Determine whether b can be written as a linear combination of Bold a Subscript Bold 1a1​, Bold a Subscript Bold 2a2​, and Bold a Subscript Bold 3a3. In other​ words, determine whether weights x 1x1​, x 2x2​, and x 3x3 ​exist, such that x 1x1Bold a Subscript Bold 1a1plus+x 2x2Bold a Subscript Bold 2a2plus+x 3x3Bold a Subscript Bold 3a3equals=b. Determine the weights x 1x1​, x 2x2​, and x 3x3 if possible.

Answer:

  x - y = 0

Step-by-step explanation:

We see that in both cases, y = x. The standard-form version of this equation is ...

  x - y = 0

Answer:

x = -1            x = -5/3

Step-by-step explanation:

Assuming we want the zeros

(2x+2) (3x+5) =0

Using the zero product property

2x+2 = 0   3x+5 =0

2x = -2       3x = -5

x = -2/2      x = -5/3

x = -1            x = -5/3

Answer:

x=-1, or -5/3

Step-by-step explanation:

When you add (2x+2)(3x+5)=0, it becomes a equation that you can solve for. I would advise you to separate both the parts of the equation so it becomes (2x+3)=0 and (3x+5)= 0 and that's how you can subract and divide easier in order to get the solutions. Hope this helps!!

Answer:

the answer for the question is 26√13/12

Answer:

The maximum value is +√21 and the minimum value is -√21

Step-by-step explanation:

f(x,y,z) = x² + y² + z². Let g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

Using Lagrange multipliers,

df/dx = λg/dx, df/dy = λg/dy. and df/dz = λg/dz

df/dx = 2x, df/dy = 2y, df/dz = 2z

dg/dx = 4x³, dg/dy = 4y³, dg/dz = 4z³

So, df/dx = λg/dx ⇒ 2x = 4λx³     (1)

df/dy = λg/dy ⇒ 2y = 4λy³           (2)

df/dz = λg/dz ⇒ 2z = 4λz³           (3)

From (1) 4λx³ - 2x = 0

2λx³ - x = 0

x(2λx² - 1) = 0

solving, x = 0 or (2λx² - 1) = 0 ⇒ 2λx² = 1 ⇒ x = ±1/√(2λ) since x ≠ 0

From (2) 4λy³ - 2y = 0

2λy³ - y = 0

y(2λy² - 1) = 0

solving, y = 0 or (2λy² - 1) = 0 ⇒ 2λy² = 1 ⇒ y = ±1/√(2λ) since y ≠ 0

From (3) 4λz³ - 2z = 0

2λz³ - z = 0

z(2λz² - 1) = 0

solving, z = 0 or (2λz² - 1) = 0 ⇒ 2λz² = 1 ⇒ z = ±1/√(2λ) since z ≠ 0

g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

(1/√(2λ))⁴ + (1/√(2λ))⁴ + (1/√(2λ))⁴ - 7 = 0

3 (1/√(2λ))⁴ = 7

(1/√(2λ))⁴ = 7/3

1/√(2λ) = ⁴√7/3

√(2λ) = ⁴√3/7

2λ = √3/7

λ = 1/2(√3/7)

Since x = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Also y = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

and z = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Substituting x,y and z into f(x,y,z) we have

f(x,y,z) = (⁴√7/3)² + (⁴√7/3)² + (⁴√7/3)² = 3(⁴√7/3)² = 3(√7/3) = √(7 × 3) = ±√21

The maximum value is +√21 and the minimum value is -√21

Step-by-step explanation:

-11+3=-8

-8+3=-5

-5+3=-2

From the topic of sequence and series

Answer:

2.5π units^3

Step-by-step explanation:

Solution:-

- We will evaluate the solid formed by a function defined as an elliptical paraboloid as follows:-

                                  [tex]z = 4 - x^2 -4y^2[/tex]

- To sketch the elliptical paraboloid we need to know the two things first is the intersection point on the z-axis and the orientation of the paraboloid ( upward / downward cup ).

- To determine the intersection point on the z-axis. We will substitute the following x = y = 0 into the given function. We get:

                                 [tex]z = 4 - 0 -4*0 = 4[/tex]

- The intersection point of surface is z = 4. To determine the orientation of the paraboloid we see the linear term in the equation. The independent coordinates ( x^2 and y^2 ) are non-linear while ( z ) is linear. Hence, the paraboloid is directed along the z-axis.

- To determine the cup upward or downwards we will look at the signs of both non-linear terms ( x^2 and y^2 ). Both non-linear terms are accompanied by the negative sign ( - ). Hence, the surface is cup downwards. The sketch is shown in the attachment.

