Which represents the number 7,776 in exponential form? 68 36 28 65

If the cost of 10 pens is rupees 144.40, then find the cost of 7 pens

VikaD [51]

Answer: 101.08

Step-by-step explanation:

10 pens cost 144.40

1 pen will cost 144.40 /10

7 pens will therefore cost 144.40 / 10 x 7

= 101.08

6 0

3 years ago

Calculus 3 chapter 16

o-na [289]

Evaluate $\vec F$ at $\vec r$ :

$\vec F(x,y,z) = x\,\vec\imath + y\,\vec\jmath + xy\,\vec k \\\\ \implies \vec F(\vec r(t)) = \vec F(\cos(t), \sin(t), t) = \cos(t)\,\vec\imath + \sin(t)\,\vec\jmath + \sin(t)\cos(t)\,\vec k$

Compute the line element $d\vec r$ :

$d\vec r = \dfrac{d\vec r}{dt} dt = \left(-\sin(t)\,\vec\imath+\cos(t)\,\vec\jmath+\vec k\bigg) \, dt$

Simplifying the integrand, we have

$\vec F\cdot d\vec r = \bigg(-\cos(t)\sin(t) + \sin(t)\cos(t) + \sin(t)\cos(t)\bigg) \, dt \\ ~~~~~~~~= \sin(t)\cos(t) \, dt \\\\ ~~~~~~~~= \dfrac12 \sin(2t) \, dt$

Then the line integral evaluates to

$\displaystyle \int_C \vec F\cdot d\vec r = \int_0^\pi \frac12\sin(2t)\,dt \\\\ ~~~~~~~~ = -\frac14\cos(2t) \bigg|_{t=0}^{t=\pi} \\\\ ~~~~~~~~ = -\frac14(\cos(2\pi)-\cos(0)) = \boxed{0}$

3 0

2 years ago

Which of the following could be the value of x in the equation x^2 - 21 = 100 Choose all the correct answers

konstantin123 [22]

How to solve your problem

x^{2}-21=100

Quadratic formula

Factor

1

Move terms to the left side

x^{2}-21=100

x^{2}-21-100=0

2

Subtract the numbers

x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0

x^{2}\textcolor{#C58AF9}{-121}=0

3

Use the quadratic formula

x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x^{2}-121=0

a=\textcolor{#C58AF9}{1}

b=\textcolor{#F28B82}{0}

c=\textcolor{#8AB4F8}{-121}

x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}

4

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Add zero

Multiply the numbers

x=\frac{\pm 22}{2}

5

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x=\frac{22}{2}

x=\frac{-22}{2}

6

Solve

Rearrange and isolate the variable to find each solution

x=11

x=-11

4 0

2 years ago

A computer valued at $2500 loses 6.5% of its value every year. How much will it be worth in 4 years?

I am Lyosha [343]

Answer:

The computer will be worth $1,850 after four years.

Step-by-step explanation:

We need to find 6.5% of $2,500.

2,500 x 0.065 = $162.50

Therefore, the computer value decreases by $162.50 each year. Since we need to know the computer value after 4 years, we also need to multiply the value of decrease by 4.

162.5 x 4 = $650

Therefore, after 4 years, the computer value will decrease by $650.

To find the whole computer value after 4 years, we need to subtract the initial value of $2,500 by the 4-year decreasing value of $650.

2,500 - 650 = $1850

Therefore, the computer will be worth $1,850 after four years.

Hope this helps! :D

5 0

3 years ago

A country population in 1993 was 85 million in 1996 it was 90

inn [45]

Answer:

Ohh I think I might know what question you are referencing.

In 2003, the population will be:

P = 86.22 million

Step-by-step explanation:

P = Po exp(0.0180t)

P = 72 exp(0.0180(10))

P = 86.22 million

6 0

4 years ago