4(2 – x) > –2x – 3(4x + 1)

The coordinates of the points below represent the vertices of a rectangle.

jasenka [17]

Answer:

the answer is 28 but try D.

4 0

3 years ago

Read 2 more answers

Gia sent two radio signals from Earth to Mars. Signal A traveled to Mars in 56 minutes. Signal B took ¼ as long. How many more m

Alex777 [14]

Answer:

i know that it B got there in 14 min and 56 divide bye 4 = 14 and now we subtract 56-14 = A took 42 more minutes then B

Step-by-step explanation:

42 min

8 0

4 years ago

Water is being pumped into a conical tank that is 8 feet tall and has a diameter of 10 feet. If the water is being pumped in at

Deffense [45]

The rate of change of the depth of water in the tank when the tank is half

filled can be found using chain rule of differentiation.

When the tank is half filled, the depth of the water is changing at 1.213 ×

10⁻² ft.³/hour.

Reasons:

The given parameter are;

Height of the conical tank, h = 8 feet

Diameter of the conical tank, d = 10 feet

Rate at which water is being pumped into the tank, = 3/5 ft.³/hr.

Required:

The rate at which the depth of the water in the tank is changing when the

tank is half full.

Solution:

The radius of the tank, r = d ÷ 2

∴ r = 10 ft. ÷ 2 = 5 ft.

Using similar triangles, we have;

$\dfrac{r}{h} = \dfrac{5}{8}$

The volume of the tank is therefore;

$V = \mathbf{\dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}$

$r = \dfrac{5}{8} \times h$

Therefore;

$V = \dfrac{1}{3} \cdot \pi \cdot \left( \dfrac{5}{8} \times h\right)^2 \cdot h = \dfrac{25 \cdot h^3 \cdot \pi}{192}$

By chain rule of differentiation, we have;

$\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \cdot \dfrac{dh}{dt}}$

$\dfrac{dV}{dh}=\dfrac{d}{h} \left( \dfrac{25 \cdot h^3 \cdot \pi}{192} \right) = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64}}$

$\dfrac{dV}{dt} = \dfrac{3}{5} \ ft.^3/hour$

Which gives;

$\dfrac{3}{5} = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64} \times \dfrac{dh}{dt}}$

When the tank is half filled, we have;

$V_{1/2} = \dfrac{1}{2} \times \dfrac{1}{3} \times \pi \times 5^2 \times 8 =\mathbf{ \dfrac{25 \cdot h^3 \cdot \pi}{ 192}}$

Solving gives;

h³ = 256

h = ∛256

$\dfrac{3}{5} \times \dfrac{64}{25 \cdot h^2 \cdot \pi} = \dfrac{dh}{dt}$

Which gives;

$\dfrac{dh}{dt} = \dfrac{3}{5} \times \dfrac{64}{25 \cdot (\sqrt[3]{256}) ^2 \cdot \pi} \approx \mathbf{1.213\times 10^{-2}}$

When the tank is half filled, the depth of the water is changing at 1.213 × 10⁻² ft.³/hour.

Learn more here:

brainly.com/question/9168560

6 0

3 years ago

For which values of K with the product of K / 3 12 be greater than 12

soldier1979 [14.2K]

Answer:

The values of k are all real numbers greater than 3

Step-by-step explanation:

we have

$(\frac{k}{3})12 > 12$

Solve for k

Divide 12 by 3

$4k > 12$

Divide by 4 both sides

$4k/4 > 12/4$

$k > 3$

The solution is the interval ------> (3,∞)

All real numbers greater than 3

7 0

3 years ago

In ΔABC, if the length of side b is 3 centimeters and the measures of ∠B and ∠C are 45° and 60°, respectively, what is the lengt

Umnica [9.8K]

Answer is 3.67 centimeters

3 0

3 years ago

Read 2 more answers