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Andrews [41]
3 years ago
7

Describe the intervals over which the given function is decreasing

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
5 0

Answer:

a. is answer sure fix answer

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What is the factorization of 729^15+1000?
igomit [66]

Answer:

The factorization of 729x^{15} +1000 is (9x^{5} +10)(81x^{10} -90x^{5} +100)

Step-by-step explanation:

This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form (a^{3} +b^{3} ) or (a^{3} -b^{3}). It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of 729x^{15} +1000 by using the <em>sum and difference of cubes </em>factorization.

1.) We calculate the cubic root of each term in the equation 729x^{15} +1000, and the exponent of the letter x is divided by 3.

\sqrt[3]{729x^{15}} =9x^{5}

1000=10^{3} then \sqrt[3]{10^{3}} =10

So, we got that

729x^{15} +1000=(9x^{5})^{3} + (10)^{3} which has the form of (a^{3} +b^{3} ) which means is a <em>sum of cubes.</em>

<em>Sum of cubes</em>

(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})

with a= 9x^{5} y b=10

2.) Solving the sum of cubes.

(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )

(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)

.

8 0
3 years ago
If tan theta = 3 and cos theta &gt; 0, find sec theta and csc theta
Sliva [168]
I think it’s what the other people said!
3 0
3 years ago
Paige invested 1200 at an interest rate of 5.75% compounded quarterly. Determine the value of her investments in 7 years.
iragen [17]
Use the formula A=p(1+r)^n
where 
A= value of investment
r= rate
n= time period
p= amount invested
in this question 
r= 5.75% but compounded quarterly means divide this by 4
r= 23/1600
n=7*4
n=28
p= $1200
A=1200(1+23/1600)^28

A= $1789.54

Therefore the value of her investment in 7 years is $1789.54
4 0
3 years ago
I don’t know how to do this. can someone please help me :)
Kaylis [27]
The surface area of a cylinder is the sum of the area of the two ends and the lateral area.
.. surface area = 2*(end area) +(lateral area)
.. = 2*(π*r^2) +(2π*r*h)
.. = 2π*r*(r +h)
.. = 2*3.14*(8 in)*(8 in +8 in)
.. = 3.14*256 in^2
.. ≈ 803.8 in^2

The 3rd selection is appropriate.
8 0
4 years ago
Determine the slope of the line.
andrew11 [14]

Answer:

what line?

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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