Estimate the area under the graph of f(x)=1/x+4 over the interval [-1,2] using four approximating rectangles and right endpoints.

Answer:

(A)  (-19,-8)

Step-by-step explanation:

Given that the graph is an inverse variation.

The equation of variation is:

[tex]x=\dfrac{k}{y}[/tex]

Since point (-8, -19) is on the graph

[tex]-8=\dfrac{k}{-19}\\k=152[/tex]

Therefore, the equation connecting x and y is:

[tex]x=\dfrac{152}{y}[/tex]

[tex]\text{When y=-8},x=\dfrac{152}{-8}=-19\\\\\text{When y=19},x=\dfrac{152}{19}=8\\\\\text{When y=8},x=\dfrac{152}{8}=19\\\\\text{When y=-19},x=\dfrac{152}{-19}=-8[/tex]

Therefore, the point that is also on the graph is:

(A)  (-19,-8)

Answer:

Hey there! Your answer would be:  [tex]3x^2+4=x[/tex]

The quadratic formula is (-b±√(b²-4ac))/(2a), and helps us find roots to a quadratic equation.

All quadratic equations can be written in the [tex]ax^2+bx+c[/tex] form, and a, b, and c, are numbers we need for the quadratic equation.

Our given quadratic equation is 1±√(-1)²-4(3)(4)/2(3)

We can see that b is -1, as -b is positive 1.

That gives us  [tex]ax^2+-1x+c[/tex], which can be simplified to [tex]ax^2-x+c[/tex].

We can see that a is 3, because 2a=6, so a has to be 3.

That gives us [tex]3x^2-x+c[/tex]

Finally, we see that 4 is equal to b, clearly shown in the numerator of this fraction.

Which gives us a final answer of [tex]3x^2-x+4[/tex], or [tex]3x^2+4=x[/tex]

Answer:

D

Step-by-step explanation:

Answer:

Vertical Line

Step-by-step explanation:

A vertical line is x = [a number]

A horizontal line is y = [a number]

Answer:

vertical line

Step-by-step explanation:

A vertical line is of the form

x =

All the x values are the same and the y value changes

x = -4 is a vertical line

Answer:

30 m^3

Step-by-step explanation:

Answer:

B. 20m3

Step-by-step explanation:

i dont know if its correct, hope it is tho

Answer:

2

Step-by-step explanation:

5÷2 1/5 = 2

Answer:

2 3/11

Step-by-step explanation:

To find the original number, we need to divide 5 by 2 1/5.

5/ 2 1/5

Convert 2 1/5 to an improper fraction:

11/5

5/ 11/5

When dividing fractions, we can multiply the first number by the reciprocal of the second one to get the answer.

5*5/11

25/11

2 3/11

Answer:

B. 0.220

Step-by-step explanation:

The table is presented properly below:

[tex]\left|\begin{array}{c|cccc|c}$toppings&$Freshman&$Sophomore&$Junior&$Senior&$Total\\---&---&---&---&---&---\\$Cheese&11&15&24&28&78\\$Meat&23&28&15&11&77\\$Veggie&15&11&23&28&77\\---&---&---&---&---&---\\$Total&&&&&232\end{array}\right|[/tex]

Number of junior students who prefers veggies =23

Number of senior students who prefers veggies =28

Total =23+28=51

Therefore, the probability that a randomly selected student who is a junior or senior prefers veggie

=51/232

=0.220 (to the nearest thousandth)

The correct option is B.

Answer:

198.5

Step-by-step explanation:

() = 200 - 1.5

() = 198.5

im not sure if this is what you are asking, but i hope it helps

Answer:

S=p(200-1.5)  

Complete Question:

Find the directional derivative of g(x,y) = [tex]x^2y^5[/tex]at the point (1, 3) in the direction toward the point (3, 1)

Answer:

Directional derivative at point (1,3),  [tex]D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Step-by-step explanation:

Get [tex]g'_x[/tex] and [tex]g'_y[/tex] at the point (1, 3)

g(x,y) = [tex]x^2y^5[/tex]

[tex]g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486[/tex]

[tex]g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405[/tex]

Let P =  (1, 3) and Q = (3, 1)

Find the unit vector of PQ,

[tex]u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\[/tex]

[tex]|\bar{PQ}| = \sqrt{8}[/tex]

The unit vector is therefore:

[tex]u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }[/tex]

The directional derivative of g is given by the equation:

[tex]D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Answer:

Step-by-step explanation:

Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;

[tex]y = f(x_0) + f'(x_0)(x-x_0)[/tex]

[tex]x_n = x_n_-_1 - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}[/tex]

If [tex]x_0 = 1\\[/tex]

We will iterate using the formula;

[tex]x_1 = x_0 - \frac{f(x_0 )}{f'(x_0 )}[/tex]

