Answer:
[tex]\int_C F . dr = \pi[/tex]
[tex]C : x = cost , y = sin t, z = sin^2 t - cos^2 t , 0 \leq t \leq 2 \pi[/tex]
Step-by-step explanation:
Given that:
[tex]F(x,y,z) = x^2yi + \dfrac{1}{3}x^3j +xyk[/tex]
Here C is the curve of intersection of the hyperbolic parabolic [tex]z = y^2 - x^2[/tex] and the cylinder [tex]x^2 +y^2 =1[/tex]
Using Stokes' Theorem
[tex]\int_C F . dr =\int \int \limits_s \ curl \ F. \ds[/tex]
From above ;
S = the region under the surface [tex]z = y^2 -x^2[/tex] and above the circle [tex]x^2+y^2 =1[/tex]
Suppose, we consider [tex]f(x,y,z) =z-y^2+x^2[/tex]
therefore, S will be the level curve of f(x,y,z) = 0
Recall that:
[tex]\bigtriangledown f (x,y,z)[/tex] is always normal to the surface S at the point (x,y,z).
∴
This implies that the unit vector [tex]n = \dfrac{\bigtriangledown f}{|| \bigtriangledown ||}[/tex]
So [tex]\bigtriangledown f = <2x, -2y,1 >[/tex]
Also, [tex]|| \bigtriangledown f ||= \sqrt{4x^2+4y^2+1}[/tex]
Similarly ;
[tex]curl \ F = \begin {vmatrix} \begin{array} {ccc}{\dfrac{\partial }{\partial x} }&{\dfrac{\partial }{\partial y} }& {\dfrac{\partial }{\partial z} }\\ \\ x^2y& \dfrac{1}{3}x^3&xy \end {array} \end{vmatrix}[/tex]
[tex]curl \ F = \langle x ,-y,0 \rangle[/tex]
Then:
[tex]\int \int_s curl \ F .ds = \int \int_s curl \ F .nds[/tex]
[tex]\int \int_s curl \ F .ds = \iint_D curl \ F \dfrac{\bigtriangledown f}{ || \bigtriangledown f||} \sqrt{ (\dfrac{\partial z}{\partial x }^2) + \dfrac{\partial z}{\partial x }^2)+1 } \ dA[/tex]
[tex]\int \int_s curl \ F .ds = \iint_D \dfrac{\langle x,-y,0 \rangle * \langle 2x,-2y,1 \rangle }{\sqrt{4x^2 +4y^2 +1 }} \times \sqrt{4x^2 +4y^2 +1 }\ dA[/tex]
[tex]\int \int_s curl \ F .ds = \iint_D (2x^2 + 2y^2) \ dA[/tex]
[tex]\int \int_s curl \ F .ds = 2 \iint_D (x^2 + y^2) \ dA[/tex]
[tex]\int \int_s curl \ F .ds = 2 \int \limits ^{2 \pi} _{0} \int \limits ^1_0r^2.r \ dr \ d\theta[/tex]
converting the integral to polar coordinates
This implies that:
[tex]\int \int_s curl \ F .ds = 2 \int \limits ^{2 \pi} _{0} \int \limits ^1_0r^2.r \ dr \ d\theta[/tex]
⇒ [tex]\int_C F . dr = 2(\theta) ^{2 \pi} _{0} \begin {pmatrix} \dfrac{r^4}{4}^ \end {pmatrix}^1_0[/tex]
[tex]\int_C F . dr = 2(2 \pi) (\dfrac{1}{4})[/tex]
[tex]\int_C F . dr =(4 \pi) (\dfrac{1}{4})[/tex]
[tex]\int_C F . dr = \pi[/tex]
Therefore, the value of [tex]\int_C F . dr = \pi[/tex]
The parametric equations for the curve of intersection of the hyperbolic paraboloid can be expressed as the equations of the plane and cylinder in parametric form . i.e
[tex]z = y^2 - x^2 \ such \ that:\ x=x , y=y , z = y^2 - x^2[/tex]
[tex]x^2 +y^2 =1 \ such \ that \ : x = cos \ t , y= sin \ t, z = z, 0 \leq t \leq 2 \pi[/tex]
Set them equal now,
the Parametric equation of [tex]C : x = cost , y = sin t, z = sin^2 t - cos^2 t , 0 \leq t \leq 2 \pi[/tex]
Rename 7/12 and 1/8 using the least common denominator.
