a. Practically speaking, you compute the differential in much the same way you compute a derivative via implicit differentiation, but you omit the variable with respect to which you are differentiating.
[tex]y=\cos x\implies\boxed{\mathrm dy=-\sin x\,\mathrm dx}[/tex]
Aside: Compare this to what happens when you differentiate both sides with respect to some other independent parameter, say [tex]t[/tex]:
[tex]\dfrac{\mathrm dy}{\mathrm dt}=-\sin x\dfrac{\mathrm dx}{\mathrm dt}[/tex]
b. This is just a matter of plugging in [tex]x=\dfrac\pi3[/tex] and [tex]\mathrm dx=0.1[/tex].
[tex]\boxed{\mathrm dy\approx-0.087}[/tex]
The differential dy for y = cos(x) is evaluated by finding the derivative of y which is -sin(x), then multiplying by dx. For x = π/3 and dx = 0.1, the calculated differential dy is approximately -0.0866 when rounded to three decimal places.
Explanation:The differential dy of a function y with respect to x is given by the derivative of y with respect to x, multiplied by dx. For the function, y = cos(x), the derivative of y is -sin(x), hence dy = -sin(x)dx.
To evaluate dy for x = π/3 and dx = 0.1, we substitute x into -sin(x) and multiply by dx. This results in dy = -sin(π/3) × 0.1, which simplifies to dy = -0.1 √3/2. Rounding to three decimal places, dy ≈ -0.0866.
The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2, the fraction is now equal to 2/3.
If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?
5n = 3d and 3n + 6 = 2d + 4
5n = 3d and 4n + 4 = 3d + 6
3n = 5d and 3n + 6 = 2d + 4
Answer:
3n=5d and 3n = 5d and 3n + 6 = 2d + 4
Step-by-step explanation:
Answer: The correct option is
(A) [tex]5n=3d~~~\textup{and}~~~3n+6=2d+4.[/tex]
Step-by-step explanation: Given that the numerator and denominator of a fraction are in the ratio of 3 to 5. When the numerator and denominator are both increased by 2, the fraction is equal to \dfrac{2}{3}.
We are to select the system of equations that could be used to solve the problem.
Since n denotes the numerator and m denotes the denominator of the given fraction, so we have
[tex]\dfrac{n}{d}=\dfrac{3}{5}\\\\\\\Rightarrow 5n=3d,[/tex]
and
[tex]\dfrac{n+2}{d+2}=\dfrac{2}{3}\\\\\\\Rightarrow 3(n+2)=2(d+2)\\\\\Rightarrow 3n+6=2d+4.[/tex]
Thus, the required system of equations is
[tex]5n=3d~~~\textup{and}~~~3n+6=2d+4.[/tex]
Option (A) is CORRECT.
write the equations in logarithmic form 9^4=6,561
[tex]\log_96561=4[/tex]
The graph of function f is defined as the set of all points (x, f(x)), where x is in the domain of f.
Please select the best answer from the choices provided
T
F
Answer:
True
Step-by-step explanation:
The domain of a function is the complete set of possible values of the independent variable 'x'. Therefore, the graph of funtion is defined as the set of all points (x, f(x)) where 'x' is the domain of f(x).
Hence, the statement is TRUE
Answer:
True (Please give brainliest)
Step-by-step explanation:
Which relationship in the triangle must be true ?
Answer:
Choice B. sin(B)=cos(90-B)
Step-by-step explanation:
That cofunction identity is the one you looking for...choice B.
If you aren't convinced or don't know that identity, then maybe this will help:
90-B is actually the same thing as saying A for this right triangle since A+B=90.
So choice B basically says sin(B)=cos(A)
Well let's find both sin(B) and cos(A)
sin(B)=b/c
cos(A)=b/c
Those are the same ratios!
So they are equal!
Answer:
option B
Step-by-step explanation:
from the given options
a) sin (B) = sin (A)
b) sin (B ) = cos (90° - B)
cos (90° - B ) = Sin B
c) cos (B ) = sin(180° - B)
sin(180° - B) = sin (B)
d) cos (B) = cos(A)
so, we can clearly see from the above solution that option B is correct.
As 90° - B is in first quadrant and in first quadrant sign of cos dose not change and 90 is multiple of odd so 'cos' changes to 'sin'
What is the slope of the line represented by the equation y = -1/2x + 1/4
Answer:
Step-by-step explanation:
1/-2
Answer:
A) -1/2
Step-by-step explanation: woof
use the distributive property to write an expression that is equivalent to 5(2x - 1)
Final answer:
To use the distributive property for the expression 5(2x - 1), multiply each term inside the parentheses by 5, resulting in the equivalent expression 10x - 5.