- The boundary conditions are expressed in the form of a cylinder and a plane expressed as:

                                [tex]x^2 + y^2 = 1\\\\z = 4[/tex]

- To cylinder is basically an extension of the circle that lies in the ( x - y ) plane out to the missing coordinate direction. Hence, the circle ( x^2 + y^2 = 1 ) of radius = 1 unit is extended along the z - axis ( coordinate missing in the equation ).

- The cylinder bounds the paraboloid in the x-y plane and the plane z = 0 and the intersection coordinate z = 4 of the paraboloid bounds the required solid in the z-direction. ( See the complete sketch in the attachment )

- To determine the volume of solid defined by the elliptical paraboloid bounded by a cylinder and plane we will employ the use of tripple integrals.

- We will first integrate the solid in 3-dimension along the z-direction. With limits: ( z = 0 , [tex]z = 4 - x^2 -4y^2[/tex] ). Then we will integrate the projection of the solid on the x-y plane bounded by a circle ( cylinder ) along the y-direction. With limits: ( [tex]y = - \sqrt{1 - x^2}[/tex] , [tex]y = \sqrt{1 - x^2}[/tex] ). Finally evaluate along the x-direction represented by a 1-dimensional line with end points ( -1 , 1 ).

- We set up our integral as follows:

                            [tex]V_s = \int\int\int {} \, dz.dy.dx[/tex]

- Integrate with respect to ( dz ) with limits: ( z = 0 , [tex]z = 4 - x^2 -4y^2[/tex] ):

                           [tex]V_s = \int\int [ {4 - x^2 - 4y^2} ] \, dy.dx[/tex]

- Integrate with respect to ( dy ) with limits: ( [tex]y = - \sqrt{1 - x^2}[/tex] , [tex]y = \sqrt{1 - x^2}[/tex] )

                        [tex]V_s = \int [ {4y - x^2.y - \frac{4}{3} y^3} ] \, | .dx\\\\V_s = \int [ {8\sqrt{( 1 - x^2 )} - 2x^2*\sqrt{( 1 - x^2 )} - \frac{8}{3} ( 1 - x^2 )^\frac{3}{2} } ] . dx[/tex]

- Integrate with respect to ( dx ) with limits: ( -1 , 1 )

                       [tex]V_s = [ 4. ( arcsin ( x ) + x\sqrt{1 - x^2} ) - \frac{arcsin ( x ) - 2x ( 1 -x^2 )^\frac{3}{2} + x\sqrt{1 - x^2} }{2} - \frac{ 3*arcsin ( x ) + 2x ( 1 -x^2 )^\frac{3}{2} + 3x\sqrt{1 - x^2} }{3} ] | \limits^1_-_1\\\\V_s = [ \frac{5}{2} *arcsin ( x ) + \frac{5}{3}*x ( 1 -x^2 )^\frac{3}{2} + \frac{5}{2} *x\sqrt{1 - x^2} ) ] | \limits^1_-_1\\\\V_s = [ \frac{5\pi }{2} + 0 + 0 ] \\\\V_s = \frac{5\pi }{2}[/tex]

Answer: The volume of the solid bounded by the curves is ( 5π/2 ) units^3.

Answer:

3 units

Step-by-step explanation:

The formula for the volume of the cone is given by

[tex]V=\frac{1}{3} \pi r^{2}h[/tex]

[tex]V=18\pi\ unit^{3} \\\\ r=\frac{2x}{2} =x\ units \\ \\ h=2x\ units[/tex]

Substituting in above formula

[tex]18\pi=\frac{1}{3} \pi*x^{2}*2x\\ \\ 54=2x^{3} \\ \\ x^{3} =27\\ \\ x=\sqrt[3]{27} \\ \\ x=3\ units[/tex]

Thus, the radius of the cone is 3 units.

Answer:

first question: 36

second question: 5

Step-by-step explanation:

for the first question, the parentheses just mean you are multiplying. so it would be 2 x 3 x 6 which equals 36.

For the second question, you would add d and g together and e and f, then subtract the sum of e and f from the sum of d and g.

(2 + 12) - (3 + 6)

14 - 9 = 5

Step-by-step explanation:

d=2

e=3

f=6

g=12

therefore , (2)×(3)×(6)

=36

2. d=2

e=3

f=6

g=12

(d+g) - (e+f)

(2+12) - (3+6)

(14) -(9)

=5.

