Ask question

Ask question

All categories

andrezito [222]

2 years ago

12

Log(2t+4)=log(14-3t)

1 answer:

barxatty [35]2 years ago

4 0

Answer:

t = 2

Step-by-step explanation:

$2t + 4 = 14 - 3t$

$5t = 10$

$t = 2$

Checking:

$log(2(2) + 4) = log(8)$

$log(14 - 3(2)) = log(8)$

You might be interested in

Someone help me out with this

Trava [24]

Answer:

<u>4x = 20</u>

<u>x = 5</u>

<u></u>

Step-by-step explanation:

Have a nice day!

8 0

3 years ago

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

42°<br> X Х<br> x =<br> degrees<br> tar<br><br> PLEASE HELP ITS URGENT

Tema [17]

Answer:

x = 48°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°, thus

x = 180° - (90 + 42)° = 180° - 132° = 48°

5 0

3 years ago

The cost of a candy bar in a vending machine is $0.95. The cost of a bottle of water in the same machine is $1.25. Jamie has $25

Mrrafil [7]

Answer:

The answer is $16.45

Step-by-step explanation:First, you have to multiply $0.95 x 9 = $8.55

Then, you have to subtract $25.00-$8.55 = $16.45

Please mark this brainliest and I will be glad to help anytime

6 0

3 years ago

Jenny is trimming the edge of pillows with lace. Each pillow requires 15 inches of lace. She has one piece of lace that is 3 fee

Anna71 [15]

Answer:

I think Jenny will be able to do 9 pillows with the lace trim.

4 0

3 years ago