Integrate with respect to x

3√(2-5x)

Answer:

a = - [tex]\frac{9}{2}[/tex] , b = - [tex]\frac{25}{4}[/tex]

Step-by-step explanation:

To obtain the required form use the method of completing the square

add/ subtract ( half the coefficient of the x- term)² to x² - 9x

y = x² + 2(- [tex]\frac{9}{2}[/tex] )x + [tex]\frac{81}{4}[/tex] - [tex]\frac{81}{4}[/tex] + 14

  = (x - [tex]\frac{9}{2}[/tex] )² - [tex]\frac{81}{4}[/tex] + [tex]\frac{56}{4}[/tex]

  = (x - [tex]\frac{9}{2}[/tex] )²- [tex]\frac{25}{4}[/tex] ← in the form (x + a)² + b

with a = - [tex]\frac{9}{2}[/tex] and b = - [tex]\frac{25}{4}[/tex]

Answer:

a = 4.5

b = -6.25

Step-by-step explanation:

The given equation to us is ,

[tex]\implies y = x {}^{2} - 9x + 14[/tex]

And its given that it can we written in the form of ,

[tex]\implies (x + a) {}^{2} + b[/tex]

Where ,

Therefore ,

[tex]\implies y = x^2 -9x + 14 [/tex]

Multiplying 9x by 2/2 ,we have ,

[tex]\implies y = x^2 -\dfrac{2}{2}\times 9 x + 14 [/tex]

Adding and subtracting (9/2)² ,

[tex]\implies y = \bigg\{ x^2 -\dfrac{2}{2}\times 9 x + \bigg(\dfrac{9}{2}\bigg)^2 \bigg\} +14 -\bigg(\dfrac{9}{2}\bigg)^2[/tex]

Therefore , we can write it as ,

[tex]\implies y = \bigg( x + \dfrac{9}{2}\bigg)^2 + 14 - 20.25 \\\\\implies \underline{\underline{ y = \bigg( x + \dfrac{9}{2}\bigg)^2 - 6.25 }}[/tex]

Hence the value of a is 9/2 and b is -6.25 .

Answer:

C.

Step-by-step explanation:

i guess it's letter c. y=50

Answer:

[tex] \frac{ - 81}{9} [/tex]

[tex] - 9[/tex]

Answer:

3ft and 24 ft.

Step-by-step explanation:

The longer piece is 8 times as long as shorter piece

therefore,

Total length of the wooden board = 27 ft.

27 = longer length + shorter length

27 = x + 8x

27 = 9x

dividing both sided by 9

3 = x

since x was the length of the shorter piece

shorter piece is 3 ft. long

and the longer piece was equal to 8x

longer piece is 24 ft. long

[tex]\large {\text {$ \sf \cfrac{1}{2x^2} -2 = 0 $}}[/tex]

[tex]\large {\text {$ \sf \cfrac{1}{2x^2}\cdot \:2x^2-2\cdot \:2x^2=0\cdot \:2x^2 $}[/tex]

                 [tex]\searrow[/tex]

                     [tex]\large {\text {$ \sf 1-4x^2=0$}}[/tex]

[tex]\large {\text {$ \sf -4x^2+1 = 0 $}}[/tex]

[tex]\large {\text{$\sf x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2a} \quad\rightarrow\quad x=\cfrac{-0\pm\sqrt{0^2-4\cdot (-4) \cdot1} }{2\cdot (-4) } \:\rightarrow\:\: x=\cfrac{-0^2 \pm4}{2 \cdot(-4)} $}}[/tex]  

                                                             [tex]\huge {\text {$ \sf \downarrow$}}[/tex]

           [tex]\large {\text {$\sf {\bf x_1} = \cfrac{-0+4}{2\left(-4\right)}= \cfrac{-1}{2} $}}[/tex]                        [tex]\large {\text {$\sf {\bf x_2 }=\cfrac{-0-4}{2\left(-4\right)} = \cfrac{1}{2} $}}[/tex]