Answer:
7/12 and 1/8
Step-by-step explanation:
they don't have a least common denominator because there is no common factor between 7 and 12, and 1 and 8. the least common denominator of 7/12 and 1/8 is 7/12 and 1/8.
Answer:
14/24 and 3/24
Step-by-step explanation:
answer for plato mastery test
6x + 3y = 45, solve for y in terms of x
Answer:
y=13
Step-by-step explanation:
Corbin is helping his grandfather plant the corn in the field. The field covers an area of 43,200 square feet. The length of the field is triple the width. What are the dimensions?
Answer:
the length is 360 feet and the width is 120 feet.
Step-by-step explanation:
Set up an equation with the area formula, A = lw
The width can be represented by x, and the length can be represented by 3x since it is 3 times the width
43,200 = (3x)(x)
43,200 = 3x²
Solve for x:
14,400 = x²
120 = x
So, the width is 120 feet.
The length is 3 times this, so multiply the width by 3 to find the length
120(3)
= 360
So, the length is 360 feet and the width is 120 feet.
What is the reciprocal of?
Answer:
8
Step-by-step explanation:
Just flip it up... it will be 8
Answer:
0.125
When you multiply fractions, multiply numerators to find solution numerator, then multiply denominators to find solution of denominator. Divide your fractions, multiply the first fraction by reciprocal of the second fraction. It can be crossed multiplied.
On a coordinate plane, kite W X Y Z is shown. Point W is at (negative 3, 3), point X is at (2, 3), point Y is at (4, negative 4), and point Z is at (negative 3, negative 2). What is the perimeter of kite WXYZ? units units units units
Answer:
[tex]P = 10 + 2\sqrt{53}[/tex] units
Step-by-step explanation:
Given
Shape: Kite WXYZ
W (-3, 3), X (2, 3),
Y (4, -4), Z (-3, -2)
Required
Determine perimeter of the kite
First, we need to determine lengths of sides WX, XY, YZ and ZW using distance formula;
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
For WX:
[tex](x_1, y_1)\ (x_2,y_2) = (-3, 3),\ (2, 3)[/tex]
[tex]WX = \sqrt{(-3 - 2)^2 + (3 - 3)^2}[/tex]
[tex]WX = \sqrt{(-5)^2 + (0)^2}[/tex]
[tex]WX = \sqrt{25}[/tex]
[tex]WX = 5[/tex]
For XY:
[tex](x_1, y_1)\ (x_2,y_2) = (2, 3)\ (4,-4)[/tex]
[tex]XY = \sqrt{(2 - 4)^2 + (3 - (-4))^2}[/tex]
[tex]XY = \sqrt{-2^2 + (3 +4)^2}[/tex]
[tex]XY = \sqrt{-2^2 + 7^2}[/tex]
[tex]XY = \sqrt{4 + 49}[/tex]
[tex]XY = \sqrt{53}[/tex]
For YZ:
[tex](x_1, y_1)\ (x_2,y_2) = (4,-4)\ (-3, -2)[/tex]
[tex]YZ = \sqrt{(4 - (-3))^2 + (-4 - (-2))^2}[/tex]
[tex]YZ = \sqrt{(4 +3)^2 + (-4 +2)^2}[/tex]
[tex]YZ = \sqrt{7^2 + (-2)^2}[/tex]
[tex]YZ = \sqrt{49 + 4}[/tex]
[tex]YZ = \sqrt{53}[/tex]
For ZW:
[tex](x_1, y_1)\ (x_2,y_2) = (-3, -2)\ (-3, 3)[/tex]
[tex]ZW = \sqrt{(-3 - (-3))^2 + (-2 - 3)^2}[/tex]
[tex]ZW = \sqrt{(-3 +3)^2 + (-2 - 3)^2}[/tex]
[tex]ZW = \sqrt{0^2 + (-5)^2}[/tex]
[tex]ZW = \sqrt{0 + 25}[/tex]
[tex]ZW = \sqrt{25}[/tex]
[tex]ZW = 5[/tex]
The Perimeter (P) is as follows:
[tex]P = WX + XY + YZ + ZW[/tex]
[tex]P = 5 + \sqrt{53} + \sqrt{53} + 5[/tex]
[tex]P = 5 + 5 + \sqrt{53} + \sqrt{53}[/tex]
[tex]P = 10 + 2\sqrt{53}[/tex] units
C is the answer.
That is all.
