Find the angle between V and W, Round your answer to one decimal place, if necessary V=-5i+2j W=-8i+2j A 17.8° B 353.9° C 3.9° D 7.8°
Answers
Answer:
D. 7.8°
Step-by-step explanation:
There are many ways to work this problem. One is to subtract the angle of V from that of W:
∠V = arctan(2/-5) ≈ 158.20°
∠W = arctan(2/-8) ≈ 165.96°
Then ∠W -∠V = 165.96° -158.20° = 7.76° ≈ 7.8°
___
Another is to divide W by V, since the quotient will have an angle that is the difference of their two angles.
(-8i +2j)/(-5i +2j) = (1/29)(44i +6j)
Then the angle of that is ...
arctan(6/44) ≈ 7.8°
___
You can also divide the dot product by the product of the two magnitudes to find the cosine of the angle between the vectors.
(V•W)/(|V|·|W|) = 44/√(68·29) = cos(x)
x = arccos(0.990830168...) ≈ 7.8°
___
A plot on graph paper will let you measure the angle with a protractor. You can obtain sufficient accuracy to choose between the offered answers.
___
Your graphing calculator may have complex number functions that let you work directly with the angles of the vectors. (See second attachment. The calculator is in degrees mode.) Doing 2-dimensional vector calculations on a calculator may best be accomplished by treating them as complex numbers.
The angle between two vectors can be found using the dot product formula. Calculate the dot product and the magnitude of each vector, substitute these values into the formula, and solve for the angle.
Explanation:To find the angle between two vectors V and W, you can use the dot product formula, which states that the dot product of two vectors is equal to the magnitude of each vector multiplied by the cosine of the angle between them. In this case, the vectors are V=-5i+2j and W=-8i+2j. The dot product of V and W is (-5*-8) + (2*2) = 44. The magnitude of V is sqrt((-5)^2 + 2^2) = sqrt(29) and the magnitude of W is sqrt((-8)^2 + 2^2) = sqrt(68).
Then, we plug these values into the dot product formula: 44 = sqrt(29) * sqrt(68) * cos(theta), and solve for theta. The resulting angle, rounded to one decimal place, is the correct answer. Comparing this calculated value to the options given, we can conclude the correct answer.
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Related Questions
Charles factors the expression 4/3xy+1/3x using a factor of 1/3x. He writes the factored expression 1/3x(4y+1). Which best describes the accuracy of Charles solution?
A. His solution is accurate
B. His solution is inaccurate. The factor does not divide evenly into both terms.
C. His solution is inaccurate. The factoring of 4/3xy using the given GCF is incorrect.
D. His solution is inaccurate. The factoring of 1/3x using the given GCF is incorrect.
Answers
A. His solution is accurate
You can verify this by expanding his factored expression: 1/3x(4y+1), which gives you back the original expression 4/3xy+1/3x
Charles' solution is accurate because expression after factorization is similar to Charles factor's of expression option (A) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm = \dfrac{4}{3}xy+\dfrac{1}{3}x[/tex]
Taking common as (1/3)x
[tex]\rm = \dfrac{1}{3}x(4y+1)[/tex]
The above expression is similar to Charles factor's of expression.
Thus, Charles solution is accurate because expression after factorization is similar to Charles factor's of expression option (A) is correct.
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"Solve the problem of exponential growth. According to the U.S. Census Bureau, the population of the United States in 2010 was 308 million. This is a 9.6% increase over the 2000 count. Assuming this continued what would the population be in 2030?"
Answers
Answer:
370 million
Step-by-step explanation:
In the 10 years from 2000 to 2010, the population was multiplied by the factor ...
100% + 9.6% = 109.6% = 1.096
In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:
2030 population = (308 million)·(1.096²) ≈ 370 million
Answer:
370 million
Step-by-step explanation:
In the 10 years from 2000 to 2010, the population was multiplied by the factor ...
100% + 9.6% = 109.6% = 1.096
In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:
2030 population = (308 million)·(1.096²) ≈ 370 million
A cylindrical container has a radius of 0.2 meter and a height of 1 meter. The container is filled with honey. The density of honey is 1417 kg/m³. What is the mass of the honey in the container? Enter your answer in the box. Use 3.14 for π . Round your final answer to the nearest whole number.
Answers
Answer:178
Step-by-step explanation: I took the test :)
Answer:
The mass of the container is 178 kg.