Explanation:
To use the distributive property to write an expression equivalent to 5(2x - 1), you simply multiply each term inside the parentheses by the factor outside, which is 5 in this case. So, you will multiply 5 by 2x and then 5 by -1.
Multiply 5 by 2x: 5 × 2x = 10x.
Multiply 5 by -1: 5 × -1 = -5.
Combine the two results to get the equivalent expression: 10x - 5.
Therefore, using the distributive property, the expression equivalent to 5(2x - 1) is 10x - 5.
\sum _{n=1}^{\infty }−4\left(\frac{−1}{2}\right)^{n-1}
Answer: [tex]\bold{-\dfrac{8}{3}}[/tex]
Step-by-step explanation:
[tex]\sum \limits_{n=1}^{\infty}-4\bigg(\dfrac{-1}{2}\bigg)^{n-1}\implies a_1=-4, r=-\dfrac{1}{2}\\\\\\\text{Use the formula for the sum of an infinite geometric series:}\\S=\dfrac{a_1}{1-r}\\\\\\.\ =\dfrac{-4}{1-(-\frac{1}{2})}\\\\\\.\ =\dfrac{-4}{\frac{3}{2}}\\\\\\.\ =-4\times \dfrac{2}{3}\\\\\\.\ =\large\boxed{-\dfrac{8}{3}}[/tex]
Which polynomial has factors of 4x – 7 and x + 4?
answer: 4x² + 9x - 28.
multiply the factors together:
4x times x = 4x²
4x times 4 = 16x
-7 times x = -7x
-7 times 4 = 28
therefore, (4x-7) times (x+4) = 4x² + 16x -7x = 28
next, you must condense and simplify your answer:
16x -7x equals 9x
your final answer should be 4x² + 9x - 28.
Answer:
The answer is B aka 4x² + 9x - 28.
Step-by-step explanation:
The temperature in Miami, Florida is 22 degrees warmer than three times the temperature in Bangor, Maine. The temperature in Miami is 82 degrees. Write an equation to determine the temperature in Bangor. 3x + 82 = 22 3x + 22 = 82 3x − 22 = 82 3x − 82 = 22
The equation to determine the temperature in Bangor is 3x + 22 = 82. Solving the equation gives the temperature in Bangor as 20 degrees.
Explanation:To write an equation to determine the temperature in Bangor, let's assume the temperature in Bangor is represented by the variable 'x'. The temperature in Miami is 22 degrees warmer than three times the temperature in Bangor. So, we can write the equation as follows:
3x + 22 = 82
Now, to find the temperature in Bangor, we need to solve for 'x'. We can do this by subtracting 22 from both sides:
3x = 82 - 22
3x = 60
Finally, divide both sides of the equation by 3 to solve for 'x':
x = 60 ÷ 3
x = 20
Therefore, the temperature in Bangor is 20 degrees.
Final answer:
The correct equation to find the temperature in Bangor, Maine, given the temperature in Miami, Florida, is 3x + 22 = 82. After solving, the temperature in Bangor is found to be 20 degrees Fahrenheit.
Explanation:
The temperature in Miami, Florida is given as 82 degrees Fahrenheit. According to the problem statement, this temperature is 22 degrees warmer than three times the temperature in Bangor, Maine. Thus, we can express this relationship algebraically as:
Miami temperature = 3 × Bangor temperature + 22
Substituting the known Miami temperature into the equation, we have:
82 = 3 × Bangor temperature + 22
To solve for the temperature in Bangor, we need to subtract 22 from both sides of the equation:
82 - 22 = 3 × Bangor temperature
60 = 3 × Bangor temperature
Finally, divide both sides by 3 to get the temperature in Bangor:
Bangor temperature = 60 / 3
Bangor temperature = 20 degrees Fahrenheit
Therefore, the correct equation to determine the temperature in Bangor is:
3x + 22 = 82
What is the point-slope form of the equation for the line with a slope of -2 that passes through (1,4)?
[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-2(x-1)[/tex]
Nick found the quotient of 8.64 and 1.25....
Answer:
No, the power multiplied to 8.64 should havean exponent of zero.
HOPE THIS WILL HELP YOU
Answer:
No, The power multiplied to 8.64 should have an 0 exponent.
Option 2 is correct
Step-by-step explanation:
Nick found the quotient of 8.64 and 1.25 × 10⁵.
Quotient of two number is form of division.
