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3 years ago

Determine two consecutive odd integers such that the sum of their squares is a minimum.

Mathematics

1 answer:

Nesterboy [21]3 years ago

8 0

Answer:

5 or -7, the two integers are either 5 and 7 or -7 and -5.

Step-by-step explanation:

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3-2|x+4|+3=1 the answer for this

blagie [28]

Answer:

x={-3/2,-13/2}

Step-by-step explanation:

3-2|x+4|+3=1

-2|x+4|+6=1

-2|x+4|=-5

|x+4|=5/2

x+4=5/2

x+4=-5/2

x=5/2-4

x=-3/2

x=-5/2-4

x=-13/2

7 0

2 years ago

Calculus= Integrate 5^x dx please break down how answer is 1/6x^6+C

aleksley [76]

Answer:

$\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c$

Step-by-step explanation:

Note that the integral of $5^x$ is not $\frac{1}{6}x^6 + c$

The solution is as follows:

Given

$5^x$

Required

Integrate

Represent the given expression using integral notation

$\int\limits {5^x} \, dx$

This question can't be solved directly;

We'll make use of exponential rules which states;

$\int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c$

By comparing $\int\limits {5^x} \, dx$ with $\int\limits {a^x} \, dx$ ;

we can substitute 5 for a;

Hence, the expression $\int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c$ becomes

$\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c$

-------------------------------------------------------------------------------------

However, the integral of $x^5$ is $\frac{1}{6}x^6 + c$

This is shown below:

Given that $x^5$

Applying power rule;

Power rule states that

$\int\limits{x^n}\ dx = \frac{x^{n+1}}{n+1} + c$

In this case ( $x^5$ ), n = 5;

So, $\int\limits{x^n}\ dx= \frac{x^{n+1}}{n+1} + c$

becomes

$\int\limits{x^5}\ dx = \frac{x^{5+1}}{5+1} + c$

$\int\limits{x^5}\ dx = \frac{x^{6}}{6} + c$

$\int\limits{x^5}\ dx= \frac{x^{6}}{6} + c$

4 0

3 years ago

Y=10 when x=4, find x when y=80

Mrac [35]

The answer is x=32 when y=80

6 0

3 years ago

I need help please with this

prohojiy [21]

Answer:

9.2 yd

Step-by-step explanation:

Given,

hypotenuse(h)=10 yd

base(b)=4yd

perpendicular(p)=?

we have Pythagoras Theorem

h²=p²+b²

p²=h²-b²

p=(h²‐b²)½

=(10²-4²)½

=(100-16)½

=(84)½

=9.2

5 0

3 years ago

Bryan has a collection of baseball cards which he shares equally with his brother,

Rus_ich [418]

Answer:

Step-by-step explanation:

If he shares it equally with his brother, that is 12÷2=6

Then he receives 2, so 2+6=8

3 0

2 years ago