Name a plane parallel to plane KLM.

Answer:

49/2 or 24 1/2

Step-by-step explanation:

Divide both sides by 2 to get x by itself.

Answer:

x = 7

Step-by-step explanation:

➟ x² = 49

in order to find the value of x will have to take square root of both side

➟ \( \sf \sqrt{x} = \sqrt{49} \)

Calculate

➟ \( \sf \: x = 7\)

The line integral of the conservative vector field F along C is approximately 14.45.

To compute the line integral of a conservative vector field along a curve, we can use the fundamental theorem of line integrals, which states that if F = ∇f, where f is a scalar function, then the line integral of F along a curve C is equal to the difference in the values of f evaluated at the endpoints of C.

In this case, we have the conservative vector field F(x, y) = (25x² + 9y, 225x² + 973). To find the potential function f, we integrate each component of F with respect to its respective variable:

∫(25x² + 9y) dx = (25/3)x³ + 9xy + g(y),

∫(225x² + 973) dy = 225xy + 973y + h(x).

Here, g(y) and h(x) are integration constants that can depend on the other variable. However, since C is a closed curve, the endpoints are the same, and we can ignore these constants. Therefore, we have f(x, y) = (25/3)x³ + 9xy + (225/2)xy + 973y.

Next, we parameterize the portion of the unit circle C in the first quadrant. Let's use x = cos(t) and y = sin(t), where t ranges from 0 to π/2.

The line integral of F along C is given by:

∫(F · dr) = ∫(F(x, y) · (dx, dy)) = ∫((25x² + 9y)dx + (225x² + 973)dy)

= ∫((25cos²(t) + 9sin(t))(-sin(t) dt + (225cos²(t) + 973)cos(t) dt)

= ∫((25cos²(t) + 9sin(t))(-sin(t) + (225cos²(t) + 973)cos(t)) dt.

Evaluating this integral over the range 0 to π/2 will give us the line integral along C. Let's calculate it using numerical methods:

∫((25cos²(t) + 9sin(t))(-sin(t) + (225cos²(t) + 973)cos(t)) dt ≈ 14.45 (rounded to 2 decimal places).

Therefore, the line integral of the conservative vector field F along C is approximately 14.45.

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The number of points of intersection for the graphs of the equations is infinite.

Point of intersection refers to the point at which two lines intersect on a graph. The graph of the equation refers to the visual demonstration of the equation obtained by plotting all the points of an equation on a graph. If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates.

Simplifying the given equations:

i) x/2 + 5y = 6

x + 10y = 12

ii) 3x + 30y = 36

3(x + 10y) = 36

x + 10y = 12

As the equations are equal lines, they will intersect at infinite times.

Note: The question is incomplete. The complete question probably is: How many intersections are there of the graphs of the equations below? x/2 + 5y = 6 3x + 30y = 36 none one two infinitely many

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Answer:

Maybe -10

Hope this helps :)

Let us set up some variables:

Now let us set up some equations based on the facts:

Equations:

   L = 4W     -- equation 1

   2L + 2W = 80 -- equation 2

   Plug the value of L from equation 1 into equation 2

    2(4W) + 2W = 80

     8W + 2W = 80

        10W = 80

           W = 8 -- equation 3

   Plug the value of W from equation 3 into equation 1:

    L = 4W = 4 * 8 = 32

Therefore the length is 32 and the width is 8.

Hope that helps!

Answer:

Step-by-step explanation:

1/4 of 300 is equal to 75

1/10 of 300 is equal to 30

75 + 30 = 105

300 - 105 = 195

195 cupcakes are vanilla.

195/300 = 65% of the cupcakes are vanilla

13/20 of the cupcakes are vanilla/195 cupcakes are vanilla.