Answer:

1.88

Step-by-step explanation:

From Trigonometry Identity;

Cos 20° = AC/ CB

AC = Cos 20° × CB

= Cos 20° × 2

= 1.879

= 1.88 ( to the nearest hundredth)

Approximately 3.6

:) Hope this helps

Answer:

2 and 3

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

<JKB = <FGC (SINCE BITH THEIR BISECTORS BISECT THEM MAKING A 90° ANGLE)

AND

<BKL = 90° (BECAUSE OF THE BISECTOR)

Answer:

B and D

Step-by-step explanation:

B and D

Answer:

-14, 14

Step-by-step explanation:

[tex] {x}^{2} = 196 \\ x = \pm \sqrt{196} \\ x = \pm \: 14 \\ x = 14 \: \: or \: \: x = - 14 \\ x = \{ - 14, \: \: 14 \}[/tex]

Answer:

[tex]x = 14[/tex]

x= -14

Step-by-step explanation:

[tex] {x}^{2} = 196 \\ x = \sqrt{196} \\ x = 14[/tex]

x= -14

To check whether the answer is correct,

[tex] {x}^{2} = 196 \\ [/tex]

[tex]x = 14[/tex]

[tex] {14}^{2} = 196 \\ 14 \times 14 = 196 \\ 196 = 196[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

y = x/2 +9/2

Step-by-step explanation:

y = -2x - 6.

The equation of the line perpendicular to the above equation has a slope 1/2

The equation of a slope is

y2-y1/x2-x1 = 1/2

To form an equation of the line we chose a point that lies on the graph which is perpendicular to y = -2x - 6 and an arbitrary point (x,y)

A point is given us already and that point is (3, 6).

Tie all together to compute the slope we have;

y-6/x-3 = 1/2

2(y-6) = x-3

2y-12= x-3

2y = x-3+12

2y= x+9

Dividing through by 2 we have

y = x/2 +9/2

y = x/2 + 4.5

The required equation is 2x-y =0, interception point is (0,0) and the equation is in integers.

Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.

The equation of a line which passes through point (x₁, y₁) with slope m can be given by,

y - y₁ = m(x - x₁)

The given equation of line k is y= -2x-6    (1).

The slope of line k = -2.

Since, line l is perpendicular to line k,

Slope of line l = 2

Line l passes through the point (3,6), therefore, the equation of line l,

y-6= 2(x-3)

⇒2x-y =0   (2)

To find interception point of slope of line l,

Substitute y=0, in equation (2) ,

x intercept = 0

Substitute x=0, in equation (2),

y intercept = 0

The equation is 2x-y =0, and it is in integer form.

To know more about Slope on :

https://brainly.com/question/16180119

#SPJ2

Answer:

Step-by-step explanation:

The total pressure of a gas is the sum of the partial pressures of the gases that it consists of. It means that

N2 + O2 + H2 + F2 = pressure of mixture

1 kpa = 7.50061683 mmhg

The total pressure of the mixture is 511.56 kPa. Converting to mmHg, it becomes

511.56 × 7.50061683 = 3837.02 mmhg

The pressure of the O2 is 196 kPa. Converting to mmhg, it becomes

196 × 7.50061683 = 1470.12 mmhg

Since the the pressure of the H2 is standard pressure, it means that the pressure is 760 mmhg

Also, pressure of the N2 is 584 mm Hg

Therefore,

1470.12 + 760 + 584 + F2 = 3837.02

2814.12 + F2 = 3837.02

F2 = 3837.02 - 2814.12

F2 = 1022.9 mm Hg

Answer:

  C.  38°

  D.  30°

Step-by-step explanation:

The relevant relation in both cases is the inscribed angle measures half the measure of the arc it intercepts.

__

C. Angle TSQ intercepts arc TQ, so the measure of arc TQ is 2(86.5°) = 173°. The measure of arc TR is the difference between the measures of arcs TQ and RQ, so is ...

  arc TR = 173° -135° = 38°

__

D. Inscribed angle PQR intercepts arc PR, so is half its measure.

  angle PQR = 60°/2 = 30°

Answer:

A.

Step-by-step Explanation:

P(A or B) = P(A)+P(B)-P(A and B)

Now

Putting the givens

0.68 = 0.2 + P(B) - 0.12

P(B) = 0.68 - 0.2 +0.12

P(B) = 0.6

Answer:

24 cm

Step-by-step explanation:

Assuming that the triangles are similar,

then the ratio of their sides must be the same.

in this case you are dealing with  2 longest sides and the 2 shortest sides.

