(3, 5), (4, 6), (3, 8), (2, 4), (1, 3), as a mapping

If you mean

[tex]\displaystyle \lim_{x\to0^+} \frac{(1+\sin(7x))^8}x[/tex]

then the limit doesn't exist, since 1 + sin(7x) approaches 1 while the denominator approaches 0.

However, if instead you mean

[tex]\displaystyle \lim_{x\to0^+}(1+\sin(7x))^{8/x}[/tex]

rewrite the limand as

[tex](1+\sin(7x))^{8/x} = \exp\left(\ln(1+\sin(7x))^{8/x}\right) \\\\ = \exp\left(\dfrac{8\ln(1+\sin(7x))}x\right) \\\\ =\exp\left(\dfrac{\ln(1+\sin(7x))}x\right)^8[/tex]

The exponential function is continuous at 0, so we can pass the limit through it:

[tex]\displaystyle\lim_{x\to0^+}\exp\left(\dfrac{\ln(1+\sin(7x))}x\right)^8 = \exp\left(\lim_{x\to0^+}\dfrac{\ln(1+\sin(7x))}x\right)^8[/tex]

The remaining limit takes the indeterminate form 0/0, since ln(1 + sin(7x)) approaches ln(1) = 0, and so does x in the denominator. Apply L'Hopital's rule:

[tex]\displaystyle\exp\left(\lim_{x\to0^+}\dfrac{7\cos(7x)}{1+\sin(7x)}\right)^8 = \exp\left(7\right)^8 = \left(e^7\right)^8 = \boxed{e^{56}}[/tex]

Step-by-step explanation:

12 months

7 days

19 hours

Answer:

Step-by-step explanation:

Let [tex]z=r\cos \theta + i\sin \theta[/tex]

then by the Moivre

[tex]z^6 = r^6 \left( \cos \theta +i\sin \theta)^6= r^6\left(\cos (6\theta) + i\sin(6\theta)\right)[/tex]

Answer:

Step-by-step explanation:

selecting Bag |1/2

p(red from bag ||)=1/2×5/11=5/22

Area of rectangle = Length * Width

Area = 11.3 cm * 14.8 cm

Area = 167.24

Perimeter of rectangle = 2 (L + W)

Perimeter = 2 (11.3 cm + 14.8 cm)

Perimeter = 2 (26.1 cm)

Perimeter = 52.2 cm²

Area of rectangle is 167.24 cm²

Perimeter of rectangle is 52.2 cm²

Answer:

3X2 =6-y

6-y

——-

-6-y = -y squared

Step-by-step explanation:

Step-by-step explanation:

Number of Elements in Power Set - For a given set S with n elements, number of elements in P(S) is 2^n. As each element has two possibilities (present or absent), possible subsets are 2x2x2.. n times = 2^n. Therefore, power set contains 2^n elements.

This is because the fraction 1/10 turns into 0.1

Note that in 0.1, the "1" is in the tenths place to represent "one tenth".

Answer:

[tex]4( \sqrt[5]{ {x}^{2} y} ) + 3( \sqrt[5]{ {x}^{2}y } ) \\ [/tex]

factorise out the 5th root of x²y :

[tex] = \sqrt[5]{ {x}^{2}y } (4 + 3) \\ = 7( \sqrt[5]{ {x}^{2} y} )[/tex]

9514 1404 393

Answer:

  (a) the diagram is incorrect

Step-by-step explanation:

There is no overlap between the sets of rational and irrational numbers. The diagram is incorrect.

Replace k with 3 and m with 5/6

3^4 x 5/6

Simplify 3^4 which is 3 x 3 x 3 x 3= 81

Now you have :

81 x 5/6 = 67 and 1/2 ( 67.5 as a decimal)

Answer:

D. 3×2

This is ur answer ...

Answer:

58

Step-by-step explanation:

I think you add it when you add it you get 58. You add the angles

Answer:

your answer is 70.

Step-by-step explanation:

mean=Efx/n=1050/15=70

Formula-

If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}

Symbol that can be used-

The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".

Hope it helps you... pls mark brainliest if it helped you.

Answer:

-6 + 4 = -2

Step-by-step explanation:

Just start from -6 then go to the right four places and you'll get -2

Answer:

Step-by-step explanation:

L = w + 10

w = w

P = 2w + 2L

P = 80 m

2L + 2w = 80                      Substitute for L

2(w + 10) + 2w = 80           Remove the brackets

2w + 20 + 2w = 80           Combine on the left

4w + 20 = 80                     Subtract 20 from both sides

4w = 80 - 20

4w = 60                              Divide by 4

w = 60/4

w = 15

L = 15 + 10 = 25

Check

2*25 + 2*15

50 + 30

80

So this checks

it is under mapping and function

f of x is equal to -2 root x-7 plus one

v=t^2-8t+15

[tex]\boxed{\sf {\displaystyle{\int}^b_a}x^ndx=\left[\dfrac{x^{n+1}}{n+1}\right]^b_a}[/tex]

[tex]\\ \sf\longmapsto s={\displaystyle{\int}}vdt[/tex]

[tex]\\ \sf\longmapsto s={\displaystyle{\int^4_2}}t^2-8t+15[/tex]

[tex]\\ \sf\longmapsto s=\left[\dfrac{t^3}{3}-8\dfrac{t^2}{2}+15t\right]^4_2[/tex]