If g(x) = 2x + 2 and h(x) = 4x2 + 8x + 8, find a function f such that f ∘ g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)
Answer:
Step-by-step explanation:
Hello,
[tex](\forall x \in \mathbb{R}) (fog)(x)=f(g(x))=f(2x+2)=h(x)=4x^2+8x+8\\\\=(2x+2)^2-2^2+4(2x+2)\\\\=(2x+2)^2+4(2x+2)-4\\\\\text{So, we conclude by.}\\\\\large \boxed{\sf \bf f(x)=x^2+4x-4}[/tex]
If g(x) = 2x + 2 and h(x) = 4x2 + 8x + 8, then function f is 16x²+48x+40
What is a function?A relation is a function if it has only One y-value for each x-value.
The given functions are g(x) = 2x + 2 and h(x) = 4x² + 8x + 8.
fog=h
Now we have to find f(x)
fog=h
f(g(x))=h
f(2x+2)=4x² + 8x + 8.
=4(2x+2)²+8(2x+2)+8
=4(4x²+4+8x)+16x+16+8
=16x²+16+32x+16x+16+8
=16x²+32x+16x+16+16+8
=16x²+48x+40
Hence, function f is 16x²+48x+40
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What is the value of the expression? 3 x [(30 - 8) divided by 2 + 2]
Answer:
3×30=90
3×8=24
90-24=66
66÷4=16.5
Answer ASAP and I'll make you the brainliest Alberto multiplied a whole number by a fraction. The whole number is greater than 1. The fraction is greater than 0 and less than 1. Which BEST describes the product of the whole number and the fraction? A. equal to the fraction B. equal to the whole number C. less than the whole number D. greater than the whole number
Answer:
C. less than the whole number
Step-by-step explanation:
Think of the product as 1/2(0.5)×3 ; the answer would equal 1.5, half of 3. Any number less than 1, multiplied by a whole number, always comes out with a product less than the whole numbers. i.e. 1/3(0.3)×9 = 3
1/4(0.25)×8 = 2
1/5(0.20)×5 = 1
(Anyone correct me if I'm wrong.)
Answer: C) less than the whole number
Step-by-step explanation: I tried examples and they are less than the whole number. The first choice is also equal to the fraction but that’s not for most cases.
бу – 8 = 2(3y – 4)
Is it no solution if it’s not what’s the answer
Answer:
All real numbers.
Step-by-step explanation:
So we have the equation:
[tex]6y-8=2(3y-4)[/tex]
First, distribute the right side:
[tex]6y-8=6y-8[/tex]
As we can see, both expressions on both sides of the equation are the exact same. In other words, every value of y will make the equation true. Thus, the answer is all real numbers.
Answer:
infinite solutions
Step-by-step explanation:
1 solution means that only 1 number can replace that variable
No solution means that no numbers can replace that variable. If the 2 sides of the question cannot be solved or they are different, then that equation has no solutions.
Infinite solution means that any number can replace that variable. If the 2 sides of the equation the same, then it is an infinite solution.
6y - 8 = 2(3y - 4)
=> 6y - 8 = 6y - 8
Since both sides of the equations are the same, "y" can be any number.
So, this equation has infinite solutions.
g If a bowling ball with a radius of 12 centimeters rolls down an 18 meter lane, through how many radians does it rotate
Answer:
150 radians
Step-by-step explanation:
Arc length as a function of angle is ...
s = rθ
Then the angle is ...
θ = s/r = (1800 cm)/(12 cm) = 150 . . . radians
Solve for q. |q+8|≥2 Write a compound inequality like 1 3. Use integers, proper fractions, or improper fractions in simplest form.
Answer:
(-inf,-10] U [-6,inf)
Step-by-step explanation:
separate into possible cases
q+8≥2, q+8≥0
-(q+8)≥2, q+8<0
solve inequalities
x≥-6, x≥-8
x≤-10, x<-8.
The contingency table below shows the results of a survey of video viewing habits by age. Find the following probabilities or percentages: Probability that viewers is aged 18-34.
Answer:
The answer is ( 0.74 ) or ( 74/100 ).
I need to find the slope-intercept form equation for the line shown in the graph
The U.S. Open Golf Tournament was played at Congressional Country Club, Bethesda, Maryland, with prizes ranging from $465,000 for first place to $5000. Par for the course is 70. The tournament consists of four rounds played on different days. The scores for each round of the 32 players who placed in the money (more than $17,000) are given. The scores for the first round were as follows.