We are asked to find the y (the length of the shortest side of the blue triangle)

because they are similar, we can form a ratio with their sides:

Purple Long Side / Blue Long Side = Purple Short Side / Purple Long side

100 / 80 = 30 / y

100y = (30)(80)

y = (30)(80) / 100

y = 24 cm

Answer:

y = 24

Step-by-step explanation:

Since these triangles are similar, you can set up a proportion like this:

[tex]\frac{100}{80} =\frac{30}{y}[/tex]

→Cross multiply:

[tex]\frac{100y}{2400}[/tex]

→Divide 2400 by 100:

y = 24

Answer:

According to the Law of Cosines, the correct answer would be D) 50.2 feet

Answer:(-12,15)

Step-by-step explanation:

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Answer:

D

Step-by-step explanation:

3 to 7 is about 4.

Answer:

[tex]y^{-1}[/tex]

Step-by-step explanation:

This question is asking us to rewrite the original expression it in the form [tex]y^n[/tex]

First we have

[tex](y^{-4} )y^3[/tex]

By the law of exponents we know that when we are multiplying expressions that have the same base, we need to add up the exponents.

Thus, this would mean that, in order to multiply this expression, we need to sum up the exponents so we have:

[tex]-4+3=-1[/tex]

Thus, this expression can be rewritten as:

[tex](y^{-4} )y^3=y^{-4+3} =y^{-1}[/tex]

Answer:

its A for the domain and B for the range

domain: (-infinity,infinity) Range: (-infinity,4]

Step-by-step explanation:

Answer:

its 3

Step-by-step explanation:

Answer:

4:14 or 2:7

Step-by-step explanation:

there are 4 girls and 14 boys

the ratio is 4:14

correct me if this is wrong

Answer:

2/7

Step-by-step explanation:

two find the answer you need to reduce 4 and 14 into the lowest common denominator.

Answer:

a) The null and alternative hypothesis are:

[tex]H_0: \mu=35.1\\\\H_a:\mu< 35.1[/tex]

b) The 95% confidence interval for the mean stocks traded in 2014 in millions is (21.13, 29.07).

c)  D. Reject the null hypothesis because μ= 35 1 million shares does not fall in the confidence interval.

Step-by-step explanation:

The claim is that 2014 stock volumes are significantly different from 2011 stock volumes (35.1 millions).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=35.1\\\\H_a:\mu< 35.1[/tex]

We can test this by calculating a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=25.1.

The sample size is N=40.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{12.4}{\sqrt{40}}=\dfrac{12.4}{6.32}=1.961[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=40-1=39[/tex]

The t-value for a 95% confidence interval and 39 degrees of freedom is t=2.023.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.023 \cdot 1.961=3.966[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 25.1-3.966=21.13\\\\UL=M+t \cdot s_M = 25.1+3.966=29.07[/tex]

The 95% confidence interval for the mean is (21.13, 29.07).

The value 35.1 is not included in the interval, so we can conclude that there is significant difference from the 2011 stock volume.

Answer:

2 and 1/12

Step-by-step explanation:

pls mrk brainliest

Answer: 25/12

Step-by-step explanation: One and two thirds is equal to 5/3, so now all you have to do is divide 5/3 by 4/5. To divide fractions you multiply the first fraction to the reciprocal of the second fraction. The reciprocal simply means to switch the numerator with the denominator. Multiply 5/3 by 5/4. To multiply fractions you need to multiply straight across. 5 times 5 is 25 and 3 times 4 is 12, so the answer is 25/12.

Answer: .250

Step-by-step explanation:

Answer:

V = 175 yd^3

Step-by-step explanation:

V = B*h

The base is the area of the triangle

B = 1/2 (5*7) = 35/2

so

V = 35/2 * 10

V = 175 yd^3

Answer:

175 yd

Step-by-step explanation:

The volume of a triangular prism can be calculated by the area of the base times its height. The bases are always the odd shapes out, so here it is the triangles with the "height" being the distance between the two bases.

The area of the base here is [tex]\frac{5*7}{2}[/tex]=17.5.

Multiplying that by the "height" gives 17.5×10= 175 yards.

Answer:

Sin(460 radians)= .97054

sin(460 degrees)= 0.98480775301

Step-by-step explanation:

I'm not sure where you are from, but usually you are allowed to use a calculator. (At least I was when I took Algebra 2/Trig in 6th grade.)

You never specified radians or degrees so I will answer both.

sin(460 radians)= .97054

sin(460 degrees)= 0.98480775301

If you are not allowed to use a calc, then I suggest looking at unit circle videos on Khan Academy.