[tex]\large {\boxed {\boxed { \bf x_1 + x_2= -\cfrac{1}{2}+ \cfrac{1}{2} = 0} }}[/tex]

                                           [tex]\huge {\text {$ \it Alternative \: A $}}[/tex]

Answer:

y = -4/3 x - 1/3

Step-by-step explanation:

y = -4/3 x + b

5 = -4/3 (-4) + b

15 = 16 + 3b

b = -1/3

y = -4/3 x - 1/3

The equation of line b, parallel to line a and passing through the point (-4,5), is y = (3/4)x + 8.

To find the equation of line b, which is parallel to line a and passes through the point (-4,5), we need to use the fact that parallel lines have the same slope.

Given that line a has the equation y = (3/4)x - 3, we can determine its slope. The slope of line a is the coefficient of x, which is 3/4.

Since line b is parallel to line a, it will also have a slope of 3/4.

Using the slope-intercept form of a linear equation (y = mx + b), we can substitute the slope and the coordinates (-4,5) into the equation to solve for the y-intercept, b.

5 = (3/4)(-4) + b

Simplifying, we have:

5 = -3 + b

Adding 3 to both sides, we find:

b = 8

Therefore, the equation of line b, parallel to line a and passing through the point (-4,5), is y = (3/4)x + 8.

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Answer:

40 degrees

Step-by-step explanation:

The 100 degree angle is supplementary to angle CED. This means CED will end up being 80 degrees. Since the angles in all triangles equate to 180 degrees 80 + 60 + angle D must equal 180 degrees. Therefore, angle D has to be 40 degrees.

Answer:

2/3 ÷ 8/9

[tex] \frac{2}{3} \div \frac{8}{9} [/tex]

[tex] \frac{2}{3} \times \frac{9}{8} [/tex]

[tex] \frac{1}{1} \times \frac{3}{4} [/tex]

[tex] \frac{3}{4} [/tex]

hope this will help you more

Answer:

check footprints and then check finger print the finger print pour powder on it and Trace

Answer:

x = -4.5

Step-by-step explanation:

Given:

0.1x + 0.008 = 0.06x − 0.172

Collect like terms

0.1x - 0.06x = -0.172 - 0.008

0.04x = - 0.18

x = -0.18/0.04

x = -4.5

Check:

0.1x + 0.008 = 0.06x − 0.172

0.1(-4.5) + 0.008 = 0.06(-4.5) - 0.172

- 0.45 + 0.008 = -0.27 - 0.172

-0.442 = -0.442

Answer:

107,100

Step-by-step explanation:

[tex]h(t) = 9 {t}^{2} + 900t \\ \\ plug \: t = 70 \\ \\ h(70) = 9 {(70)}^{2} + 900(70) \\ = 9 \times 4900 + 63000 \\ = 44100 + 63000 \\ = 107,100 \: cm[/tex]

Answer:

Um

Step-by-step explanation:

Its half of diameter

Are you thinking of circumference and area?

Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Here you have to use the Pythagorean Theorem.

Pythagorean Theorem: a^2 + b^2 = c^2

STEP 1: Define your variables

a and b are the legs of the triangle, and c is the hypotenuse

a = 7

b = x

c = 9

STEP 2: Plug the variable into the equation

7^2 + x^2 = 9^2

STEP 3: Solve

7^2 + x^2 = 9^2

49 + x^2 = 81

49 - 49 + x^2 = 81 - 49

[tex]\sqrt{x}[/tex]^2 = [tex]\sqrt{32}[/tex]

x = [tex]\sqrt{32}[/tex]

STEP 4: Simplify

Since the questions asks you to put it in simplified radical form, you do not have to approximate the answer, but you do have to simplify the radical.

x = [tex]\sqrt{32}[/tex]

x = [tex]\sqrt{16}[/tex] * [tex]\sqrt{2}[/tex]

x = 4[tex]\sqrt{2}[/tex]

Hope this helps

Answer:

8 inches

Step-by-step explanation:

Given:

t = 2 ( 2h/32 ) ^1/2 ( or: t = 2 * sqrt ( 2h/32) ).