[tex]\\ \sf\longmapsto s=\left[\dfrac{t^3}{3}-4t^2+15t\right]^4_2[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{4^3}{3}-4(4)^2+15(4)\right)-\left(\dfrac{2^3}{3}-4(2)^2+15(2)\right)[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{64}{3}-64+60\right)-\left(\dfrac{8}{3}-16+30\right)[/tex]

[tex]\\ \sf\longmapsto s=\left(\dfrac{64}{3}-4\right)-\left(\dfrac{8}{3}+14\right)[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{64}{3}-4-\dfrac{8}{3}-14[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{64}{3}-\dfrac{8}{3}-4-14[/tex]

[tex]\\ \sf\longmapsto s=\dfrac{46}{3}-18[/tex]

[tex]\\ \sf\longmapsto s=15.3-18[/tex]

[tex]\\ \sf\longmapsto s=|-2.7|[/tex]

[tex]\\ \sf\longmapsto s=2.7km[/tex]

Answer:

-20

Step-by-step explanation:

Since we are adding two negative integers, we can write it as -16 - 4 to make it easier.

-16 - 4 = -20

Best of Luck!

Answer:

0.91 (make sure to include unit of measurement)

Step-by-step explanation:

10.49 - 9.58 = 0.91

Answer:

Given [tex]f(x)=2x^3+4[/tex], the average rate of change of [tex]f[/tex] on the interval [tex][4,6][/tex] is [tex]152[/tex]

Step-by-step explanation:

Applying the average rate of change formula, we find[tex]\frac{f(6)-f(4)}{6-4}=\frac{2\cdot6^3+4-2\cdot4^3-4}2=\frac{432-128}2=\frac{304}2=152[/tex]

Answer:

you go this! i ant expain but its mostly false and rue but sorry

Step-by-step explanation:

1 : you would use a graduated cylinder . 2 : , you would use a yard stick or maybe a ruler if you are not able to find one. You can also use a meter stick.

Answer:

1.309

Step-by-step explanation:

75° =the radian of 1.309

hope it's right have a great day!

Answer:

[tex] \frac{5 {\pi}^{c} }{12} [/tex]

Step-by-step explanation:

Radian measure of 75°

[tex] = 75 \times \frac{ {\pi}^{c} }{180 \degree} \\ \\ = \frac{5 {\pi}^{c} }{12} [/tex]

Answer: y = 8, x =5

Step-by-step explanation:

x+y = 13

or, x = 13-y

so

2x - y = 2

substituting x's value

2(13-y)-y = 2

or, 26-2y-y = 2

or, 26-3y=2

or, 26-2 = 3y

or, 24  = 3y

so, y = 8

now

x = 13-y

so, x = 13-8 = 5

Answer:

[tex]\$\ 6400[/tex]

Step-by-step explanation:

1. Approach

The easiest way to solve this problem is to find the area of the first room with the dimensions of (12ft) by (14ft). Then one will divide the cost of carpeting the room by the area of the room, this will yield the price of carpeting per square foot. After finding the price of carpeting per square foot, one will find the area of the second room, with the dimensions of (48ft) by (56ft). Finally, one will multiply the price per square foot of carpeting by the area of the second room to find the price for carpeting the second room.

2. Find the area of the first room

Assume that the first room is a rectangle. the following formula can be used to find the area of a rectangle,

[tex](length)(width)=Area[/tex]

The following are the dimensions of the given room,

[tex]length = 14\\width = 12[/tex]

Substitute into the formula to find the area and simplify to solve,

[tex](length)(width)=Area[/tex]

[tex](14)(12)=Area_1[/tex]

[tex]168=Area_1[/tex]

3. Find the price of carpeting per square foot

To find the price of carpeting per square foot, divide the total price for carpeting the first room by the area of the first room.

[tex]\frac{carpeting\ price_1}{area_1}[/tex]

[tex]=\frac{400}{168}[/tex]

Simplify,

[tex]=\frac{400}{168}[/tex]

[tex]=\frac{50}{21}[/tex]

4. FInd the area of the second room

Assume that the second room is also a rectangle. Use a similar strategy to find the area of this room as used for the area of the first room.

[tex](length)(width)=Area[/tex]

[tex]length = 48\\width = 56[/tex]

Substitute and simplify to sovle,

[tex](length)(width)=Area[/tex]

[tex](48)(56)=Area_2[/tex]

[tex]2688=Area_2[/tex]

5. Find the price for carpeting the room

Multiply the area of the room by the price for carpeting per square foot to find the price for carpeting the second room.

[tex](Area_2)*(carpeting\ price)[/tex]

[tex]2688=Area_2[/tex]

[tex]\frac{50}{21}=carpeting\ price[/tex]

[tex](Area_2)*(carpeting\ price)[/tex]

[tex]=(2688)*(\frac{50}{21})[/tex]

Simplify to solve,

[tex]=(2688)*(\frac{50}{21})[/tex]

[tex]=(2688)*(\frac{50}{21})[/tex]

[tex]=6400[/tex]

Answer:

A positive number.

Step-by-step explanation:

Absolute value means that no matter if the number is positive or negative, it will always be positive, e.g. | -4 | would be 4 or | 4 | would also be 4.

Answer:

Washington had 115 hits and Sanchez had 111 hits.

Step-by-step explanation:

2s + 4 = 226

2s = 222

s = 111

s + 4 = 115