Step-by-step explanation:
Since, the volume of a cylinder is,
[tex]V=\pi (r)^2 h[/tex]
Where r is the radius of the cylinder
And, h is its height
Here, r = 0.2 meters,
h = 1 meter,
So, the volume of the cylindrical container is,
[tex]V=\pi (0.2)^2(1)[/tex]
[tex]=3.14\times 0.04=0.1256\text{ cubic meters}[/tex]
Now,
[tex]Density = \frac{Mass}{Volume}[/tex]
[tex]\implies Mass = Density\times Volume[/tex]
Given, Density of the container = 1417 kg/m³,
By substituting the values in the above formula,
[tex]\text{Mass of the container}=1417\times 0.1256=177.9752\text{ kg}\approx 178\text{ kg}[/tex]
What are the solutions to the system of equations?
x = x^2 - 4x +3
y = -x +3
( , ) and ( , )
Answers
Answer:
(0,3) and (3,0)
Step-by-step explanation:
The first thing to do is graph the two equations to see where they intersect. Then you know what answer to look for. The graph is below. It was done on desmos.
I take it the first equation is a typo and should be y = x^2 - 4x + 3
Equate the two equations.
-x + 3 = x^2 -4x + 3 Subtract 3 from both sides
-x = x^2 - 4x + 3-3
-x = x^2 - 4x Add x to both sides.
0 = x^2 - 4x + x
0 = x^2 - 3x Factor
0 = x(x - 3)
So x can equal 0
or x can equal 3
In either case the right side will reduce to 0.
Case 1. x = 0
y= - x + 3
y = 0 + 3
y = 3
So the point is (0,3)
Case 2. x = 3
y = - x + 3
y = - 3 + 3
y = 0
So the point is (3,0)
How do you simplify this expression step by step using trigonometric identities?
Answers
[tex]\bf \textit{Pythagorean Identities}\\\\ 1+tan^2(\theta)=sec^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(\theta )cos^2(\theta )+tan^2(\theta )\implies \cfrac{1}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} +tan^2(\theta ) \\\\\\ 1+tan^2(\theta )\implies sec^2(\theta )[/tex]
What is the value of x? Enter your answer in the box
Answers
Answer:
x = 20
Step-by-step explanation:
Formula
x1/x2 = x3/x4
Givens
x = 11
x2 = 11 + 121 = 132
x3 = 10
x4 = 10 + 5x + 10
Solution
11/132 = 10 / (5x + 10 + 10) Combine
11/132 = 10/(5x + 20) Cross multiply
11*(5x + 20) = 132 * 10 Combine on the right.
11(5x + 20 ) = 1320 Divide by 11. (You could remove the brackets, but this is easier.
11(5x + 20)/11 = 1320/11 Do the division
5x + 20 = 120 Subtract 20 from both sides
5x + 20-20 = 120 - 20 Combine
5x = 100 Divide by 5
5x/5 = 100/5
x = 20
please help and thank you.
Answers
Answer:
Step-by-step explanation:
This is a negative x^2 quadratic. I'm not sure if there's anything else you need.
Using the distributive property to find the product (y — 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y2 – ay – 64. What is the value of a in the polynomial?
Answers
Answer:
a=16
Step-by-step explanation:
Given
(y-4)(y^2+4y+16)
To find the value of a in the resulting polynomial we have to solve the given expression
=y(y^2+4y+16)-4(y^2+4y+16)
= y^3+4y^2+16y-4y^2-16y-64
To find the value of a, both the polynomials will be compared
y^3+4y^2+16y-4y^2-16y-64
y^3+4y^2+ay-4y^2-ay-64
Comparing the coefficients of both polynomials gives us that
a=16
So, the value of a is 16 ..
help please
greatest common factor find the GCF of each
must show work
Answers
11) Factors of 55 are 1,5,11,55 Factors of 75 are 1,3,5,15,25,75
The greatest common factor is 5.
12) With algebraic expressions you just simplify and multiplier in the simplification is the greatest common factor.
66yx + 30x^2y --) 6yx( 11 + 5x ) so the greatest common factor is 6yx.
13) 60y + 56x^2 --) 4( 15y + 14x^2 ) so the greatest common factor is 4.
14) 36xy^3 + 24y^2 --) 12y^2( 3xy + 2 ) so the greatest common factor is 12y^2.
15) 18y^2 + 54y^2 --) 18y^2( 1 + 3 ) so the greatest common factor is 18y^2.
16) 80x^3 + 30yx^2 --) 10x^2( 8x + 3y ) so the greatest common factor is 10x^2.