71 65 67 73 74 73 71 71 74 73 71 70 75 71 72 71 75 75 71 71 74 75 66 75 75 75 71 72 72 73 71 67
The scores for the fourth round for the same players were as follows:
69 69 73 74 72 72 70 71 71 70 72 73 73 72 71 71 71 69 70 71 72 73 74 72 71 68 69 70 69 71 73 74
Required:
a. Make a stem and leaf display for the first-round scores.
b. Make a stem and leaf display for the fourth-round scores.
c. Describe how the 2 plots overall shapes differ.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following data:
First round of scores :
71 65 67 73 74 73 71 71 74 73 71 70 75 71 72 71 75 75 71 71 74 75 66 75 75 75 71 72 72 73 71 67
STEM AND LEAF PLOT of 1st ROUND SCORES:
Stem - - | - - Leaf
______________
6 - - - | - - 5 6 7 7
7 - - | - - 0 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 3 4 4 4 5 5
- - - | - - 5 5 5 5 5
Second round scores :
69 69 73 74 72 72 70 71 71 70 72 73 73 72 71 71 71 69 70 71 72 73 74 72 71 68 69 70 69 71 73 74
STEM and LEAF PLOT of 2nd ROUND SCORES:
Stem - - | - - Leaf
______________________________
6 - - | - - 8 9 9 9 9 9
7 - - | - - 0 0 0 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3
- - - | - - 4 4 4
Both set of data have similar shape, showcasing what we can call a negative skew with the tail to the leaf and peak to the right of the distribution.
What's 4+4. I am having a really hard time figuring this out. Hurry quick and I will dramatically mark you as the bran-list
The independent variable of interest in an ANOVA procedure is called a a. partition. b. factor. c. treatment. d. response.
Answer:
B
Step-by-step explanation:
ANOVA means analysis of variance
The independent variable is the input that explains the dependent variable.
The dependent variable is called the response
points (2,7) ana (5,10).
3. Convert 3x + 5y = 15, from standard form to
slope intercept form.
Answer:
Below.
Step-by-step explanation:
3x + 5y = 15
Subtract 3x from both sides:
5y = -3x + 15
Divide through by 5:
y = -3/5 x + 3 <-----------slope-intercept form
Which representations display nonlinear functions? Check all that apply
Answer:
B and D
Step-by-step explanation:
A and C both show linear relationships (in this case negative). B is a parabolic curve, and D is a non-linear tread.
I hope this helps!
-The Business Man
Answer:
The fist Person Is correct it is B and D
Step-by-step explanation:
Amber has been saving quarters and dimes. She opened up the piggy bank and determined that it contained 18 coins worth $2.85. Determine how many dimes and quarters were in the piggy bank.
PLSS HElP WITH THIS !!!! MARKING BRAINLIST!!!!
NO ONE WILL HELP:(
Answer:
1. 2/3
2. -3
3. -1/2
4. 4/3
18. A sum of money was shared among
Okpala, Olu and Bello such that
Okpala had one sixth of the money.
Olu had one quarter of the money
and Bello had the rest. By what
fraction of the money is Bello's share
greater than Okpala's and Olu's
shares put together?
Answer is something I’m not sure of
Bello's share is greater than Okpala's and Olu's shares combined by a fraction of 1/6 of the total sum of money.
Here, we have,
Let's assign variables to represent the shares of Okpala, Olu, and Bello.
Let M be the total sum of money.
Okpala's share = (1/6)M
Olu's share = (1/4)M
Bello's share = M - Okpala's share - Olu's share
To find the fraction of the money by which Bello's share is greater than Okpala's and Olu's shares put together, we need to calculate the difference between Bello's share and the sum of Okpala's and Olu's shares, and then express it as a fraction of the total sum of money M.
Bello's share - (Okpala's share + Olu's share) = (M - Okpala's share - Olu's share) - (Okpala's share + Olu's share)
= M - Okpala's share - Olu's share - Okpala's share - Olu's share
= M - 2(Okpala's share) - 2(Olu's share)
= M - 2[(1/6)M] - 2[(1/4)M]
= M - (1/3)M - (1/2)M
= M - (2/6)M - (3/6)M
= M - (5/6)M
= (1/6)M
Now, let's express this difference as a fraction of the total sum of money M:
Fraction of Bello's share greater than Okpala's and Olu's shares
= [(1/6)M] / M
= (1/6)
Therefore, Bello's share is greater than Okpala's and Olu's shares combined by a fraction of 1/6 of the total sum of money.
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Write the equation the line that has a slope of 2 and a y-intercept (0,-9) then graph.
