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klio [65]
3 years ago
7

What is the domain of f in the equation F(x)=5/x2-18x+45

Mathematics
1 answer:
Hitman42 [59]3 years ago
6 0

f(x)=\dfrac{5}{x^2-18x+45}\\\\The\ domain:\\\\x^2-18x+45\neq0\\\\x^2-15x-3x+45\neq0\\\\x(x-15)-3(x-15)\neq0\\\\(x-15)(x-3)\neq0\iff x-15\neq0\ \wedge\ x-3\neq0\\\\\boxed{x\neq15\ \wedge\ x\neq3}\to\boxed{x\in\mathbb{R}-\{3,\ 15\}}

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Jackie is selling smoothies at a school fair. She starts the day with $15 in her cash box to provide change to her customers. If
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Answer:

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8 0
3 years ago
Big Louie's Pizza House sells a 12" square pan pizza for $3.95 and a 24" square pan pizza for $14.95. Which pizza is a better de
Alex_Xolod [135]

Answer:

The pizza that is a better deal is 12" square pan pizza for $3.95.

Step-by-step explanation:

This is because if you get 2 of the 12" square pan pizzas it will be 24" and you will only have to pay $7.90. but if you bought the 24" square pan pizza you would have to pay $14.95 which isnt a fair price.

4 0
2 years ago
Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your
Darina [25.2K]

Answer:

Given definite  integral as a limit of Riemann sums is:

\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Step-by-step explanation:

Given definite integral is:

\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}

Substituting (2) in above

f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

Riemann sum is:

= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]

4 0
3 years ago
Simplify the expression.<br> 2³ times 2^5<br><br> A. 4^15<br> B. 4^8<br> C. 2^15<br> D. 2^8
Luden [163]
(x^m)(x^n)=x^{m+n}
so
(2^3)(2^5)=2^{3+5}=2^{8}
D is answer
7 0
3 years ago
Read 2 more answers
The mean value of 500 homes in a county is $225,000 and the standard deviation is $25,000. approximately how many of the homes i
dusya [7]

240 homes in the county are between $175,000 and $225,000.

The image attached is associated with this question and m in it refers to the mean value which is $225000 here and d refers to the standard deviation which is $25000 here.

Now since m= $225000

and $175000= $225000-$50000= $225000-(2* $25000)= m-2d

Thus, as per the image area covered between m and m-2d=  $225000

and $175000 is (34%+14%)of 500 homes= 68% of 500= 240 homes, is the answer.

A random variable X is said to follow a normal distribution if its parameters are mean and standard deviation. Every other distribution can be reduced to a normal distribution.

Learn to know more about normal distributions on brainly.com/question/4079902

#SPJ4

3 0
2 years ago
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