17) 105x + 30yx + 75x --) 15x( 7 + 2y + 5 ) so the greatest common factor is 15x.
18) 140n + 140m^2 + 80m --) 20( 7n + 7m^2 + 4m ) so the greatest common factor is 20.
If you want a further explanation step by step just ask :)
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=72t-16t^2. What is the maximum height that the ball will reach?
Do not round your answer
Answers
Answer:
The maximum height that the ball will reach is 81 ft
Step-by-step explanation:
Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.
For an equation of the form
[tex]at ^ 2 + bt + c[/tex]
So
the t coordinate of the vertice is:
[tex]t =-\frac{b}{2a}[/tex]
In this case the equation is:
[tex]h(t)=72t-16t^2[/tex]
So
[tex]a=-16\\b=72\\c=0[/tex]
Therefore
[tex]t =-\frac{72}{2(-16)}[/tex]
[tex]t=2.25\ s[/tex]
Finally the maximum height that the ball will reach is
[tex]h(2.25)=72(2.25)-16(2.25)^2[/tex]
[tex]h=81\ ft[/tex]
The ball thrown vertically upwards will reach the maximum height of 81 feet after 2.25 seconds.
Explanation:To find the maximum height the ball will reach, first, we need to recognize that the equation 'h(t)=72t-16t^2' is a quadratic function in the form of 'f(t)=at^2+bt+c'. The maximum point of a quadratic function, also known as the vertex, happens at 't=-b/2a'. In this case, 'a' is -16 and 'b' is 72.
So the maximum height is achieved at 't=-72/(2*-16)' or 't=72/32 = 2.25' seconds.
To find out the maximum height, we just need to substitute this value of t into the equation for h(t):
h(2.25)=72*2.25-16*2.25^2
The above calculation gives a maximum height of 81 feet.
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If f (x) = – 4x3 + 2x2 – 1, find f (– 1)
Answers
Answer:
[tex]f(-1)=5[/tex]
Step-by-step explanation:
We know that the equation is
[tex]f(x)=-4x^3+2x^2-1[/tex]
We can then plug -1 in for x
[tex]f(-1)=-4(-1)^3+2(-1)^2-1\\\\f(-1)=-4(-1)+2(1)-1\\\\f(-1)=4+2-1\\\\f(-1)=5[/tex]
ANSWER
[tex]f( - 1) = 5[/tex]
EXPLANATION
The given function is
[tex]f(x) = - 4 {x}^{3} + 2 {x}^{2} - 1[/tex]
We substitute x=-1 to obtain:
[tex]f( - 1) = - 4 {( - 1)}^{3} + 2 {( - 1)}^{2} - 1[/tex]
We simplify to obtain;
[tex]f( - 1) = 4 + 2 - 1[/tex]
.
This evaluates to
[tex]f( - 1) = 5[/tex]
Write these expressions in exponential form:
1. 10 * 10 * 10 * 10 *10
2. y * y * x * x * x * z * z * z * z *z
3. What is 14 to the zero power?
Answers
1. 10^5
2. z^5*x^3*y^2
3. 1
Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.
Answers
ANSWER
[tex]\sin( \theta) = - \frac{15}{17} [/tex]
[tex]\csc( \theta) = - \frac{17}{15} [/tex]
[tex]\cos( \theta) = \frac{8}{17} [/tex]
[tex]\sec( \theta) = \frac{17}{8} [/tex]
[tex]\tan( \theta) = - \frac{15}{8} [/tex]
[tex]\cot( \theta) = - \frac{8}{15} [/tex]
EXPLANATION
From the Pythagoras Theorem, the hypotenuse can be found.
[tex] {h}^{2} = 1 {5}^{2} + {8}^{2} [/tex]
[tex] {h}^{2} = 289[/tex]
[tex]h = \sqrt{289} [/tex]
[tex]h = 17[/tex]
The sine ratio is negative in the fourth quadrant.
[tex] \sin( \theta) = - \frac{opposite}{hypotenuse} [/tex]
[tex]\sin( \theta) = - \frac{15}{17} [/tex]
The cosecant ratio is the reciprocal of the sine ratio.
[tex]\csc( \theta) = - \frac{17}{15} [/tex]
The cosine ratio is positive in the fourth quadrant.
[tex]\cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos( \theta) = \frac{8}{17} [/tex]
The secant ratio is the reciprocal of the cosine ratio.
[tex]\sec( \theta) = \frac{17}{8} [/tex]
The tangent ratio is negative in the fourth quadrant.
