Which of the following is a Geometric Series?

How is the quotient 5 to the 8th power expressed as a power of 5

Sauron [17]

Answer:

5^4

Step-by-step explanation:

When dividing exponents with the same base, you subtract their exponents.

8-4=4

This means that 5^8 / 5^4 is equal to:

5^4

6 0

3 years ago

A trough has ends shaped like isosceles triangles, with width 5 m and height 7 m, and the trough is 12 m long. Water is being pu

Svet_ta [14]

Answer:

$\dfrac{dh}{dt}=21 \text{m/min}$

the rate of change of height when the water is 1 meter deep is 21 m/min

Step-by-step explanation:

First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)

$V = \dfrac{1}{2}(bh)\times L$

here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).

As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:

$\dfrac{b}{h} = \dfrac{5}{7}$

$b=\dfrac{5}{7}h$ this can be substituted back in the volume equation

$V = \dfrac{5}{14}h^2L$

the rate of the water flowing in is:

$\dfrac{dV}{dt} = 6$

The question is asking for the rate of change of height (m/min) hence that can be denoted as: $\frac{dh}{dt}$

Using the chainrule:

$\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}$

the only thing missing in this equation is dh/dV which can be easily obtained by differentiating the volume equation with respect to h

$V = \dfrac{5}{14}h^2L$

$\dfrac{dV}{dh} = \dfrac{5}{7}hL$

reciprocating

$\dfrac{dh}{dV} = \dfrac{7}{5hL}$

plugging everything in the chain rule equation:

$\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}$

$\dfrac{dh}{dt}=\dfrac{7}{5hL}\times 6$

$\dfrac{dh}{dt}=\dfrac{42}{5hL}$

L = 12, and h = 1 (when the water is 1m deep)

$\dfrac{dh}{dt}=\dfrac{42}{5(1)(12)}$

$\dfrac{dh}{dt}=21 \text{m/min}$

the rate of change of height when the water is 1 meter deep is 21 m/min

6 0

3 years ago

Read 2 more answers

What are the coordinates of the image of C if it is reflected across the x-axis?

Svetradugi [14.3K]

Answer:

(-2, 4)

Step-by-step explanation:

~When reflecting a point of the x-axis, the x value (or first number inside the parenthesis) does not change.

The reason the x-value does not change is because you are reflecting over the x-axis, making the point go up or down. That will change the y-value but the x-value only changes if you move to the left or the right. In this case, you can see that the point's x-value is -2, so that will not change. It's current y-value however is -4. When reflecting over an axis, the number that is changing (in this case the y-value) will just be flipped from positive to negative, or vise versa. In this case, -4 will be reflected to be 4, making point C reflected over the x-axis (-2, 4).

5 0

3 years ago

Read 2 more answers

Which expressionism equivalent to -60 / 5 select all that apply 60 divided by negitive 5 60 times 1/5 60 times negitive 1/5 Negi

GaryK [48]

Answer:

Equivalent expressions

A) $\frac{60}{-5}$