Given f(x) = x³ + 5x +2

f(x0) = f(-1) = (-1)³ + 5(-1) +2

f(-1) = -1 -5 +2

f(-1) = -4

f'(x) = 3x²+5

f'(-1) = 3(-1)²+5

f'(-1) = 8

[tex]x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}[/tex]

f(-0.5) = (-0.5)³ + 5(-0.5) +2

f(-0.5) = -0.125-2.5+2

f(-0.5) = -0.625

f'(-0.5) = 3(-0.5)²+5

f'(-0.5) = 3(0.25)+5

f'(-0.5) = 0.75+5

f'(-0.5) = 5.75

[tex]x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913[/tex]

The estimated solution is -0.3913 (to 4dp)

Answer:

The value will decrease.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

JN* NK = LN * NM

3x = 2*6

3x = 12

Divide by 3

3x/3 =12/3

x =4

Answer:

  B

Step-by-step explanation:

You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).

The shading is below the line because y-values are less than (or equal to) values on the line.

Choice B matches the attached graph.

Answer:

it is graph b

Step-by-step explanation:

Answer:

given,

AB= 17

AC= 8

angle BCA =90°

as it is a Right angled triangle ,

taking reference angle BAC

we get,h=AB=17

b=AC=8

p=BC=?

now by the Pythagoras theorem we get,

p=

[tex] \sqrt{h { }^{2} - b {}^{2} } [/tex]

so,p=

[tex] \sqrt{17 {}^{2} - 8 {}^{2} } [/tex]

[tex] = \sqrt{225} [/tex]

=15 is the answer....

hope its wht u r searching for....

Answer:

6

Step-by-step explanation:

We want to find the units digit of [tex]2^{4000}[/tex]. Let's first look for a pattern:

[tex]2^{1}=2[/tex]

[tex]2^{2}=4[/tex]

[tex]2^{3}=8[/tex]

[tex]2^{4}=16[/tex]

[tex]2^{5}=32[/tex]

[tex]2^{6}=64[/tex]

[tex]2^{7}=128[/tex]

[tex]2^{8}=256[/tex]

...and so on

Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!

This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.

The answer is thus 6.

~ an aesthetics lover

Answer:

The price of one reusable bottle is $8.12

Step-by-steetp explanation:

Ms stone wanted to purchase two reusable bottles but discovered she had only ⅝of the Mone and that ⅝ is equal to $ 10.15.

So the cost of what she wants to purchase will be called x.

Mathematically

⅝ * x = 10.15

X = (10.15*8)/5

X = 81.2/5

X= 16.24

The price of the two bottles is $16.24

So the price if one bottle will be calculated as follows.

2 bottles=$ 16.24

One bottle= $16.24/2

One bottle= $8.12

The price of one reusable bottle is $8.12

Answer: Volume = [tex]\frac{20\pi }{3}[/tex]

Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be

V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]

For this case, the region generated by the conditions proposed above is shown in the attachment.

Because it is revolting around the y-axis, the formula will be:

[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]

Since it is given points, first find the function for points (3,2) and (1,0):

m = [tex]\frac{2-0}{3-1}[/tex] = 1

[tex]y-y_{0} = m(x-x_{0})[/tex]

y - 0 = 1(x-1)

y = x - 1

As it is rotating around y:

x = y + 1

This is R(y).

r(y) = 1, the lower limit of the region.

The volume will be calculated as:

[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]

[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]

[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]

[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]

[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]

[tex]V=\frac{20\pi }{3}[/tex]

The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].

Answer:

$41,330

Step-by-step explanation:

To find the cost to asphalt a circular path, first, calculate the area of the circular path:

Area of circular path = area of big circle (A1) - Area of small circle (A2)

Area of circle = πr²

Radius of big circle (R) = 145 ft

Area of big circle (A1) = 3.14*145²

= 3.14*21,025

A1 = 66,018.5 ft²

Radius of small circle (r) = 80ft

Area of small circle (A2) = 3.14*80²

= 3.14*6,400

A2 = 20,096 ft²

=>Area of path =  66,018.5 - 20,096 = 45,922.5 ft²

If 100ft = $90

45,922.5 ft = x

Cross multiply and find x (cost to asphalt the circular path)

100*x = 45,922.5*90

100x = 4,133,025

Divide both sides by 100

x = 4,133,025/100

x = $41,330.25

To the nearest dollar, $41,330 is needed to asphalt the circular path

Answer:

A pair of vertical angles are ADE and BDC. Vertical angles are located across from each other.

Answer:

D. Angle ADE and angle BDC

Step-by-step explanation:

Vertically opposite angles are equal.

Angle ADE and angle BDC are a pair of vertical angles.

