1/2x<13 How do you solve this?

Running out of time! Please help and show work! Thank you! Will mark brainliest!

VikaD [51]

(-3j²k³)²(2j²k)³ = When a power is raised to a power the exponents have to be multiplied.

= (-3²j⁽²*²⁾k⁽³*²⁾)(2³j⁽²*³⁾k³) = We can take out the constants

= (9)(8)(j⁴k⁶)(j⁶k³) = We can group the same variables

= 72(j⁴j⁶)(k⁶k³) = When multiplying two powers that have the same base, you have to add the exponents.

= 72 j⁽⁴⁺⁶⁾k⁽⁶⁺³⁾ = 72j¹⁰k⁹

Answer = 72j¹⁰k⁹

Hope this helps!

$\textit{\textbf{Spymore}}$

5 0

3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

Answer- Length of the curve of intersection is 13.5191 sq.units

Solution-

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago

Identify the dependent and independent variables in each situation.

klemol [59]

A. independent (x) - expenses, dependent (y) - total cost
B. independent (x) - area, dependent (y) - price
C. independent (x) - time, dependent (y) - distance
D. independent (x) - size of carton, dependent (y) - number of items

6 0

3 years ago

Read 2 more answers

What is the distance from C to D? A. 5 units B. 1 unit C. 25 units D. 7 units

Vera_Pavlovna [14]

Answer:

Option A

Step-by-step explanation:

According to the distance formula , for any 2 points P & Q whose coordinates are (x¹ , y¹) and (x² , y²) respectively. So ,

$PQ = \sqrt{(x^{2} - x^{1} )^{2} + (y^{2} - y^{1})^{2} }$

NOTE = HERE x² , y² DOESN'T MEAN THE SQUARES OF x & y . THEY ARE JUST COORDINATES.

According to the question ,

Coordinate of C = (2 , -1)

Coordinate of D = (5 , 3)

Using distance formula ,

$CD = \sqrt{(5-2)^{2} + (3 -(-1))^{2} }$

$=> CD = \sqrt{3^{2} + 4^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5$

5 0

3 years ago

Answer this simple quick question!! Pls :)

Alex_Xolod [135]

Answer:

If it is that simple then do it yourself LOL

Step-by-step explanation:

6 0

3 years ago