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forsale [732]
3 years ago
11

Need help in these to math problems

Mathematics
1 answer:
Masteriza [31]3 years ago
6 0

Question 1:

For this case we have that by definition, the GCF of two numbers is the largest number that is a factor of both numbers. For example, the number 10 is the biggest factor that 50 and 30 have in common.

We must find the GCF of the following expression:

30t ^ 2u + 12tu ^ 2 + 24tu

We look for the prime factorization of each number:

30: 2 * 3 * 5\\12: 2 * 2 * 3\\24: 2 * 2 * 2 * 3

The GCF of the three numbers is 2 * 3 = 6

So:

6tu (5t + 2u + 4)

Answer:

Option C

Question 2:

For this case we have that by definition of power properties of the same base, that:

a ^ n * a ^ m = a ^ {n + m}

That is, for multiplication of powers of the same base, the same base is placed and the exponents are added.

So:

b ^ n * b ^ m = b ^ {n + m}

ANswer:

b ^ {n + m}

Option A

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
ryzh [129]

First find the critical points of <em>f</em> :

f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7

\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1

\dfrac{\partial f}{\partial y}=6y=0\implies y=0

so the point (1, 0) is the only critical point, at which we have

f(1,0)=-7

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t

Find the critical points of <em>g</em> :

\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0

\implies\sin t=0\text{ OR }1+5\cos t=0

\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi

where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at

t=0\implies f(10,0)=155

t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299

t=\pi\implies f(-10,0)=235

t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299

So <em>f</em> has a minimum of -7 and a maximum of 299.

4 0
3 years ago
In 2018, the number of students at The Villages High School was 975 and is increasing at a rate of 2.5% per year. Write and use
avanturin [10]

Answer:

A(t)=975(1.025)^t

In 2025,the number of students at the villages high school=1159

Step-by-step explanation:

We are given that in 2018

Number of students at the villages high school=975

Increasing rate,r=2.5%=0.025

We have to write and use of exponential growth function to project the populating in 2025.

A_0=975,t=0

According to question

Number of students at the villages high School is given by

A(t)=A_0(1+r)^t

Substitute the values

A(t)=975(1+0.025)^t=975(1.025)^t

t=7

Substitute the value

Then, the number of students at the villages high school in 2025

A(7)=975(1.025)^7=1158.96\approx 1159

8 0
3 years ago
Read 2 more answers
At the market, 777 apples cost \$4.55$4.55dollar sign, 4, point, 55. how much do 999 apples cost? \$
vredina [299]
I divided $.55 by 777 and got 0.00585 cents per apple.  Then I mulitplied 0.00585 by 999 and got $5.85.
6 0
3 years ago
What is the product?
Dmitrij [34]

Answer:

-3

4

Step-by-step explanation:

You need to take something called the dot product

6 0
3 years ago
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Sara can take no more than 22 pounds of luggage on a trip.Her suitcase weighs 112 ounces.How many more pounds can she pack witho
Licemer1 [7]

Answer:

15 pounds

Step-by-step explanation:


4 0
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