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3 years ago

Write down the possible values for n: -15 < 3n ≤ 6

Mathematics

2 answers:

anygoal [31]3 years ago

8 0

Step-by-step explanation:

Move all terms that do not contain nn from the middle section of the inequality.

−5 <n≤2 - 5 <n≤2

Sliva [168]3 years ago

7 0

Answer:

- 4, - 3, - 2, - 1, 0, 1, 2

Step-by-step explanation:

Given

- 15 < 3n ≤ 6 ( divide the 3 intervals by 3

- 5 < n ≤ 2

Thus n can have values from - 4 to 2, that is

- 4, - 3, - 2, - 1, 0, 1, 2

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The robotic arm will extend a total distance of 27 feet. Find the length of each section.

kipiarov [429]

Not enough information. How many segments does the arm have?

6 0

3 years ago

One positive integer is 7 less than twice another. The sum of their squares is 346. Find the integers. should be 2 answers

vovikov84 [41]

Answer:

the two positive integers are x= 15, and y = 11

Step-by-step explanation:

Let the first integer be x

Let the second integer be y

from the problem we can decode the following equations

$x=2y-7$ ---------------------------- equation 1

$x^{2} + y^{2}= 346$ -------------------------equation 2

substituting the value of x into equation 2, we have

$(2y-7)^{2} + y^{2}= 346 --------------equation 3$

expanding, we have

$4y^{2}-28y+49+y^{2}=346$

$5y^{2}-28y-297 = 0$

from this, y = 11 or y = -5.4

since our answer is a positive integer, we will have to pick the first value of y which is y = 11

substituting the value of y into equation 1, we have

$x= 2(11)-7=15$

hence x = 15

Therefore, we have x= 15, and y = 11

these are the two positive integers

7 0

3 years ago

A number when divided by 18 has a quotient of 132 and a remainder of 9. What is the number?

postnew [5]

$\frac{n}{18} = 132 + \frac{9}{18}$
$n = 2376 + 9 
$
$n = 2385$

8 0

3 years ago

Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with

skad [1K]

Parameterize S by the vector function

$\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle$

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

$\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle$

The integral of the field over S is then

$\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv$

$\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv$

$\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}$

8 0

2 years ago

If f(x)= <br><img src="https://tex.z-dn.net/?f=x%20-%20%7Bx%7D%5E%7B2%7D%20" id="TexFormula1" title="x - {x}^{2} " alt="x - {x}^

astra-53 [7]

Answer:

f(2+h)=-(h+2/3)^2+1/4

f(x+h)=-(x+h-1/2)^2+1/4

Step-by-step explanation:

1. f(2+h)=(2+h)-(2+h)^2=2+h-4-4h-h^2=-h^2-3h-2=-(h^2+3h+2)

=-(h+2/3)^2+1/4

2. Let (x+h)=a, then rewrite the equation into f(a)=a-a^2.

a-a^2=-(a^2-a)=-[(a-1/2)^2-1/4]=-(a-1/2)^2+1/4.

Insert a=x+h, f(x+h)=-(x+h-1/2)^2+1/4

7 0

3 years ago