Step 1: First Player

0.9 = 2 * sqrt( 2h/32 )   / ^2 ( we will square both sides of equation )

0.81 = 4* 2h/32

0.81 = h/4

h 1 = 0.81 * 4 = 3.24 ft

Step 2: Second Player

0.8 = 2 * sqrt( 2h/32 ) /^2

0.64 = 4 * 2 h/32

h 2 = 0.64 * 4 = 2.56 ft

Step 3: Simplify

h 2 - h 1 = 3.24 - 2.56 = 0.68 ft

and since 12 in = 1 ft:

0.68 * 12 = 8.16 in ≈ 8 in.

Hi there!

[tex]\large\boxed{\text{ B. 2}}[/tex]

f(x) = 2x + 6

Differentiating 2x = 2 (Power rule, dy/dx xⁿ =  nxⁿ⁻¹)

Differentiating a constant always equals 0.

Thus:

f'(x) = 2

Answer:

D. Square

Step-by-step explanation:

A square is a regular tessellation because a regular tessellation is a pattern made up of only one single shape placed in some kind of pattern.

Answer:

12x36

Step-by-step explanation:

Answer:

36*12 = 432

Step-by-step explanation:

Answer:

it will be 50°

Step-by-step explanation:

I'll give you some of the other answers to see if you get it:

m <1 : 180-50 =130

m <5: 180

m <4: 180

m<7: 50

Step-by-step explanation:

I'm not good at geometry but I was trying to explain that you need to follow all your rules at geometry so that you canget your answer right

hello what I can say to you is that you need to follow the rules whereby they say the corresponding angles to the exterior angles then make sure that you follow all the rules that straight line add up into 180 degrees say for example a is equal to b

Answer:

-7x and -2x

Step-by-step explanation:

because -7x and -2x are on the same side of the equation. the equal sign in the equation, -7x+12-2x = 23+13x is basically a different way of writing -7x+12-2x and 23+13x.

they're kind of like 2 separate equations. hope this helped! :)

Answer:

Step-by-step explanation:

volume =triangular area× length

=1/2×6×3×14

=126 ft³

Answer:

About 126 ft cubed

Answer:

110x -200y

Step-by-step explanation:

10(x - 20y) + 100x

Distribute

10x-200y +100x

Combine like terms

110x -200y

Answer:

110x−200y

Step-by-Step Explanation:

Given:

10(x−20y)+100x

First Step: Distribute

(10)(x)+(10)(−20y)+100x

10x+−200y+100x

Second Step: Combine Like Terms:

10x+−200y+100x

(10x+100x)+(−200y)

110x+−200y

Answer:

=110x−200y

Answer:

I think you are being asked to evaluate the square root of 298116 by division method. Here is how its done:

546

51298116

125

104 81 10416

10861 0 0 6516 1006516

Please feel free to ask if something is not clear.

Here are the steps you will need to follow:

Step 1:

We find the largest square smaller than 29, that's 25. Subtract the 25 from the 29, which leaves 4, and enter a 5 as the first digit of your quotient.

Step 2:

104

=============================================

Explanation:

The volume of a cylinder formula is

V = pi*r^2*h

where r is the radius and h is the height.

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

For the first cylinder, we have r = 2 and h = 7. This leads us to...

V = pi*r^2*h

V = pi*2^2*7

V = pi*4*7

V = pi*28

V = 28pi

This is the exact volume in terms of pi.

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

Repeat those steps for the other cylinder (r = 2 and h = 28)

V = pi*r^2*h

V = pi*2^2*28

V = pi*4*28

V = 112pi

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

To recap so far, we have these two cylinder volumes:

We see that cylinder B has the larger volume (since 112 > 28).

