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kap26 [50]
3 years ago
8

Ling's elementary school principal wants to hire some new teachers. 6 teachers applied for one 1st grade teaching job, and 3 tea

chers applied for one 2nd grade teaching job. There is also a job opening for a 3rd grade teacher, and 3 teachers applied for the job. How many different ways can Ling's principal hire new teachers?​
Mathematics
1 answer:
kolbaska11 [484]3 years ago
8 0

Answer:

Ling's principal can hire new teachers in 54 different ways.

Step-by-step explanation:

Since Ling's elementary school principal wants to hire some new teachers, and 6 teachers applied for one 1st grade teaching job, and 3 teachers applied for one 2nd grade teaching job, and there is also a job opening for a 3rd grade teacher, and 3 teachers applied for the job, to determine how many different ways can Ling's principal hire new teachers the following calculation has to be done:

6 x 3 x 3 = X

18 x 3 = X

54 = X

Therefore, Ling's principal can hire new teachers in 54 different ways.

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3 years ago
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6 0
3 years ago
A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.
irakobra [83]

Answer:

The integral is equal to 5\sec^2(2x)+C for an arbitrary constant C.

Step-by-step explanation:

a) If u=\tan(2x) then du=2\sec^2(2x)dx so the integral becomes \int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C. (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case u=\sec(2x) hence du=2\tan(2x)\sec(2x)dx. We rewrite the integral as \int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C.

c) We use the trigonometric identity \tan(2x)^2+1=\sec(2x)^2 is part b). The value of the integral is 5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C. which coincides with part a)

Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.  

3 0
3 years ago
D2 =81-1 find the positive value of d that makes the equation true
Lubov Fominskaja [6]
81-1= 80
80 / 2 = 40
D = 40
So:
40(2) = 81 - 1
4 0
3 years ago
Surface area of prisms need help ASAP I will give brainliest​
trasher [3.6K]

Step-by-step explanation:

A=2πr(r+h)

A=6.28×14mm(+29mm)

A=77.92(14mm+29mm)

A=77.92×43

A=3350.56 mm

Hope it helps

KC

6 0
2 years ago
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