1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vedmedyk [2.9K]
1 year ago
6

Help me asap! I will give you marks

Mathematics
1 answer:
Law Incorporation [45]1 year ago
6 0

Recall the binomial theorem.

(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k

1. The binomial expansion of \left(1+\frac x3\right)^7 is

\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}

Observe that

k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x

k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2

When we multiply these by 8-9x,

• 8 and \frac73 x^2 combine to make \frac{56}3 x^2

• -9x and \frac73 x combine to make -\frac{63}3 x^2 = -21x^2

and the sum of these terms is

\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}

2. The binomial expansion is

\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k

We get the a^6b^2 term when k=2 :

k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2

You might be interested in
Nicole works Monday through Friday and make $250 for her efforts. How much money does she make per day?
bixtya [17]

Answer:

$50 per day

Step-by-step explanation:

she works five days in week and she gets 250 bucks

250/5=50

5 0
3 years ago
I'm stuck on this. Please help!!
Sveta_85 [38]
I think it is F, but I am a not sure.
3 0
3 years ago
Read 2 more answers
As shown in the diagram of the right triangles below, Triangle: ABC ~ Triangle: DEF, AB = 7x, BC = 4, DE = 7, EF = x. What is th
charle [14.2K]

since triangles are similar

4/x = 7x/7

=》 4/x = x

=》x^2 = 4

=》 x = 2

for right triangles a^2 = b^2+c^2

DF^2 = 7^2+2^2 = 53

=》 DF = 7.28

perimeter of DEF = 7 +2+7.28 = 16.28

8 0
3 years ago
a car moves with the speed of 40 km/h for 15 minutes and then with a speed of 60 km/h for the next 5 minutes find the total dist
Gekata [30.6K]

Answer: 8

Step-by-step explanation:

Umm idk

4 0
3 years ago
Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil spe
Vadim26 [7]

Answer:

In this scenario, we will use the <u>femur or the thigh</u> bone length as the explanatory variable.

Step-by-step explanation:

Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variables in the model are changed.

The dependent variables are also known as response variables.

Independent variables are the variables that are being altered to see a proportionate change in the dependent variable. In a regression model there can be one or more than one independent variables.

The independent variables are also known as the explanatory variables.

Scientifically it is believed that the length of arm and legs are related and basically grow at the same time.

So, in this case the explanatory variable can either of the two bone lengths.

Thus, the complete statement is:

"In this scenario, we will use the <u>femur or the thigh</u> bone length as the explanatory variable."

8 0
3 years ago
Other questions:
  • Does the equation represent a direct variation? If so, find the constant of variation. 2x - 4y = 0 Question 1 options: yes; k =
    9·1 answer
  • The table below shows the heights of 6 pairs of brothers and sisters, ​labeled A through F .
    6·1 answer
  • For a population with a mean of 40 and a standard deviation of 8 find the z-score corresponding to each of the following samples
    15·1 answer
  • Two thousand seven thousands forty eight in standard form
    8·2 answers
  • Paula wants to tile her kitchen tht is 15 ft ×14 ft with 1 ft. Square tiles. How many tiles does she need?
    12·1 answer
  • What is the wavelength of a 320 Hz sound traveling 330 m/s?
    8·1 answer
  • Jill walked 2 1/3 miles to the
    12·1 answer
  • 0<br> Draw the graph of y = 3 - 0.5x
    8·1 answer
  • Math Help Part 2 (Please Help)
    7·1 answer
  • Tim drew a triangle with one angle of measure 40 degrees and the other 70 degrees. Which triangle did Tim draw?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!