The ratio of the volumes from larger to smaller is 112pi : 28pi

Divide both parts by pi to have those terms cancel and we get the ratio 112:28

Lastly, we divide each part by the GCF 28

112/28 = 4

28/28 = 1

Therefore, the ratio 112:28 fully reduces to 4:1 which makes the final answer choice A.

The larger volume is 4 times that of the smaller volume.

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

A fairly quick way to see why we get this ratio is to notice the smaller height h = 7 jumps to the larger height h = 28 by a factor of 4.

In other words,

larger height = 4*(smaller height)

28 = 4*7

The fact that the radius is kept the same at r = 2 won't have an effect on the volume ratio. These parts effectively cancel out.

So this jump of "times 4" directly connects to the ratio 4:1

We multiplied the height by 4, so the volume is also multiplied by 4 (when going from the smaller cylinder to the larger one).

Answer:

false

Step-by-step explanation:

Answer: Associative Property of Addition

This property says that we can group terms in any order we want, and the results of the addition would be the same.

For example, 2+(3+4) = 2+(7) = 2+7 = 9 and (2+3)+4 = (5)+4 = 5+4 = 9. Therefore, 2+(3+4) = (2+3)+4 is a true equation since both sides evaluate to 9.

This property works not only for rational numbers, but for any real numbers.

Answer:

7/50 = x/75

x = 10.5

therefore he would run 10.5 miles in 75 minutes

Answer:

In 75 minutes, she runs (7/50) x 75 = 10.5.

She runs 10.5 miles in 75 minutes.

Step-by-step explanation:

Answer:

4. 87.96 yd

5. 47.12 ft

6. 34.56 cm

Step-by-step explanation:

4. diameter(d) = 28 yd,

perimeter = πd = 87.96 yd (rounded to 2 dp)

5. radius(r) = 7.5 ft

perimeter = 2πr = 47.12 ft (rounded to 2 dp)

6. diameter (d) = 11 cm

perimeter = πd = 34.56 cm

Answered by GAUTHMATH

Formula to find the perimeter of a semicircular region:

if radius given: [tex]P=2r[/tex] +  [tex]\pi r[/tex]  {r = radius}

if diameter given: [tex]P=d+\pi r[/tex] {d = diameter}

Take [tex]\pi[/tex] as 3.14

Q4.

Diameter = 28 yd

Radius = 28/2 = 14 yd

[tex]P=28+\pi (14)[/tex]

[tex]P=28+(3.14)(14)[/tex]

[tex]P=28+14.96[/tex]

[tex]P=42.96[/tex] yd

Q5.

Radius = 7.5 ft

Diameter = 7.5 × 2 = 15 ft

[tex]P=2(7.5)+\pi (7.5)[/tex]

[tex]P=2(7.5)+(3.14)(7.5)[/tex]

[tex]P=15+23.55[/tex]

[tex]P=38.55[/tex] ft

Q6.

Diameter = 11 cm

Radius = 11/2 = 5.5 cm

[tex]P=11+\pi (5.5)[/tex]

[tex]P=11+(3.14)(5.5)[/tex]

[tex]P=11+17.27[/tex]

[tex]P=17.27[/tex] cm

I hope this helps...

Have a great day ahead :)

Answer: 216cm2

Step-by-step explanation: 36x6

Answer:

Increasing

Step-by-step explanation:

Decreasing means that its moving down (from the right) and Increasing means that its moving up (from the right), while constand means that it goes in a straight line.

Since it is moving up from the right, that means it's increasing.

The slope is positive, then the graph is increasing. Then the correct option is A.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The graph is given below.

The line is passing through origin.

At x = 1, the value of y will be 3.

Then the slope will be

m = 3 / 1

m = 1

Then the equation of line will be

y = 3x

The slope is positive.

Then the graph is increasing.

Then the correct option is A.

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