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Vikki [24]
3 years ago
15

F $1 \le a \le 10$ and $1 \le b \le 36$, for how many ordered pairs of integers $(a, b)$ is $\sqrt{a + \sqrt{b}}$ an integer?

Mathematics
1 answer:
svetlana [45]3 years ago
3 0
You have such entry data: 
1\ \textless \ a\ \textless \ 10 \\ 1\ \textless \ b\ \textless \ 36

Consider expression \sqrt{a+ \sqrt{b} }. If this expression becomes an integer, then b=4,9,16,25, because then \sqrt{b} = 2,3,4,5, respectively. In other cases \sqrt{b} is not integer and thus the expression \sqrt{a+ \sqrt{b} } also is not integer.

1. b=4, then \sqrt{a+ \sqrt{b} }=\sqrt{a+2}. Here a=2,7 (in other cases \sqrt{a+2} is not integer). When a=2, \sqrt{a+2}=\sqrt{2+2}=2 and when a=7, \sqrt{a+2}=\sqrt{7+2}=3.

2. b=9, then a=6 and \sqrt{a+ \sqrt{b} }= \sqrt{a+3}=\sqrt{6+3}=3.

3. b=16, then a=5 and \sqrt{a+ \sqrt{b} }= \sqrt{a+4}=\sqrt{5+4}=3.

4. b=25, then a=4 and \sqrt{a+ \sqrt{b} }=\sqrt{a+5}=\sqrt{4+5}=3.

Answer: (2,4), (7,4), (6,9), (5,16), (4,25).







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aleksandr82 [10.1K]

Give a reason for each step of the proof. 

Given: <1 and <2 are complimentary 

<1 is congruent to <3, 

<2 is congruent to <4 

Prove: <3 and <4 are complimentary 

Statements: Reasons: 

1. <1 and <2 are complimentary 1.Given 

2. m<1 + m<2=90* 2.<u>DEFINITION OF COMPLEMENTARY ANGLES</u>

3. <1 is congruent to <3, <2 is congruent to <4 3.__GIVEN______ 

4. m<1=m<3, m<2=m<4 4.<u>DEFINITION OF CONGRUENT ANGLES_</u>

5. m<3 + m<2=90* 5. <u>SUBSTITUTION PROPERTY (m<1 is replaced by m<3.) </u>

6. m<3 +m<4=90* 6. <u>DEFINITION OF COMPLEMENTARY ANGLES </u>

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8 0
3 years ago
I don’t understand the polynomials
Serhud [2]
Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

A polynomial can have:

constants (like 3, −20, or ½)
variables (like x and y)
exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed
that can be combined using addition, subtraction, multiplication and division ...

... except ...

... not division by a variable (so something like 2/x is right out)

So:

A polynomial can have constants, variables and exponents,
but never division by a variable.

Also they can have one or more terms, but not an infinite number of terms.

These are polynomials:

3x
x − 2
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These are not polynomials

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1/x is not either
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7 0
3 years ago
2. An exam readiness awareness taskforce at a Fremont National university sampled 200 students after the midterm to ask them whe
k0ka [10]

Answer:

c) (40+60+25)/200 or 63%

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n= 200 students

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Did Poorly on the Midterm and Studied for the Midterm = 25

Did Poorly on the Midterm and Went Partying = 60

The number of students that did poorly on the midterm or went partying the weekend before the midterm is given by the sum of all students who did poorly to all students who went partying minus the number of students who did Poorly on the Midterm and Went Partying:

N=(25+60)+(40+60) - 60\\N= 125

The probability that a randomly selected student did poorly on the midterm or went partying the weekend before the midterm is given by:

P = \frac{N}{n}=\frac{125}{200} = 0.63 = 63\%

3 0
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Step-by-step explanation:

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Read 2 more answers
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aleksandr82 [10.1K]
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