Answer:

Step-by-step explanation:

c.)because it gives more options of numbers and about half the rolls is 90

Answer:

Hello,

Step-by-step explanation:

\((((x^3)+3x+2)/5)+((5x^2)/2)-(x^6)\\\\=\dfrac{x^3}{5} +\dfrac{3*x}{5} +\dfrac{2}{5} +\dfrac{5*x^2}{2} -x^6\\\\\\=-x^6+0x^5+0x^4+\dfrac{x^3}{5} +\dfrac{5*x^2}{2} +\dfrac{3*x}{5}+\dfrac{2}{5} \\\\\\a)\ \dfrac{3}{5} \\\\b)\ -1\\\\c)\\degree=6\\\)

18. ∆PQR =~ ∆RPA ( by SAS )

19. ∆DQR =~ ∆PQR ( by AAS )

20. ∆ARO =~ ∆PQO ( by AAS )

Hey there! I'm happy to help!

We have 24 total beads, and we have 6 red ones. This gives us a probability of 6/24, which simplifies to 1/4. However, we do this twice with replacement (we put the bead back, so the probability stays the same), so we multiply that probability twice to find the probability of it happening twice.

1/4×1/4=1/16

Therefore, the probability that both beads are red is 1/16.

Have a wonderful day! :D

Answer:

$3100 is invested at 9%

$4900 is invested at 11%

Step-by-step explanation:

Let's take "x" be the amount invested at 9%.

(x + 1800) is invested in another account at 11%.

The interest amount earned by the two accounts is $818.

Here we can use the simple interest formula and find the amount invested in each account.

Simple interest (I) = , where P- is the principal , N is the number of years and R is the interest rate.

Simple interest =

0.09x + 0.11(x+1800) = 818

Now we have to simplify and find the value of x .

Use the distributive property and simplify the second term.

0.09x + 0.11x + 198 = 818

0.2x + 198 = 818  

0.2x =818 - 198

0.2x = 620

x = 620/0.2

x = 3100.

So $3100 is invested at 9%

x + 1800 = 3100 + 1800

= $4900

$4900 is invested at 11%

Hope this helped.

The number of downloads of the high quality version that was made was 600.

This is a great system of equations problem

If we call the number of standard version downloads (S)  

The high quality downloads (H).

To find S, we can rearrange the first statement to H = 910 - S,

Then we would substitute (910 - S) wherever you see an H in the second equation so that you have only S's in your equation.

Thus:

2.8(S) + 4.4(910 - S) = 3044

2.8S + 4004 - 4.4S = 3044

-1.6S = -960

s = 600

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The given integral is ₁∫₀^(π/2) sin²(x)dx.

The trapezoidal rule is given by:(b - a) [(f(a) + f(b))/2]And, the Gauss-Quadrature formula for n = 2 is: ∫ᵇₐ f(x) dx = (b - a) [ w₁ f( [ (b - a)/2 ] gp₁ + (b + a)/2 ) + w₂ f( [ (b - a)/2 ] gp₂ + (b + a)/2 ) ]

Here, a = 0, b = π/2, gp₁ = -0.5773, gp₂ = 0.5773, w₁ = w₂ = 1.

(i) Trapezoidal Rule: The trapezoidal rule with one interval is given by:(b - a) [(f(a) + f(b))/2] = π/4 [sin²(0) + sin²(π/2)] = 0.7854

(ii) Gauss-Quadrature: Using the Gauss-Quadrature formula with n = 2, we get:∫ᵇₐ f(x) dx = (b - a) [ w₁ f( [ (b - a)/2 ] gp₁ + (b + a)/2 ) + w₂ f( [ (b - a)/2 ] gp₂ + (b + a)/2 ) ]= π/2 [ sin²( [ (π/2)/2 ] (-0.5773) + π/4 ) + sin²( [ (π/2)/2 ] (0.5773) + π/4 ) ]= 0.7853Comparing the above two methods, the trapezoidal rule and Gauss-Quadrature method are nearly the same and are close to the exact value.

Exact value = (π/2)/2 - sin(π)/4 = 0.7854Conclusion:Thus, it can be concluded that the given integral using the trapezoidal rule (using only one interval) and Gauss- Quadrature (n=2) is approximately equal to 0.7854.

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Answer:

Step-by-step explanation:

45 total hair bands

Answer:

B

Step-by-step explanation:

Since you have the adjacent value, the best way to do this is with tangent. You can do tan(50) = x/3. From there you multiply by 3, and get x = 3(tan50)

Answer:

Step-by-step explanation:

True.

