step(iii):-
Given
Substitute [tex]x=\frac{\pi }{4}[/tex] in y = x cot (x)
[tex]y = \frac{\pi }{4} cot (\frac{\pi }{4} )[/tex]
[tex]y = \frac{\pi }{4}[/tex]
The point of the tangent line [tex](x ,y ) = (\frac{\pi }{4} , \frac{\pi }{4} )[/tex]
The equation of the tangent line
[tex]y - y_{1} = m ( x - x_{1} )[/tex]
[tex]y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )[/tex]
4(2x+6)=5(x+5)+2 Infinite solutions Infinite solutions No solution No solution One solution; x=0One solution; x is equal to 0 One solution; x=1
Answer:
x = 1
Step-by-step explanation:
Solve for x:
4 (2 x + 6) = 5 (x + 5) + 2
Hint: | Distribute 5 over x + 5.
5 (x + 5) = 5 x + 25:
4 (2 x + 6) = 5 x + 25 + 2
Hint: | Group like terms in 5 x + 2 + 25.
Grouping like terms, 5 x + 2 + 25 = 5 x + (25 + 2):
4 (2 x + 6) = 5 x + (25 + 2)
Hint: | Evaluate 25 + 2.
25 + 2 = 27:
4 (2 x + 6) = 5 x + 27
Hint: | Write the linear polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
8 x + 24 = 5 x + 27
Hint: | Move terms with x to the left hand side.
Subtract 5 x from both sides:
(8 x - 5 x) + 24 = (5 x - 5 x) + 27
Hint: | Combine like terms in 8 x - 5 x.
8 x - 5 x = 3 x:
3 x + 24 = (5 x - 5 x) + 27
Hint: | Look for the difference of two identical terms.
5 x - 5 x = 0:
3 x + 24 = 27
Hint: | Isolate terms with x to the left hand side.
Subtract 24 from both sides:
3 x + (24 - 24) = 27 - 24
Hint: | Look for the difference of two identical terms.
24 - 24 = 0:
3 x = 27 - 24
Hint: | Evaluate 27 - 24.
27 - 24 = 3:
3 x = 3
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 3 x = 3 by 3:
(3 x)/3 = 3/3
Hint: | Any nonzero number divided by itself is one.
3/3 = 1:
x = 3/3
Hint: | Any nonzero number divided by itself is one.
3/3 = 1:
Answer: x = 1
sita purchased 100 pencils of rs600. when she sold all the pencils she lost 20%. find the selling price of each pencils.
Answer:
rs480
Step-by-step explanation:
100%=r600 100%-20%=80%
80%=x
80 x 600 =48000
[tex]\frac{48000}{100}[/tex]=480
52=4z
HELP PLS ILL MARK BRAINLIEST
Answer:
Z- 13
Step-by-step explanation:
Divide 52 by 4
[tex]52 \div 4 =13[/tex]
find the absolute value of -0.909?
0.909 is the absolute value of -0.909
What is Number system?A number system is defined as a system of writing to express numbers.
The given number is a decimal number
-0.909
Minus zero point nine zero nine
We need to find the absolute value of -0.909
Absolute value of a Decimal is its numeric value without its sign
The absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign.
0.909 is the absolute value of -0.909
Hence, 0.909 is the absolute value of -0.909
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I get paid $40 a month. If i want 5 less each month, how much should i get paid every week?
Answer:
$5 each week
Step-by-step explanation:
$40 a month
$10 a week
$10-$5 is $5 each week
If you want to be paid $5 less, then every month you will be paid $35
There the amount that you get paid every week will be:
35 ÷ 4 ( 1 month have 4 weeks )
= $8.75
3x+2y=4 solve for y?
The given equation term of y is, y=(3/2)x-2.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Given equation in the problem is;
3x+2y=4
To solve the given equation for y first rearrange the equation and put the y variable on the left-hand side as;
2y=3x-4
Divide the whole equation by 2 we get;
y=(3/2)x-2
Hence, the given equation term of y is, y=(3/2)x-2.
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46 winners divided $33 equally. what decimal is equivalent to the fraction of a dollar that each winner received? round to the nearest hundredths.
Answer:
1.39
Step-by-step explanation:
Why did I get this question wrong?
Answer:
9.25
Step-by-step explanation:
M₄ means the area using 4 rectangles with heights equal to the function evaluated at the midpoints.
The width of each rectangle is (4−0)/4 = 1.