[tex]\tan( \theta) = - \frac{opposite}{adjacent} [/tex]
[tex]\tan( \theta) = - \frac{15}{8} [/tex]
The reciprocal of the tangent ratio is the cotangent ratio
[tex]\cot( \theta) = - \frac{8}{15} [/tex]
Answer:
sin=-15/17
cos=8/7
tan=-15/8
csc=-17/15
sec=17/8
cot=-8/15
what is the sum of the fractions
Answers
Answer:
[tex]6\frac{7}{9}[/tex]
Step-by-step explanation:
[tex]6\frac{2}{3}+\frac{1}{9} = 6\frac{6}{9}+\frac{1}{9}=6 \frac{7}{9}[/tex]
Answer:
Step-by-step explanation:
its D
Write the product of the monomials (8x6y)2 and (x3y4).
Answers
Answer:
The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
Step-by-step explanation:
* Lets explain how to solve the problem
- We need to find the product of the monomials (8x 6y)² and
[tex]x^{3}y^{4}[/tex]
- At first lets solve the power of the first monomial
- Because the power 2 is on the bracket then each element inside the
bracket will take power 2
∵ (8x 6y)² = (8)²(x)²(6)²(y)²
∵ (8)² = 64
∵ (x)² = x²
∵ (6)² = 36
∵ (y)² = y²
∴ (8x 6y)² = [64x² × 36y²]
∵ 64 × 36 = 2304 x²y²
∴ The first monomial is 2304 x²y²
∵ The first monomial is 2304 x²y²
∵ The second monomial is [tex]x^{3}y^{4}[/tex]
- Lets find their product
- Remember in multiplication if two terms have same bases then we
will add their powers
∵ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] =
2304 [ [tex]x^{2}*x^{3}[/tex] ] [ [tex]y^{2}*y^{4}[/tex] ]
∵ [tex]x^{2}*x^{3}[/tex] = [tex]x^{2+3}[/tex] = [tex]x^{5}[/tex]
∵ [tex]y^{2}*y^{4}[/tex] = [tex]y^{2+4}[/tex] = [tex]y^{6}[/tex]
∴ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] = 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]
Joan Arlington has twice as much money invested at 5% simple annual interest as
she does at 4%. If her yearly income from the two investments is $399, how much
does she have at each rate?
at each rate?
Please Help me
Answers
[tex]5 \div 100 \times 399 \times 1 = 19.95 \: and \: 4 \div 100 \times 399 \times 1 = 15.96[/tex]
A mother who is 40 years old has a daughter and a son. The son is twice as old as the daugther. In 15 years the sum of all their ages will be 100 years. How old are the siblings now?
Answers
Answer:
The son's age is 10 and the daughter's age is 5 now
Step-by-step explanation:
Let
x-----> the son's age now
y----> the daughter's age now
we know that
x=2y ----> equation A
(x+15)+(y+15)+(40+15)=100
x+y+85=100
x+y=15 -----> equation B
Substitute equation A in equation B and solve for y
2y+y=15
3y=15
y=5 years
Find the value of x
x=2(5)=10 years
therefore
The son's age is 10.
The daughter's age is 5
Corey bought 2 1/2 liters of paint for $60. What was the cost per liter of paint
Answers
Hello there!
Answer:
$24
Step-by-step explanation:
In order to find the answer to your problem, we're going to need to find out how much ONE liter of paint costs.
Lets gather the information of what we know:
2 1/2 liters of paint
↑ Cost $60.
With the information we know, we can solve to find the answer.
In order to get the answer, we would need to divide 60 by 2 1/2 (or 2.5). We would need to do this because when we divide it, it would allow us to get the cost for 1 liter.
Lets solve:
[tex]60 \div 2.5=24[/tex]
When you divide, you should get the answer of 24.
This means that one liter of paint cost $24.
$24 should be your FINAL answer.
Answer:
$24/liter
Step-by-step explanation:
Write the the dollar amount first and the paint volume second in this ratio:
$60.00
--------------- = $24/liter
2.5 liters
Please respond quickly!!
Answers
Answer:
Area of triangle = 6 in^2
Step-by-step explanation:
We need to find the area of triangle. The formula used is:
Area of triangle = 1/2 * b*h
where b=base and h= height
In the given question, b =2 and h= 6
Putting values in the formula:
Area of triangle = 1/2 *2*6
= 12/2
= 6 in^2
Answer:
The area is 6 in^2
Step-by-step explanation:
Alice has a total of 12 dimes and nickels. She has 2 more nickels than dimes. Which equation represents the given problem situation?