A Data Flow Diagram (DFD) is a graphical representation of a system or a process that shows how data flows through different components of the system. It provides a visual representation of the system's inputs, processes, and outputs.

While a DFD can provide information on the data that flows between the different components of a system, it does not provide any information about the timing or sequence of those processes. A DFD is a static diagram that only depicts the flow of data in a system and does not provide any indication of when or how frequently processes occur

Answer:

see explanation

Step-by-step explanation:

If the ratios of the 3 pairs of corresponding sides of the 2 triangles are equal , then the triangles are similar (SSS postulate )

the3 ratios of the 2 triangles , left to right are all equal to

\(\frac{3}{4}\)

Then the triangles are similar by the SSS postulate

the corresponding angles of similar triangles are congruent, then

∠ c = 60°

Also both triangles have 3 congruent sides and are therefore equilateral triangles with all angles equal to 60°, so

c = 60°

Answer:

I really also need the answer

Step-by-step explanation:

Answer:

the answer is "C"

Step-by-step explanation:

i dont have time to explain im doing the test to

Step-by-step explanation:

sorry if answer is wrong

Answer:

c

Step-by-step explanation:

In 60 minutes, minute hand completes 360

0

 i.e., one rotation.

⇒ in 1 minute, minute hands completes  

60

360

∘

​

=6

∘

Hence, in 5 minutes the angle covered is is 6×5=30

o

.

The angle of sector formed is 30

o

.

The area swept by the minute hand in 5 minutes=

360

30

​

×π×14×14

Using π=

7

22

​

, we get

The area swept by the minute hand in 5 minutes =

3

154

​

 sq. cm

Answer:

Step-by-step explanation:

The distance between two points or a line segment can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4, 1) and (2, 9)

The length of segment AB is

\( |AB| = \sqrt{ ({ - 4 - 2})^{2} + ({1 - 9})^{2} } \\ = \sqrt{( { - 6})^{2} + ({ - 8})^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100} \: \: \: \: \: \: \: \: \\ = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

We have the final answer as

Hope this helps you

Answer:

The length of segment AB is 10

Step-by-step explanation:

The distance formula is d=\(\sqrt{ (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}\)

With the points (-4,1) and (2,9) you know that \(-4=x_{1}, 2=x_{2}, 1=y_{1} ,9=y_{2}\)

Now you put the numbers into the distance formula

d=\(\sqrt{(2-(-4))^{2}+(9-1)^2\)

(2-(-4) turns into (2+4) because two negatives equal a positive.

After adding and subtracting you get d=\(\sqrt{6^2+8^2\)

You then square \(6^2\) and \(8^2\) to get \(\sqrt{36+64\)

After adding 34+64 you get \(\sqrt{100\), which is 10

So the length of segment AB is 10

Answer:

20

Step-by-step explanation:

50%=10

100%=20

Answer:

20

Step-by-step explanation:

50% basically means half, so if 10 is 50% then the other 50% is also 10.

so 10x2=20

The required thickness of member BC to the nearest 1/16​ in. and the diameter of the pins at A and B is dA​= \(1\frac{1}{8}\) in

To solve thsi It is necessary to determine the thickness of BC. The allowed normal stress is σ\(_{allow\)=29 ksi and the permissible shear stress is τ\(_{allow\)=10 ksi.

In the first we will determine the reactions of the system.

We apply the conditions of equilibrium:

→+∑Fₓ=0

+↑∑F\(_y\)=0

+↺∑M=0

From picture b

∑M\(_B\)=0

⇒−2⋅8⋅4+Ay⋅8=0

⇒Ay​=8 kip

∑Fy=0

⇒−2⋅8+Ay​+By​=0

⇒−2⋅8+8+By​=0

⇒By=8 kip

From picture c)

∑M\(_C\)=0

⇒+By​⋅cos60∘−Bx​⋅sin60∘=0

⇒+8⋅cos⁡60∘−Bx⋅sin⁡60∘=0

⇒Bx=4.6188 kip

In the next step we will determine the dimensions of the BC rod:

\(\sigma BC= \frac {F_{BC}}{A_{BC}}\leq \sigma _{allow}\) =29 ksi

The cross-sectional area has a value:

\(A_{BC}=1.5.t\)

The force acting in the BC stick is calculated as follows:

\(F_{BC}=\sqrt{4.6188^2+8^2}=9.258 \ kip \\\\=\frac{9.258}{1.5.t}=29 \\\\=t=0.2128 \ in=1/4in\)

Now we can switch to determining the diameter of the pins.