Answer:

  y

Step-by-step explanation:

The expression

  y = f(x)

tells you that y is the dependent variable, and that it depends on x, the independent variable. The independent variable is always the function argument. Any variable that depends on that is the dependent variable.

Hey there! :)

Answer:

C. (0, -6).

Step-by-step explanation:

In slope-intercept form ( y = mx + b), the 'b' value represents the y-intercept.

In this instance:

y = 4x - 6

The 'b' value is equal to -6. This means that the y-intercept is at (0, -6).

-------------------------------------------------------------------------------------------

The y-intercept can also be solved for by substituting in 0 for x:

y = 4(0) - 6

y = 0 - 6

y = -6.

Answer:

C. (0, –6)

Step-by-step explanation:

y = 4x - 6

The equation is:

y = mx + b

where b is the y-intercept.

In this case, - 6 is the vertical intercept.

Do not confuse from (-6, 0) because that represents an x-intercept.

Answer:

x=4200, y=2700

Step-by-step explanation:

let x be first account

y the second

x+y=6900

0.03x+0.08y=342

solve by addition/elimination)

multiply first equation by 0.03

0.03x+0.03y=207  subtract from second

0.03x+0.03y-0.03x-0.08y=207-342

0.05y=135

y=2700, x=4200

Answer:

(a) remainder is -40

(b) The remaining zeroes are (x+3) and (x-3)

Step-by-step explanation:

p(x) = x^4 - 2x^3 -7x^2 + 18x – 18

(a) Remainder of P(x) / (x+1) can be found using the remainder theorem, namely

let x + 1 = 0 => x = -1

remainder

= P(-1)

= (-1)^4 - 2(-1)^3 -7(-1)^2 + 18(-1) – 18

= 1 +2 -7-18-18

= -40

remainder is -40

(b)

If one zero is 1-i, then the conjugate 1+i is another zero.

in other words,

(x-1+i) and (x-1-i) are both factors.

whose product = (x^2-2x+2)

Divide p(x) by (x^2-2x+2) gives

p(x) by (x^2-2x+2)

= (x^4 - 2x^3 -7x^2 + 18x – 18) / (x^2-2x+2)

= x^2 -9

= (x+3) * (x-3)

The remaining zeroes are (x+3) and (x-3)

Answer:

173.20 ft

Step-by-step explanation:

[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]

Answer:

C. 44 °

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

180 - 88 = 92

Angles in a triangle add up to 180 degrees.

y + y + 92 = 180

y + y = 88

2y = 88

y = 88/2

y = 44

Answer:

The answer is 46"

Step-by-step explanation:

A triangle is 180 degrees

so u already know one side

180"-88" is 92

then divide 92 by 2 which is 46

Answer: 46"

Answer:

  8 : 1

Step-by-step explanation:

The graph shows a point at the location corresponding to 8 cups of raspberry juice and 1 cup of lemon-lime soda. So the ratio is ...

  raspberry juice : lemon-lime soda = 8 : 1

Answer:

D

Step-by-step explanation:

raspberry : lemon lime soda::8:1

Answer:

[tex]f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }\\[/tex]

Step-by-step explanation:

[tex]1/u=1/f-1/v\\\frac{1}{f} = \frac{1}{u} +\frac{1}{v}\\Divide- both- sides- by; 1\\\frac{1}{f} \div \frac{1}{1} = ( \frac{1}{u} +\frac{1}{v}) \div \frac{1}{1}\\\\f = \frac{1}{\frac{1}{u}+ \frac{1}{v} }[/tex]

The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.

This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.

a(n) = a(1) + d( n- 1)

d = 3

This is the formula of an arithmetic sequence.

an = a(1) + d( n- 1)

Substitute in the values of

a(1) = 7 and

d = 3

a(n) = 7 + 3 ( n- 1)

Simplify each term.

a(n) = 7 + 3n- 3

Subtract 3 from 7.

a(n) =  3n + 4

The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.

Substitute in the value of n to find the nth term.

a(55) = 3 (55) + 4

Multiply 3 by 55 .

a(55) = 165 + 4

Add 165 and 4.

a(55) = 169

Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.

To learn more about Aritmetic sequence

https://brainly.com/question/6561461

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Answer:

Area = 40×20

=800Step-by-step explanation:

Answer:

B) [tex]x^2-3x+15[/tex]

Step-by-step explanation:

[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]

A) [tex]x^2+15x+15[/tex]

B) [tex]x^2-3x+15[/tex]

C) [tex]13x^2 + 3x + 15[/tex]

D) [tex]x^4-3x + 15[/tex]

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▹ Answer

B. x² - 3x + 15

▹ Step-by-Step Explanation

7x² + 6x - 9x - 6x² + 15

Collect like terms

x² + 6x - 9x + 15

Subtract

x² - 3x + 15

Final Answer

x² - 3x + 15

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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