Answer:
The equation is y = 2x - 9
Step-by-step explanation:
To graph, start at 0,-9 and go up twice and right one.
|4х + 6| — 1 =
- 1 = 3х
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Answer: 7
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Absolute value is the distance between that number and zero. To find the absolute value, you basically just take the negative sign away if there is one. So you need to find the absolute value of 4x+6. Since you can't simplify this equation, you just keep it the way it is. The absolute value of 4x+6 is 4x+6.
So now you have 4x + 6 - 1. Since 6 and 1 are both constant variables, you can directly subtract it. 6-1 equals 5. Now you have 4x-5.
Now you have 4x-5 = -1 = 3x. You should isolate the variables as well as "removing" an equal sign. To bring away the -1, you have to add 1. -1 + 1 equals 0, AKA nothing. But you also have to do it with all the other expressions too...
4x - 5 + 1 = 4x-6
3x+1 = 3x+1
Now the equation is 4x-6 = 3x+1
So now you have to get rid of the 6. To do that, add 6 to each side of the equation.
4x-6+6 = 4x
3x+1+6 = 3x+7
Now the equation is 4x = 3x+7
Did you notice that you have to add 1x to 3x to get 4x?
3x+1x = 4x (AKA the left side of the equation)
Also, you added the 7.
So that means 7 is the 1x.
So x equals 7.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Write the equation of a line with a slope of 3 and passes through the point (-1,-8). Show steps please
Answer:
y = 3x-5
Step-by-step explanation:
[tex](-1,-8) = (x_1,y_1) \\ m = 3[/tex]
Substitute values into point slope form
[tex]y - y_1 = m(x - x_1) \\ y - ( - 8)) = 3(x - ( - 1)) \\ y + 8 = 3(x + 1) \\ y + 8 = 3x + 3[/tex]
[tex]y = 3x + 3 - 8 \\ y = 3x - 5[/tex]
Answer:
y=3x-5
Step-by-step explanation:
We are given a point and a slope, so we can use the point-slope formula.
[tex]y-y_{1}=m(x-x_{1})[/tex]
where m is the slope and (x₁, y₁) is the point.
The slope is 3 and the point given is (-1,-8). Therefore,
[tex]m=3 \\x_{1} =-1\\y_{1}=-8[/tex]
Substitute the values into the formula.
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y--8=3(x- -1)[/tex]
Simplify the signs. Two negative signs become a positive sign.
[tex]y+8=3(x+1)[/tex]
Distribute the 3. Multiply each term inside the parentheses by 3.
[tex]y+8= (3*x)+(3*1)[/tex]
[tex]y+8=3x+3[/tex]
We want to find the equation in slope-intercept form: y=mx+b. Therefore, we must isolate y. 8 is being added to y. The inverse of addition is subtraction. Subtract 8 from both sides.
[tex]y+8-8=3x+3-8[/tex]
[tex]y=3x+3-8[/tex]
[tex]y=3x-5[/tex]
The equation of the line is y=3x-5 ⇒ m= 3, b= -5
63 1/4 divided by 2 1/5
Answer:
[tex] \boxed{ \bold{ \huge{\boxed{ \sf{28 \frac{3}{4} }}}}}[/tex]
Step-by-step explanation:
[tex] \sf{63 \frac{1}{4} \div 2 \frac{1}{5} }[/tex]
Convert mixed fraction into improper fraction
⇒[tex] \sf{ \frac{63 \times 4 + 1}{ 4} \div \frac{5 \times 2 + 1}{5} }[/tex]
⇒[tex] \sf{ \frac{252 + 1}{4} \div \frac{10 + 1}{5} }[/tex]
⇒[tex] \sf{ \frac{253}{4} \div \frac{11}{5} }[/tex]
We know that division by fraction is the inverse of multiplication. If any number or fraction is divided by a fraction, we multiply the dividend by the reciprocal of the divisor.
⇒[tex] \sf{ \frac{253}{4} \times \frac{5}{11} }[/tex]
Reduce the numbers with Greatest common factor 11
⇒[tex] \sf{ \frac{23}{4} \times \frac{5}{1} }[/tex]
To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator
⇒[tex] \sf{ \frac{23 \times 5}{4 \times 1} }[/tex]
⇒[tex] \sf{ \frac{115}{4} }[/tex]
Convert improper fraction into mixed fraction
⇒[tex] \sf{28 \frac{3}{4} }[/tex]
Hope I helped!
Best regards!