If quotient of a and b then expression is [tex]\dfac{a}{b}[/tex]
Correct steps:
[tex]\Rightarrow \dfrac{8.64\times 10^0}{1.25\times 10^5}[/tex]
[tex]\Rightarrow (8.64\div1.25)\times 10^{0-5}[/tex]
[tex]\Rightarrow 6.912\times 10^{-5}[/tex]
Nick steps:
[tex]\Rightarrow \dfrac{8.64\times 10^1}{1.25\times 10^5}[/tex] wrong step
[tex]\Rightarrow (8.64\div1.25)\times 10^{1-5}[/tex]
[tex]\Rightarrow 6.912\times 10^{-4}[/tex]
The power multiplied to 8.64 should have an 0 exponent.
Therefore, Nick was wrong.
5g>25 solve the inequality
Answer:
g>5
Step-by-step explanation:
5g>25 Take this equation, using the division property of equality, divide both sides by 5, leaving you with
g>5
Answer:
g > 5
Step-by-step explanation:
Divide by 5 both sides.
Since there is no negatives the sign stays the same.
The factored form of polynomial P(x) shows only two of its roots. Assuming all of the
coefficients in the expanded form of P(x) are real, select each number that could be a
missing root of p(x)
Answer:
C and E
Step-by-step explanation:
Recall that according to the complex conjugate theorem, if P(x) is a polynomial function with real coefficients, and a+bi is an imaginary root of P(x), then its conjugate (i.e a-bi) must also be a root.
Here we see that 2 of the given roots are imaginary : i and 2+i
by the theorem given above, the conjugates of these must also be roots
i.e -i and 2-i
5x - 47< 3(12x - 108) – 2
Answer:
9 < x
Step-by-step explanation:
5x - 47< 3(12x - 108) – 2
Distribute
5x - 47< 36x - 324 – 2
Combine like terms
5x - 47< 36x-326
Subtract 5x from each side
5x-5x - 47< 36x-5x-326
- 47< 31x-326
Add 326 to each side
326 - 47< 31x-326+326
279 < 31x
Divide by 31 on each side
279/31 < 31x/31
9 < x
15p!!!!What is the percent of change from 56 to 22? round to the nearest percent
Answer:
60.7143% decrease or 60%
Step-by-step explanation:
The percent of change from 56 to 22 is 60%.
The percent of change from 56 to 22 is 60%.
What is problem-solving?
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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which is the measure of XBA if ray BA bisects XBY, which measures 86 grades?
Answer:
∠XBA=43°
Step-by-step explanation:
we know that
If ray BA bisect angle ∠XBY
then
∠XBA=∠XBY/2
we have
∠XBY=86°
substitute
∠XBA=86°/2=43°
15p!!what is the percent of change from 72 to 14? round to the nearest percent!
Here is the set up:
Let p = percent of change
(72 - 14)/72 = p/100
Solve for p.
Which of the following is equivalent to a real number?
ANSWER
[tex]{ (- 6745)}^{ \frac{1}{7} } [/tex]
EXPLANATION
If we have an exponential expression of the form:
[tex] { (- x)}^{ \frac{1}{n} } [/tex]
then, the result is a real number, if and only if n is an odd number.
We analyze the options and find out that,the first option is where n is odd, because we have n=7.
Hence the only option that is equivalent to a real number is
[tex] { (- 6745)}^{ \frac{1}{7} } [/tex]
The correct choice is A.
Real numbers encompass all positive and negative integers, fractions, and decimals excluding imaginary numbers. In the given options, options B depicting a set of positive integers and C depicting a decimal number are examples of real numbers.
Explanation:In mathematics, a real number includes all positive and negative integers, fractions, and decimals without imaginary components. From the provided options, options B and C directly depict real numbers. Option B declares the values of x as a set of positive integers from 1 to 14.
While C represents a real number as a decimal 0.9417. To further understand, real numbers are embedded in our daily calculations, for instance, if you own 1 apple, spend $14, or measure a distance of 0.9417 km, these are all instances of real numbers.
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Solve this rational equation
Answer:
x = -1Step-by-step explanation:
[tex]\text{Domain:}\\\\x-4\neq0\ \wedge\ x-2\neq0\ \wedge\ x^2-6x+8\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x^2-4x-2x+8\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x(x-4)-2(x-4)\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ (x-4)(x-2)\neq0\\\\x\neq4\ \wedge\ x\neq2\ \wedge\ x-4\neq0\ \wedge\ x-2\neq0\\\\\boxed{D:x\neq4\ \wedge\ x\neq2}[/tex]
[tex]\dfrac{1}{x-4}+\dfrac{x}{x-2}=\dfrac{2}{x^2-6x+8}\\\\\dfrac{1(x-2)}{(x-4)(x-2)}+\dfrac{x(x-4)}{(x-4)(x-2)}=\dfrac{2}{(x-4)(x-2)}\\\\\dfrac{x-2+x(x-4)}{(x-4)(x-2)}=\dfrac{2}{(x-4)(x-2)}\iff x-2+x(x-4)=2\\\\x-2+(x)(x)+(x)(-4)=2\\\\x-2+x^2-4x=2\qquad\text{subtract 2 from both sides}\\\\x^2-3x-4=0\\\\x^2-4x+x-4=0\\\\x(x-4)+1(x-4)=0\\\\(x-4)(x+1)=0\iff x-4=0\ \wedge\ x+1=0\\\\x-4=0\qquad\text{add 4 to both sides}\\x=4\notin D\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1\in D[/tex]
A circuit is supplied with 24 volts and its load offers a total resistance of 400 ohm. What’s the total circuit power?
