Evaluate the following limit, if it exists : limx→0 (12xe^x−12x) / (cos(5x)−1)

Answer:

The answer is g(x) = 10x + 15

Step-by-step explanation:

Here, If we assume the value of x is 1 we get,

g(x) = 10x + 15

g(1) = 10(1) + 15

g(1) = 10 + 15

g(1) = 35

Here, We get the answer 35.

Now,

f(x) = 2•3ˣ

f(1) = 2•3¹

f(1) = 2•3

f(1) = 6

Here, We get the answer 6.

Now,

h(1) = 5x² + x + 10

h(1) = 5(1)² + 1 + 10

h(1) = + 5 + 1 + 10

h(1) = + 16

Thus, The answer is g(x) = 10x + 15.

-TheUnknownScientist 72

The approximate total volume of the two largest spheres on the Oriental Pearl Tower 113105.45 m³.

The volume of the sphere is calculated as follows:

volume = 4 / 3 πr³

where

The lower two larger spheres in the tower has a radius of 25 meters and 22.5 meters. Therefore, the total volume of the two largest sphere is as follows:

volume of lower sphere = 4 / 3 × 3.14 × 25³

volume of lower sphere = 196250 / 3

volume of lower sphere = 65416.6666667

volume of lower sphere = 65416.7 m³

volume of higher sphere = 4 / 3 × 3.14 × 22.5³

volume of higher sphere = 143066.25 / 3

volume of higher sphere = 47688.75

volume of higher sphere = 47688.8 m³

The approximate total volume = 65416.7 + 47688.8  = 113105.45 m³

learn more on sphere here: https://brainly.com/question/13833611

The area of a parallelogram is the product of:

   --> length of the base and the height

Thus the area = 7 * 5 = 35 square feet

Hope that helps!

Answer:

20.1168

Step-by-step explanation:

Step-by-step explanation:

The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions

The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)

The function increases at (-8,4).

So, we have:

4x - 3 ≥ 2 - x^2

Rewrite as:

x^2 + 4x - 2 - 3 ≥ 0

Evaluate the like terms

x^2 + 4x - 5 ≥ 0

Expand

x^2 + 5x - x - 5 ≥ 0

Factorize the expression

x(x + 5) - 1(x + 5) ≥ 0

Factor out x + 5

(x - 1)(x + 5) ≥ 0

Solve for x

x ≥ 1 or x ≥ -5

Rewrite as:

-5 ≤ x ≤ 1

Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)

The function decreases at (-∞,4).

So, we have:

5 - x^2 ≥ 3x - 5

Rewrite as:

x^2 + 3x - 5 - 5 ≤ 0

Evaluate the like terms

x^2 + 3x - 10 ≤ 0

Expand

x^2 + 5x - 2x - 10 ≤ 0

Factorize the expression

x(x + 5) - 2(x + 5) ≤ 0

Factor out x + 5

(x - 2)(x + 5) ≤ 0

Solve for x

x ≤ 2 or x ≤ -5

Rewrite as:

-5 ≤ x ≤ 2

Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

Read more about inequalities at:

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Answer:

1/27 units cubed or 0.037037... units cubed

Step-by-step explanation:

Volume of a cube = s*s*s : Where s is a side length.

The volume of the first cube is 1 cubed, which means that each side length is 1. (s=1)

The volume of the second cube in relation to the first cube can be found by multiplying each side length by 1/3.

Volume of second cube= (1/3s)(1/3s)(1/3)s

Volume of second cube= (1/3)(1/3)(1/3)

Volume of second cube= 1/27

Answer:

(-3, 0) and (1, 0)

(0, 4)

Step-by-step explanation:

x-intercept is the point where y = 0.

y-intercept is the point where x = 0.

or points ...

f(x) = y = -4×|x + 1| + 8

let's start with the y-intercept (x = 0)

y = -4×1 + 8 = -4 + 8 = 4

the y-intercept point (only 1 point) is (0, 4).

for x = 0 the absolute value function contains 0+1. and that is always +1.

the x-intercept(s) :

0 = -4×|x + 1| + 8 (dividing by -4)

0 = |x + 1| - 2

|x + 1| = 2

because of the absolute value we have 2 possibilities :

+(x + 1) = 2

x + 1 = 2

x = 1

and

-(x + 1) = 2

-x - 1 = 2

-x = 3

x = -3

so the points of x-intercept are (-3, 0) and (1, 0)

Answer:

When you subtract, the numbers decrease however when you add the numbers increase.

Step-by-step explanation: Theres the answer but is it multiple choice? if so than you can give me the choices and ill tell you the answer. But i hope this helped and if u need anything u can ask!

Answer:

3/4 ratio

Step-by-step explanation:

This is the answer

[tex] \frac{12}{16} = \frac{x}{13} [/tex]

[tex]16x = 12 \times 13[/tex]

[tex]x = \frac{12 \times 13}{16} [/tex]

[tex]x = \frac{156}{16} = 9.75[/tex]

Answer:

vertex is a point where two sides meet

Step-by-step explanation:

a volume is created (calculated) by multiplying 3 dimensions (e.g. length, width and height).

am area is created by multiplying 2 dimensions (e.g. length and width).

but a scale factor applies only to any length in the model (but then separately for every dimension of the model).

so, when we multiply 2 dimensions, we have to multiply the scale factor with every dimension (2 times) in there too.

and for 3 dimensions 3 times.

so,

1.

the scale factor 1/100 or 0.01 says that every side of the model cube is 1/100 the side length of the real cube.

