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2 years ago

The sum of two consecutive odd integers is 96. what is the product of these integers?

Mathematics

2 answers:

Korolek [52]2 years ago

6 0

Answer:

2303

Step-by-step explanation:

Let the smaller of the two odd integers be x.

Then the next odd integer is x + 2.

Since the sum of these 2 integers is 96, we may write x + (x + 2) = 96

Now solving for x we obtain:

2x = 94

x = 47

To find the next value we can subtract 47 from 96, which is 49.

Hence, the required two integers are 47 and 49. Multiplying them, we get a product of 2303.

hope this helps!

liubo4ka [24]2 years ago

3 0

Answer:

47 and 49

Step-by-step explanation:

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How do you do this question?

polet [3.4K]

Answer:

Step-by-step explanation:

1 / ((n + 1) + 2)³ ≤ 0.001

1 / (n + 3)³ ≤ 0.001

(n + 3)³ ≥ 1000

n + 3 ≥ 10

n ≥ 7

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3 years ago

Use separation of variables to solve dy dx − tan x = y2 tan x with y(0) = √3. Find the value of c in radians, not degrees

a_sh-v [17]

Answer:

$y(x)=tan(-log(cos(x))+\frac{\pi }{3} )$

Step-by-step explanation:

Rewrite the equation as:

$\frac{dy(x)}{dx}-tan(x)=y(x)^{2} *tan(x)$

Isolating $\frac{dy}{dx}$

$\frac{dy}{dx} =tan(x)+tan(x)*y^{2}$

Factor:

$\frac{dy}{dx} =tan(x)*(1+y^{2} )$

Dividing both sides by $(1+y^{2} )$ and multiplying them by $dx$

$\frac{dy}{1+y^{2} } =tan(x)dx$

Integrate both sides:

$\int\ \frac{dy}{1+y^{2} } = \int\ tan(x) dx$

Evaluate the integrals:

$arctan(y)=-log(cos(x))+C_1$

Solving for y:

$y(x)=tan(-log(cos(x))+C_1)$

Evaluating the initial condition:

$y(0)=\sqrt{3} =tan(-log(cos(0))+C_1)=tan(-log(1)+C_1)=tan(0+C_1)$

$\sqrt{3} =tan(C_1)\\arctan(\sqrt{3} )=C_1\\60=C_1$

Converting 60 degrees to radians:

$60degrees*\frac{\pi }{180degrees} =\frac{\pi }{3}$

Replacing $C_1$ in the diferential equation solution:

$y(x)=tan(-log(cos(x))+\frac{\pi }{3} )$

3 0

3 years ago

Plz help me I’m so confused 23 points plz explain it to me in sooo stuck

anzhelika [568]

Answer:

6. D

7. B

Step-by-step explanation:

Nancy takes a test that has two sections: essay and true/false. She scores 56 points on the essay. Each true/false question is 4 points. So x number of true/false is worth 4 points each or 4x.

Together her score will be 56 + 4x.

She wants to score more than 80 or > 80.

So her test can be represented as the inequality 56 + 4x > 80.

This is solved using inverse operations.

56 + 4x > 80

4x > 24

x > 6

This should be graphed as an open circle at 6 on the umber line pointing and shaded to the the right for numbers greater than 6.

3 0

3 years ago

Solve problems <br>5 1/2×3 1/3

makvit [3.9K]

5 1/2 X 3 1/3=18 1/3

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2 years ago

Natalia bought 8 glitter wands for $50. Determine whether or not each wand purchase below has the same price per wand as glitter

viva [34]

Answer:

Sparkle wands: NO

Fairy wands: YES

Glass wands: NO

Step-by-step explanation:

To find the price per glitter wand, you have to divide the price of the wands by the amount of wands you have.

$50/8 = $6.25

Divide the price of the wands by the amount you get.

Sparkle wands: $20/4 = $5

Fairy wands: $37.50/6 = $6.25

Glass wands: $65/10 = $6.50

The sparkle wands and the glass wands do not have the same price per wand as glitter wands.

The fairy wands have the same price per wand as glitter wands.

8 0

3 years ago