A. c + (c + 2) = 12, where c is the number of dimes
B. c + 2c = 12, where c is the number of nickels
C. c + (c + 2) = 12, where c is the number of nickels
D. c + 2c = 12, where c is the number of dimes
Answers
Answer: The correct option is
(A) [tex]c+(c+2)=12,[/tex] where c is the number of dimes.
Step-by-step explanation: Given that Alice has a total of 12 dimes and nickels and she has 2 more nickels than dimes.
We are to select the correct equation that represents the given problem situation.
Let c represents the number of dimes. Then, the number of nickels will be (c + 2).
Since there are total 12 coins, so the required equation is given by
[tex]c+(c+2)=12.[/tex]
Thus, the required equation is
[tex]c+(c+2)=12,[/tex] where c is the number of dimes.
Option (A) is CORRECT.
The expression for the total number of dimes and nickels is c+(c+2)=12. Option A is the correct answer.
How do you express the number of dimes and nickels?Given that Alice has a total of 12 dimes and nickels.
Also given that she has 2 more nickels than dimes.
Let us consider that c is the number of dimes. Then the number of nickels is given as,
Number of nickels = c+2
The total sum of dimes and nickels is 12, then,
Number of dimes + Number of nickels = 12
c + (c+2) = 12
Hence the expression for the total number of dimes and nickels is c+(c+2)=12. Option A is the correct answer.
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https://brainly.com/question/24412452.
Solve the equation of exponential decay. The population of a city is expected to be 440,000 in 2020. This is a decline of 12% from 2010 to 2020. Assuming this continued what would the population of the city be in 2040? Round to the nearest ten thousand
Answers
Answer:
about 340,000
Step-by-step explanation:
In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:
2040 population = 440,000·0.88² ≈ 340,000
Answer:
about 340,000
Step-by-step explanation:
In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:
2040 population = 440,000·0.88² ≈ 340,000
The recursive rule for a geometric sequence is given. a1=2; an=1/3a subscript (n−1) Enter the explicit rule for the sequence. an=
Answers
ANSWER
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
EXPLANATION
The recursive formula is given as:
[tex]a_n= \frac{1}{3} a_{n-1}[/tex]
where
[tex]a_1=2[/tex]
The explicit rule is given by:
[tex]a_n=a_1 {r}^{n-1}[/tex]
From the recursive rule , we have
[tex]r = \frac{1}{3} [/tex]
We substitute the known values into the formula to get;
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
Therefore, the explicit rule is:
[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]
how much string is left when 1 and 3/4 in are cut from a piece measuring 3 and 1 /6 inches
Answers
Answer:
1 5/12 inches.
Step-by-step explanation:
That is 3 1/6 - 1 3/4
= 19/6 - 7/4
The lowest common denominator of 4 and 6 is 12, so we have:
38/12 - 21/12
= 17 /12
= 1 5/12 inches (answer).
The remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.
The correct option is (a).
find out how much string is left when [tex]\(1 \frac{3}{4}\)[/tex] inches are cut from a piece initially measuring[tex]\(3 \frac{1}{16}\)[/tex]inches.
1. Convert the mixed numbers to improper fractions:
[tex]- \(1 \frac{3}{4}\) inches = \(\frac{7}{4}\) inches[/tex]
[tex]- \(3 \frac{1}{16}\) inches = \(\frac{49}{16}\) inches[/tex]
2. Make the denominators equal:
- Multiply the numerator and denominator of [tex]\(\frac{7}{4}\)[/tex]by 16 to make the denominators equal:
[tex]\(\frac{7}{4} = \frac{112}{64}\)[/tex]
- Now we have:
- Initial length = [tex]\(\frac{49}{16}\)[/tex] inches
- Cut length = [tex]\(\frac{112}{64}\)[/tex] inches
3. Subtract the two fractions:
- Subtract the cut length from the initial length:
[tex]\(\frac{49}{16} - \frac{112}{64}\)[/tex]
- To subtract, we need a common denominator. The least common multiple (LCM) of 16 and 64 is 64.