Answer:
P = 1.44 Watts
Step-by-step explanation:
We know that the relation between voltage and current in a simple circuit with a resistor is
V = I.R
Where
V = the voltage of the source
I = current of the circuit
R = resistance
The power is defined as
P = V.I
Which is the same as
P = V.(V/R)
P = (24 v)^2 / (400 ohm)
P = 1.44 Watts
What is the common ratio in the geometric sequence?
1, 9, 81, 729,
Answers below
8
9
72
648
Answer:
9
Step-by-step explanation:
Common ratio is found by raking the second term and dividing by the first term
9/1 = 9
We can check by taking the third term and dividing by the second term
81/9 = 9
The common ratio is 9
Answer:
b
Step-by-step explanation:
What is the value of k?
k = 28
k = 29
K=31
K=42
The attachment should answer some of your guys “what does k=?” Questions
Please help. This is a math vocabulary crossword puzzle
Answer: i cant read that m8 take a better picture
Step-by-step explanation:
Usted tiene ________ clases de ciencias en la tarde.
a) una
b) un
c) unos
d) unas
how do you know a dilation will produce similar figures?
Answer:
The corresponding side lengths of the figure will be proportional based on the scale factor.
Step-by-step explanation:
A dilation can either be an enlargement or reduction. If the scale factor is less than one then the figure will be a reduction. If the scale factor is one or larger then the figure will be an enlargement. Since a dilation is basically multiplying the figure will always be proportional to the original figure.
By what number should we multiply 3 raise to -4 so that the product is 32?
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x\cdot 3^{-4}=32\implies x\cdot \cfrac{1}{3^4}=32\implies \cfrac{x}{81}=32\implies x=2592[/tex]
Answer:
x = 2592
Step-by-step explanation:
Equation: x * 3⁻⁴ = 32
Simplify: x/81 = 32
Multiply: x = 2592
Graph this solution x < 4
Answer:
see below
Step-by-step explanation:
x < 4
x is less than 4
Since it is less than, there is an open circle at 4
less than means the line goes to the left
Write your answer without using negative exponents.
(w^5)^-7
Your answer would be [tex]\frac{1}{w^{35} }[/tex]
This is because (w^5)^-7 expands to give w^-35 because you multiply the exponents. When you have a negative exponent, this can also be written as a reciprocal, i.e. x^-2 = 1/x². This means that we can write w^-35 as 1/(w^35), which doesn't include any negative exponents.
I hope this helps! Let me know if you have any questions :)
The answer without using negative exponents [tex](w^{5})^{-7}[/tex] is [tex]\frac{1}{w^{35} }[/tex] .
What are the properties of exponents ?The following properties of exponents are -
[tex](a^{m})^{n}[/tex] = [tex]a^{m*n}[/tex] [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] How to solve expression using properties of exponents ?Given expression is [tex](w^{5})^{-7}[/tex] .
Using the properties of exponents, we have -
= [tex]w^{-35}[/tex]
= [tex]\frac{1}{w^{35} }[/tex] which does not have any negative exponents.
Thus, the answer without using negative exponents [tex](w^{5})^{-7}[/tex] is [tex]\frac{1}{w^{35} }[/tex] .
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Where each input has only one output value is called a(n)
C. Function
Hope this helps.
r3t40
BIG POINTS!
A cone with a base radius of 8 cm fits inside a sphere of radius 10 cm. Find the perpendicular height of the cone.
Thank you very much for your help!
The solution is:: the area cross sectional area of triangle form in the cone is 80ft²
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
Given in the question,
radius of cone's base = 8ft
cone's base = base of triangle
height of cone = 10 ft
height of cone = height of triangle
Area of triangle
Area = 1/2(h)(b)
here h = height of triangle
b = base of triangle
A = 1/2(8)(10)
A = 40ft²
Since the section is 2 similar triangles back to back around the vertical center
so the area cross sectional area of triangle form in the cone is 2(40)ft² = 80ft²
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complete question:
You have a cone with a radius of 8 ft and a height of 10 ft. Find the area of the triangle formed by a perpendicular cross-section through the cone’s center.