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2 years ago

What are the two cases for 丨4x - 1丨= 19?

Mathematics

2 answers:

11111nata11111 [884]2 years ago

8 0

Answer:

Step-by-step explanation:

x = 5

sineoko [7]2 years ago

4 0

Answer:

x=5 and -17/4

Step-by-step explanation:

The two equations for 丨4x - 1丨= 19 is

4x-1=19

and

4x-1=-19

So for 4x-1=19

4x=20

x=5

4x-1=-18

4x=-17

x=17/4

Hope this helps!

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What is the sum of the first seven terms of the geometric series? 3 12 48 192 ...

Ad libitum [116K]

Hence, the sum of the given GP is 16347

<h2>What is a series?</h2>

a series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers, but much more generality is possible.

<h3>How to solve?</h3>

we can identify from the given geomertric series.

first term = a(say) = 3

geometric factor of progression = r(say) = 4

Sum of the first 7 terms = a( $\frac{r^n-1}{r-1}$ ) ,where n is 7

Sum = 3( $\frac{4^7-1}{3}$ ) = 16348-1

= 16347

Hence, the sum of the given GP is 16347.

to learn more about series: brainly.com/question/12578626

#SPJ4

8 0

1 year ago

Which equation shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation

Andrej [43]

Answer:

$5x= 15$

Step-by-step explanation:

Given

$3x - 5 = -2x +10$

Required

Write the variables and constants on different sides

$3x - 5 = -2x +10$

Add 2x to both sides

$2x + 3x - 5 =2x -2x +10$

$5x - 5 =10$

Add 5 to both sides

$5x - 5 + 5 = 10 + 5$

$5x= 10 + 5$

$5x= 15$

Hence, the equation is

$5x= 15$

Solving further [divide both sides by 5]

$x = 3$

3 0

3 years ago

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

5 0

2 years ago

HELP ME PLEASE THIS IS DUE TODAY

Usimov [2.4K]

Angle1=103°
angle2=77°
angle3=103°
angle4=77°

5 0

2 years ago

Fifteen students are going hiking on their spring break. They plan to travel in three vehicles—one seating 7, one seating 5, and

andriy [413]

Answer:

The students can group themselves in 360360 ways

Step-by-step explanation:

For this exercise we need to use the following equation:

$\frac{n!}{n1!*n2!*...*nk!}$

This equation give us the number of assignation of n elements in k cell, where n1, n2, ..nk are the element that are in every cell

In this case we have 15 student that need to be assign in three vehicles with an specific capacity. This vehicles would be the equivalent to cells, so we can write the equation as:

$\frac{15!}{7!*5!*3!}$

Because the first vehicle have 7 seating, the second vehicle have 5 seating and the third vehicle have 3 seating.

Solving the equation we get 360360 ways to organized 15 students in three vehicles with capacity of 7, 5 and 3 seating.

5 0

2 years ago