The area of each rectangle is:
M₁ = (1) (1.12) = 1.12
M₂ = (1) (1.80) = 1.80
M₃ = (1) (2.69) = 2.69
M₄ = (1) (3.64) = 3.64
The total area is therefore:
M = 1.12 + 1.80 + 2.69 + 3.64
M = 9.25
Identify the line(s) of symmetry for kite ABCD.
les )
A)line BD
B)line AC
C)line EF
D)no line of symmetry
Answer:Line BD
Step-by-step explanation:
The top is shorter than the bottom, so it can't be AC. EF will only have about half of the section covered. BD is symmetrical so it can't be no lines. So it must be BD.
c
Which equation could you use to solve for x in the proportion 5
- 2
Vx
4X= 14
4x=45
5x= 13
5x = 36
ANSWER QUICK!!
Answer:
4x= 14
Step-by-step explanation:
If a woodchuck could chuck 2
pieces of wood every hour, how big is a beavers dam?
Answer:
How many hours?
Step-by-step explanation:
the answer to this is 2x
X is the number of hours and you multipy it by 2 wood
Which of the following would be considered the most conservative alpha level?
a. .01
b. .05
c. .10
d. .15
Answer:
C.0.1
Step-by-step explanation:
Because this is 10% confidence confirmed
I need help with d ASAP plz explain
Answer:
a. g(0)= 1
b. f(-2)= 0
d. g(x-2)= 5x-9
Step-by-step explanation:
a. g(x)=5x+1 *substitute 0 for x*
g(0)= 5(0)+1
g(0)= 1
b. f(-2)= [tex](-2)^2-4[/tex] *substitute -2 for x*
f(-2)= 4-4 =0
c. g(x-2)= 5(x-2)+1 *substitute x-2 for x*
g(x-2)= 5x-10+1 *distributive property*
g(x-2)=5x-9 *simplify*
Helppppppppppppp0ppppppp
One-third of a number decreased by four
Answer: (X/3)*4
Step-by-step explanation:
(1/3)*x
decreased by 4: (1/3)*x-4
Select all that apply.
Which expressions are equivalent to 6x +18?
6(2+3)
3(2x + 6)
2 (32 +9)
6(x + 18)
3(x+6)
The expression equivalent to 6x + 18 is 3(2x + 6) thus option (B) is correct.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that are all constrained and create an equation.
Expression is very useful to determine the end or root value of constraint.
As per the given,
6x + 18
Take 3 as common,
3(2x + 6)
Hence "The expression equivalent to 6x + 18 is 3(2x + 6)".
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(30 points) the line contains the point (5,-7) and is parallel to 4x+ 3y =-9 The equation of the line is:
Answer:
4x +3y = -1
Step-by-step explanation:
To find the new constant for the equation, use the given x- and y-values:
4(5) +3(-7) = 20 -21 = -1
The equation of the parallel line in standard form is ...
4x +3y = -1
twice this number is 1 less than half of 26
Answer:
2x = (1/2)(26) - 1
The number is 6.
Step-by-step explanation:
2x = (1/2)(26) - 1
2x = 13 - 1
2x = 12
x = 6
Someone please help me ❤️
Answer:
week 5!
Step-by-step explanation:
Answer:
yes, week 55️⃣
Step-by-step explanation:
just see the little blue points
This equation will be in standard form if you subtract 6x2 from
both sides, add 30 to both sides and subtract ex from both
sides.
6x2 + 2x - 30 = 4x2 +9x
A.True
B.False
The answer to it is true
Solve for m.
7
D= (m - 64)
2
==
=(D-64)2
We move all terms to the left:
-((D-64)2)=0
We calculate terms in parentheses: -((D-64)2), so:
(D-64)2
We multiply parentheses
2D-128
Back to the equation:
-(2D-128)
We get rid of parentheses
-2D+128=0
We move all terms containing D to the left, all other terms to the right
-2D=-128
D=-128/-2
D=+64
Solve for y. 6 x + 2y = z
Answer:
[tex]y = \frac{z}{2} -3x[/tex]
Step-by-step explanation:
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents & roots
Multiplication
Division
Addition
Subtraction
& is the order of operation.
First, subtract 6x from both sides:
6x (-6x) + 2y = z (-6x)
2y = z - 6x
Next, divide 2 from both sides:
(2y)/2 = (z - 6x)/2
y = (z - 6x)/2
y = (z/2) - 3x
[tex]y = \frac{z}{2} -3x[/tex] is your answer.
~
y varies inversely with x. If y = 5 when x = 60, find y when x = 150
Answer:
y =2 when x = 150
Step-by-step explanation:
Inverse variation is
xy = k
5*60 = k
300 = k
xy = 300
150y = 300
Divide by 150
150y/150 = 300/150
y = 2
Which set of numbers could be the side lengths of a right triangle?