- Convert both fractions to have a denominator of 64:
[tex]\(\frac{49}{16} = \frac{196}{64}\)[/tex]
[tex]\(\frac{112}{64}\) remains the same.[/tex]
- Subtract the numerators:
[tex]\(\frac{196}{64} - \frac{112}{64} = \frac{84}{64}\)[/tex]
4. Simplify the result:
- Divide both the numerator and denominator by their greatest common factor (GCF), which is 4:
[tex]\(\frac{84}{64} = \frac{21}{16}\)[/tex]
5. Convert back to a mixed number:
- Divide the numerator by the denominator:
[tex]\(\frac{21}{16} = 1 \frac{5}{16}\)[/tex]
Therefore, the remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.
rx+2x=4r+3
Solving for X
Answers
Answer:
x = (4r +3)/(r +2)
Step-by-step explanation:
Collect x terms, then divide by the coefficient of x.
x(r +2) = 4r +3
x = (4r +3)/(r +2)
what is the solution in this equation -8x+4=36
Answers
Answer:
X=-4
Step-by-step explanation:
Answer:
x = -4
Step-by-step explanation:
-8x+4=36
-4
-8x =32
/-8 /-8
x = -4
Given the function f(x)= -5+4x^2 calculate the following value:
f(a+h)
Please help ASAP!!! :(
Answers
Evaluating a function in a specific point means to substitute all occurrences of x with the specific value.
In your case, we have to substitute "x" with "a+h":
[tex]f(x)= -5+4x^2 \implies f(a+h) = -5+4(a+h)^2\\ = -5+4(a^2+2ah+h^2)=-5+4a^2+8ah+h^2[/tex]
8) Factor each sum or difference of cubes completely.
a. 8x3 + 27
Answers
Answer:
[tex]\large\boxed{(2x+3)(4x^2-6x+9)}[/tex]
Step-by-step explanation:
[tex]8=2^3\\\\8x^3=2^3x^3=(2x)^3\\\\27=3^3\\\\8x^3+27=(2x)^3+3^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+3)\bigg((2x)^2-(2x)(3)+3^2\bigg)=(2x+3)(4x^2-6x+9)[/tex]
What is the value of x?
Answers
Answer:
Step-by-step explanation:
When an angle is bisected the opposite sides and the sides of the bisected angle are in a set ratio.
That translates into
(x + 8)/10 = (2x - 5)/14 Cross multiply
14* (x + 8) = 10* (2x - 5) Remove the brackets on both sides.
14x + 112 = 20x - 50 Subtract 14x from both sides.
112 = 20x - 14x - 50 Combine
112 = 6x - 50 Add 50 to both sides.
112+50 = 6x - 50 + 50 Combine
162 = 6x Switch
6x = 162 Divide by 6
x = 27
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.]f(x) = 10/x , a= -2f(x) = \sum_{n=0}^{\infty } ______Find the associated radius of convergence R.R = ______
Answers
Rewrite [tex]f[/tex] as
[tex]f(x)=\dfrac{10}x=-\dfrac5{1-\frac{x+2}2}[/tex]
and recall that for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
so that for [tex]\left|\dfrac{x+2}2\right|<1[/tex], or [tex]|x+2|<2[/tex],
[tex]f(x)=-5\displaystyle\sum_{n=0}^\infty\left(\frac{x+2}2\right)^n[/tex]
Then the radius of convergence is 2.
The Taylor series for the function f(x) = 10/x, centered at a = -2, is given by the formula ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence (R) for the series is ∞, which means the series converges for all real numbers x.
Explanation:Given the function f(x) = 10/x, we're asked to find the Taylor series centered at a = -2. A Taylor series of a function is a series representation which can be found using the formula f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + .... For f(x) = 10/x, the Taylor series centered at a = -2 will be ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence R is determined by the limit as n approaches infinity of the absolute value of the ratio of the nth term and the (n+1)th term. This results in R = ∞, indicating the series converges for all real numbers x.
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This Venn diagram shows sports played by 10 students
Let event A - The student plays basketball.
Let event B - The student plays soccer.
What is P(AB)?
Answers
Answer:
B. 1/10 or 0.10
Step-by-step explanation:
The question asks what's the probability that a student picked randomly will be playing both basketball and soccer.
The answer is right in the diagram.
We have only one student who plays both basketball and soccer: Ella
Since we have 10 students in the selected group, the probably you'll pick Ella is:
1 / 10 = 0.10 = 10%
So, the answer is B.
The value of P(A/B) is 0.33.
Given that, the Venn diagram shows sports played by 10 students.
What is P(A/B)?P(A/B) is known as conditional probability and it means the probability of event A that depends on another event B. It is also known as "the probability of A given B". The formula for P(A/B)=P(A∩B) / P(B).
Now, P(A/B)=1/3≈0.33
Therefore, the value of P(A/B) is 0.33.
To learn more about the Venn diagram visit:
https://brainly.com/question/1605100.
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