and so, while the volume of the real cube is

side × side × side = 3,401,244 ft³,

the volume of the model cube is

side × 1/100 × side × 1/100 × side × 1/100 =

= side × side × side × (1/100)³ =

= real volume × 1/1,000,000 =

= 3,401,244 / 1,000,000 = 3.401244 ft³

2.

the scale factor is 3/4.

that means that it applies to length as well as to width of the floor.

so, the area of the first floor is

length × width = 1,260 ft²

and the area of the second floor is then

length × 3/4 × width × 3/4 =

= length × width × (3/4)² =

= area first floor × 9/16 = 1,260 × 9/16 = 708.75 ft²

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 78}}{\left( \cfrac{5}{100} \right)78}\implies 3.9[/tex]

Answer:

Step-by-step explanation:

Take one side length

Scale factor (A to B)

[tex]\\ \rm\rightarrowtail \dfrac{16}{12)=\dfrac{4}{3}[/tex]

Scale factor (B to A)=1/4/3=3/4

#4

Scale factor (A to B)

Scale factor (B to A)

Answer:

B. 38°

Step-by-step explanation:

The angles of a triangle add up to 180.

So, 62 + 80 + b will add up to 180.

First, we add 62 =80, which gives us 142.

The we subtract 142 from 180, which gives us 38.

Step-by-step explanation:

The y-intercept of the function is: b=10

Step-by-step explanation:

Given the table

x                 y

1                 8

2                6

3                4

4                2

Taking any two points to find the slope

(1, 8)

(2, 6)

The slope between (1, 8) and (2, 6) is:

We know that the slope-intercept form of the line equation is

where m is the slope and b is the y-intercept.

Substituting m=-2 and any point i.e. (1, 8) in the slope-intercept form of the line equation to find the y-intercept (b).

8 = -2(1) + b

8 = -2 + b

b = 8+2

b = 10

Thus, the y-intercept of the function is: b=10

Hello, it seems your questions didn't upload correctly. Are you able to resend it?

Answer: 6 out of 14 or 3 out of 7

Step-by-step explanation: just add up all the ties and put polka dot ties out of the total and

Answer:

x = 148⁰

Step-by-step explanation:

180⁰-32⁰= 148⁰

so 32⁰ angle is parallell to c angle so that means x equals to 148⁰

p and x are parallels

Answer:

The probability of Joe spinning a 1 is a 1 out of 4 chance and the probability of him flipping heads is a 50/50 chance

Step-by-step explanation:

The spinner only has 4 numbers therefore getting any number out of those four would be a 1/4th probability. As for the coin, the coin only has 2 sides so there is a 50% chance it lands on heads or a 50% chance it lands on tails.

Answer:

From top to bottom:

11π/12

-18 degrees

210 degrees

-5π/3

Step-by-step explanation:

Equation to change from radians to degrees:

(Radian number) x (180/π)

The trick is to remember that you want to cancel out the π when converting to degrees

Equation to change from Degrees to radians:

(degree number) x (π/180)

Bring in the π when converting to radians

So for the top one, you want to multiply 165 by π/180 to get

11π/12

Then the second one is -π/10 by 180/π to get

-18 degrees

and so forth

Answer:

Step-by-step explanation:

let be π=180 degrees.

165 degrees have to be 11π/12.

-π/10 will be -18 degrees.

7π/6 will be 210 degrees.

-300 degrees will be -5π/3

Answer:

y+2x=4

Step-by-step explanation:

use the formula of equation of line

The equation of line is y= 4 - 2x.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given co- ordinates:

A(-1,6) and B (3,-2)

slope = [tex](y_2 - y_1) / (x_2 - x_1)[/tex]

slope = ( -2 - 6)/ ( 3 -(-1))

slope = (-8) / (4)

slope = -2

Now, the equation of line

([tex]y-y_1) = m (x - x_1)[/tex]

(y- 6) = (-2)(x - (-1))

y-6 = (-2)(x + 1)

y-6 = -2x -2

y= 4 - 2x

Hence, the equation of line is y= 4 - 2x.

Learn more about slope here:

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Answer:

13 5/7

Step-by-step explanation:

7 can fit into 96 13 times, So 96-(7x13) is 5. 5/7 is remaining.

[tex]P= \dfrac FA \implies F = PA[/tex]

Answer:

Yes

Step-by-step explanation:

Because it has 4 sides and 4 x 2 = 8

19.6 gallons

Explanation:

Answer:

x³/3 - x² + C

Step-by-step explanation:

∫ x² - 2x + 8 dx

= x³/3 - x² + C

when finding the derivative, you need to take the power plus 1 then divide by the power x^(2+1)/(2+1) = x³/3

the same goes for 2x and the 2/2 is 1 so you would get x²

since you are finding the derivative for x and 8 is a constant it equals zero.

when integrating you always need to add C at the end and C stands for a constant. The only time you do not add C is when the integral goes from one constant to the next.

Example: [tex]\int\limits^1_0 {x^2 - 3x +9} \, dx[/tex] like this...

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

Answer:

The sum is 16 and the difference is 8 unless subtraction 12 from 4 and it would be -8.

Step-by-step explanation:

12 + 4 = 16

12- 4 = 8

4 - 12 = -8

Reflection is flipping. The x axis is the horizontal line. If you flip a shape over the x axis, it will still stay in the same area for the horizontal points, it's the vertical points that will change, but only their signs will because a reflection isn't moving a shapes location completely. Think of it like Flipping the page of a book. If you drew a triangle on your book page and flipped the page, it would still be in the same area just the opposite side/direction. Just make the y axis (second number in brackets) points the opposite sign to solve

-4,-4 0,-3. 1,1