A. 3,4,6
B.4,5,7
C. 5, 12, 13
D. 7. 20, 21
E. 8, 15, 16
Divide rs 21000 between Nisha and Nishan so that Nisha gets double than Nishan
let the nisha be x and nishan be y
Step-by-step explanation:
ATQ
your statement is x=2y
Name 3 rays in this geometric construction
E
A
D
B
Your answer
Open the line segment translation application. Line segment AB is a translation of line segment CD 6 units down. Drag line segment CD and try to move it onto line segment AB. Are line segments AB and CD the same? What does this mean about how a line segment changes when you translate it?
Answer:
Only the position changes with translation. Other measures, including slope and length, remain the same.
Step-by-step explanation:
Line segment CD can be placed directly on top of line segment AB. The translated segment has the same length and orientation as the original.
Answer:
Only the position changes with translation. Other measures, including slope and length, remain the same.
this should be your answer
A normal population has the mean of 10 and the variance of 25 . A random sample of size n-28 is selected.
(a) Find the standard deviation of the sample mean. Round your answer to two decimal places (e.g. 98.76)
(b) How large must the sample be if you want to halve the standard deviation of the sample mean?
Answer:
Step-by-step explanation:
Given that:
population mean = 10
variance [tex]\sigma^2[/tex] = 25 ; [tex]\sigma[/tex] =[tex]\sqrt{ 25}[/tex] = 5
sample size n = 28
The standard deviation of the sample mean:
= [tex]{\dfrac{5}{\sqrt{28}}[/tex]
= 0.95
To halve the standard deviation of the sample mean, the size of how large the sample will be can be computed as follows:
[tex]\dfrac{sd_1}{sd_2} = \dfrac{\dfrac{\sigma}{\sqrt{n}} }{\dfrac{\sigma}{\sqrt{n}} }[/tex]
[tex]\implies \dfrac{\dfrac{5}{\sqrt{28}} }{\dfrac{5}{\sqrt{28}} }[/tex]
[tex]= \dfrac{5}{\sqrt{28}} \times \dfrac{\sqrt{28}}{5}[/tex]
= 2
n = 4 × 28
n = 112
The standard deviation is 0.95 and if the standard deviation is halved then the sample mean is 112.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
A normal population has a mean of 10 and a variance of 25.
A random sample of sizes n-28 is selected.
A. The standard deviation will be
[tex]\sigma = \dfrac{\sqrt{Var(x)}}{n} \\\\\sigma = \dfrac{\sqrt{25}}{\sqrt{28}} \\\\\sigma = 0.95[/tex]
B. The sample be if you want to halve the standard deviation of the sample mean
[tex]\rm \dfrac{SD_1}{SD_2} = 2 = \dfrac{\sqrt{n}}{\sqrt{28}}\\\\n = 4*28 \\\\n= 112[/tex]
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Which of the following sets are equal? A = {2, 3, 4} n B = {XER 1 4 x < 5} n C = { ERI 1 < x < 5} n D = {xEZ| 1 < x < 59} n E = {xez | 1 < x < 59} n
Answer:
Step-by-step explanation:
The question is not too clear. check the attachment for better view of the question.
From the options The set A = {2, 3, 4} will be compared to other options to determine which of the remaining set is equivalent to the set A.
x e R means the values in the set are real numbers and real numbers can either be rational or irrational. R= Hence the real numbers between 1 and 5 are not restricted to only positive integer values but also decimal numbers. and since set A does nit contain ant rational number, hence both set B and C are not equivalent to set A.
Also, set B is not equivalent to set C even though the values in both sets are integers. They are not equal because 1 is included in set B but not in set C.
Set D and E are equivalent because they both contains integers between 1 and 5. Integers are positive whole numbers between 1 and 5 since the both sets doesn't contain any negative value. Hence the set A = set D = set E
Find the product of -3/5 • -1.5.
Answer:
0.9
Step-by-step explanation:
I am not sure how to really explain but the 2 negatives equal a positive. So if there is 2 Negatives also know as - = a positive. And a positive is just the the opposite of a negative
The product of the given fractions is 3/25.
The given fractions are -3/5 and -1/5.
What is the product of fractions?The product of two fractions can often be expressed by an equivalent fraction where the numerator and denominator have been divided by a common factor. The product of two fractions is the product of the numerators and the product of the denominators.
Now, multiply the given fractions
-3/5 × -1/5
Multiply numerators and write the result in numerator and multiply denominators and write the result in denominator.
That is, -3/5 × -1/5 = 3/25
Therefore, the product of the given fractions is 3/25.
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