21x - 12y = -15
- 7x + 4y = 5
Answer:
0
Step-by-step explanation:
_7x+4y=5 *(3)
_21x+12y=15
21x_12y=_15
____________
If I am right
I think !that is the answer
-18-3s=15 solve for s. can someone plz help
Answer:
The correct answer is s = -11.
Step-by-step explanation:
To solve this problem, we must move all of the variable terms to one side of the equation and move all of the constant terms to the other side. Let's keep the variable terms on the left and move the constants to the right. Our first step will be to add 18 to both sides of the equation to cancel out the -18 on the left side:
-18 + 18 - 3s = 15 + 18
-3s = 33
Our next and final step will be to divide both sides by -3 to get the variable s completely isolated on the left side of the equation.
-3s/-3 = 33/-3
s = -11
Therefore, the correct answer is s = -11.
Hope this helps!
Find c1 and c2 such that M2+c1M+c2I2=0, where I2 is the identity 2×2 matrix and 0 is the zero matrix of appropriate dimension.
The question is missing parts. Here is the complete question.
Let M = [tex]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right][/tex]. Find [tex]c_{1}[/tex] and [tex]c_{2}[/tex] such that [tex]M^{2}+c_{1}M+c_{2}I_{2}=0[/tex], where [tex]I_{2}[/tex] is the identity 2x2 matrix and 0 is the zero matrix of appropriate dimension.
Answer: [tex]c_{1} = \frac{-16}{10}[/tex]
[tex]c_{2}=\frac{-214}{10}[/tex]
Step-by-step explanation: Identity matrix is a sqaure matrix that has 1's along the main diagonal and 0 everywhere else. So, a 2x2 identity matrix is:
[tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
[tex]M^{2} = \left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right][/tex]
[tex]M^{2}=\left[\begin{array}{cc}31&10\\-2&15\end{array}\right][/tex]
Solving equation:
[tex]\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+c_{1}\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right] +c_{2}\left[\begin{array}{cc}1&0\\0&1\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
Multiplying a matrix and a scalar results in all the terms of the matrix multiplied by the scalar. You can only add matrices of the same dimensions.
So, the equation is:
[tex]\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+\left[\begin{array}{cc}6c_{1}&5c_{1}\\-1c_{1}&-4c_{1}\end{array}\right] +\left[\begin{array}{cc}c_{2}&0\\0&c_{2}\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
And the system of equations is:
[tex]6c_{1}+c_{2} = -31\\-4c_{1}+c_{2} = -15[/tex]
There are several methods to solve this system. One of them is to multiply the second equation to -1 and add both equations:
[tex]6c_{1}+c_{2} = -31\\(-1)*-4c_{1}+c_{2} = -15*(-1)[/tex]
[tex]6c_{1}+c_{2} = -31\\4c_{1}-c_{2} = 15[/tex]
[tex]10c_{1} = -16[/tex]
[tex]c_{1} = \frac{-16}{10}[/tex]
With [tex]c_{1}[/tex], substitute in one of the equations and find [tex]c_{2}[/tex]:
[tex]6c_{1}+c_{2}=-31[/tex]
[tex]c_{2}=-31-6(\frac{-16}{10} )[/tex]
[tex]c_{2}=-31+(\frac{96}{10} )[/tex]
[tex]c_{2}=\frac{-310+96}{10}[/tex]
[tex]c_{2}=\frac{-214}{10}[/tex]
For the equation, [tex]c_{1} = \frac{-16}{10}[/tex] and [tex]c_{2}=\frac{-214}{10}[/tex]
-6n - 6(- 8 n + 2 simplify
Answer:
42n-12Step-by-step explanation:
[tex]-6n - 6(- 8 n + 2)[/tex]
Use -6 to open the bracket
[tex]-6n+48n-12\\42n - 12\\= 6(7n -2)[/tex]
NEED HELP AND HOW U GOT THE ANSWER PLEASE find the measure of the angle greater than BXC using the figure below
Answer:
m∠BXC = 30°
Step-by-step explanation:
The symbol ∠ means "angle", so "angle ∠BXC" is actually redundant. The "greater than" symbol is "<", which sometimes is used when the proper angle symbol is not available.
Here, the question is simply asking for the measure of angle BXC.
Ray BX crosses the outer, inner scales of the protractor at 40, 140. Ray CX crosses those scales at 70, 110. The measure of angle BXC in degrees is the difference between the numbers on the same scale:
70 -40 = 30 . . . using outer scale numbers
140 -110 = 30 . . . using inner scale numbers
The measure of angle BXC is 30°.