Pin B:

τB=VB/AB⩽τallow=10 ksi

The cross-sectional area has a value:

AB=π/4⋅d²B

The force acting in the BB pin is calculated as follows:

VB=\(\sqrt{4.618^2+82^2\)=4.629 kip

\(\frac{4.629}{\pi/4 . d^2_B} =10\)

⇒dB​=0.767in=13/16in

Now we can switch to determining the diameter of the pins.

Pin A

τA=VA/AA⩽τallow=10 ksi

The cross-sectional area has a value:

\(A_A​=\pi/4 . d^2B\)

The force acting in the AA pin is calculated as follows:

\(V_A=4.618^2+8^2\)=9.258 ki

9.258 ÷ π/4⋅d²A=10

⇒dA​=1.0859in=\(1\frac{1}{8}\)in

The solution is:

{σs=208 MPa​}

{dB=13/16in}

{dA=\(1\frac{1}{8}\)in​}

Complete Question:

Determine the required thickness of member BC to the nearest 1/16in. and the diameter of the pins at A and B if the allowable normal stress for member BC is σ allow =29 ksi and the allowable shear stress for the pins is τ allow =10τ allow ​=10 ksi.

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The arc length of an arc with a central angle of 45° in a circle with area 289 cm2 is approximately 7.1 cm.

The formula for the area of a circle relates the radius and area of a circle. According to this equation, a circle's area is equal to times the radius squared. In other words, a circle's area grows in proportion to the square of its radius. Hence, if a circle's radius is doubled, its area will expand by a factor of four, a radius of three will result in an increase of nine, and so on. On the other hand, we may use the formula to determine the radius of a circle if we know its area.

Given that the area of the circle is 289 sq. cm.

The area of the circle is given as:

A = πr²

289 = πr²

r² = 289/π

r = √(289/π) ≈ 9.03 cm

The arc length is given as:

arc length = (central angle / 360) x 2πr

Substitute the value of central angle and radius:

arc length = (45/360) x 2π(9.03)

= (1/8) x 18.06π

= 2.2575π

≈ 7.1 cm

Hence, the arc length of an arc with a central angle of 45° in a circle with area 289 cm2 is approximately 7.1 cm.

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Answer:

AB

Step-by-step explanation:

The diameter has to pass  through the center of the circle and tough the outside of the circle on both ends

The diameters are

DE and AB

They can also be written as

ED and BA

Answer:

option A :  AB

Step-by-step explanation:

The diameter is the length of the line through the center that touches two points on the edge of the circle.

Both AB and DE are diameters.

Therefore, Option A : AB

Answer:

x=16.782

Step-by-step explanation:

a=40*

b=20

c=90*

d=40* (corner in lower right corner, we know it equals 40* because all triangles equal 180*)

e=26.108 (bottom side)

Hope this helps! BH

The equation representing the cost of a bag is 2x + 18 = $68 and for each bag Britney has to pay $25.

Let us consider  'x' be the total cost representing amount of money to check each bag under the weight limit.

Additional amount to pay per bag for over weight limit is equal to $9

Total amount paid by Britney to check both the bags = $68

Equation represents the cost of bags is equal to :

2x + 2(9) = $68

⇒ 2x + 18 = $68

⇒ 2x = $68 - $ 18

⇒ 2x = $50

⇒ x = $50 / 2

⇒ x = $25

Therefore, the equation which represents the cost of a bag is 2x + 18 = $68 and cost for each bag is $25.

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Answer:

117 and 39

Step-by-step explanation:

let x be the second number then 3x is the first number , then

3x - x = 78

2x = 78 ( divide both sides by 2 )

x = 39 and 3x = 3 × 39 = 117

The first number is 117 and the second is 39