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3 years ago

How to graph y=(x+3)^2+4

Mathematics

1 answer:

Karolina [17]3 years ago

7 0

Answer: It will be a positive parabola with it's point at (-3,4)

Step-by-step explanation:

The graph is parabola since x is squared. Anything inside of parentheses with the x will deal with the x axis, with the x axis you have to reverse the sign of the number (positive to negative and negative to positive). Therefore, you go left by 3. Since the 4 is outside of the parentheses, it has to do with the y axis. Wit the y axis you do not have to reverse the sign, so you go up 4.

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Solve for x 4x+ 14=6x-8

Tomtit [17]

x=11
x is equal to 11 because you subtract 4x from both sides and then add 8 to both sides where you are left with 2x=22. After dividing by 2, you get x=11

3 0

3 years ago

Determine the principal value of the function: Arc sin(square root of 3/2)

Drupady [299]

Answer:

π/3

Step-by-step explanation:

We have to find the principal value of $\text{arc sin}(\frac{\sqrt{3}}{2} )$

arc sin means sin inverse. The sin inverse is a one to one function with its range between $-\frac{\pi}{2} \textrm{ to } \frac{\pi}{2}$

The principal value of the arc sin will lie within the above given range.

value of sin (60) or sin( $\frac{\pi}{3}$ ) is $\frac{\sqrt{3}}{2}$ .

$\frac{\pi}{3}$ lies between $-\frac{\pi}{2}\textrm{ and } \frac{\pi}{2}$

So, from here we can say that the Principal Value of Arc sin(square root of 3/2) is π/3

5 0

3 years ago

For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[

Ivenika [448]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

Given value:

$1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

Solve point 1 that is $\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\$ :

when,

$k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\$

$= \frac{1}{2} - \frac{1}{3}\\\\$

$k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\$

$= \frac{1}{3} - \frac{1}{4}\\\\$

$k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\$

$= \frac{1}{4} - \frac{1}{5}\\\\$

$k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\$

Calculate the sum $(S=s_1+s_2+s_3+......+s_n)$

$S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\$

When $s_n \ \ dt_{n \to 0}$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\$

$\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}$

In point 2: $\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

when,

$k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\$

$= \frac{1}{7 \times 8}\\\\= \frac{1}{56}$

$k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\$

$= \frac{1}{8 \times 9}\\\\= \frac{1}{72}$

$k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\$

$= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\$

$k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\$

calculate the sum: $S= s_1+s_2+s_3+s_n\\$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\$

when $s_n \ \ dt_{n \to 0}$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066$

$\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}$

8 0

3 years ago

what is the slope of a line that is parallel to the line that passes through the points (2,-2) and (5,-1)

Phoenix [80]

Answer:1/3

Step-by-step explanation:

The formula for finding slope is (y2-y1)/(x2-x1)

(-1--2)/(5-2)

1/3

4 0

3 years ago

Please help me with this

Cerrena [4.2K]

Answer:

30cm³

Step-by-step explanation:

volume of cuboid =L x B x H

=5 x 3 x 2

=30cm³

<h2><em>OladipoSeun</em><em>♡˖꒰ᵕ༚ᵕ⑅꒱</em></h2>

6 0

3 years ago