Yesterday the temperature was 6°C. Today it is -5°C. In degrees Celsius, what is the change in temperature?

A box has a width of 10 cm and a length of 17 cm. The volume of the box is decreasing at a rate of 527 cubic cm per minute, with

Ber [7]

Answer:

$-3.1$ cm per minute.

Step-by-step explanation:

We have been given that a box has a width of 10 cm and a length of 17 cm. The volume of the box is decreasing at a rate of 527 cubic cm per minute, with the width and length being held constant.

We know that volume of a cuboid is length times width times height.

$V=lwh$

Upon substituting our given width and length, we will get:

$V=17\cdot 10\cdot h$

$V=170\cdot h$

Now, we will find derivative of volume with respect to time as:

$\frac{dV}{dt}=170\cdot \frac{dh}{dt}$

Since the volume of the box is decreasing at a rate of 527 cubic cm per minute, so we will substitute $\frac{dV}{dt}=-527$ as:

$-527=170\cdot \frac{dh}{dt}$

$\frac{-527}{170}=\frac{170\cdot \frac{dh}{dt}}{170}$

$\frac{dh}{dt}=-3.1$

Therefore, the rate of change in height is $-3.1$ cm per minute.

6 0

4 years ago

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.

qwelly [4]

Answer:

A)

$\displaystyle \frac{dy}{dt}=-\frac{33}{8}$

B)

$\displaystyle \frac{dx}{dt}=\frac{3}{2}$

Step-by-step explanation:

x and y are differentiable functions of t, and we are given the equation:

$xy=6$

First, let's differentiate both sides of the equation with respect to t. So:

$\displaystyle \frac{d}{dt}\left[xy\right]=\frac{d}{dt}[6]$

By the Product Rule and rewriting:

$\displaystyle \frac{d}{dt}[x(t)]y+x\frac{d}{dt}[y(t)]=0$

Therefore:

$\displaystyle y\frac{dx}{dt}+x\frac{dy}{dt}=0$

A)

We want to find dy/dt when x = 4 and dx/dt = 11.

Using our original equation, find y when x = 4:

$\displaystyle (4)y=6\Rightarrow y=\frac{3}{2}$

Therefore:

$\displaystyle \frac{3}{2}\left(11\right)+(4)\frac{dy}{dt}=0$

Solve for dy/dt:

$\displaystyle \frac{dy}{dt}=-\frac{33}{8}$

B)

We want to find dx/dt when x = 1 and dy/dt = -9.

Again, using our original equation, find y when x = 1:

$(1)y=6\Rightarrow y=6$

Therefore:

$\displaystyle (6)\frac{dx}{dt}+(1)\left(-9)=0$

Solve for dx/dt:

$\displaystyle \frac{dx}{dt}=\frac{3}{2}$

5 0

3 years ago

Help please!!!!!!!I don’t know this! Tyy

aleksley [76]

<h3>Answer: Choice C. 4*sqrt(6)</h3>

====================================================

Explanation:

Each cube has a side length of 4. Placed together like this, the total horizontal side combines to 4+8 = 8. This is the segment HP as shown in the diagram below. I've also added point Q to form triangle HPQ. This is a right triangle so we can find the hypotenuse QH

Use the pythagorean theorem to find QH

a^2 + b^2 = c^2

(HP)^2 + (PQ)^2 = (QH)^2

8^2 + 4^2 = (QH)^2

(QH)^2 = 64 + 16

(QH)^2 = 80

QH = sqrt(80)

Now we use segment QH to find the length of segment EH. Focus on triangle HQE, which is also a right triangle (right angle at point Q). Use the pythagorean theorem again

a^2 + b^2 = c^2

(QH)^2 + (QE)^2 = (EH)^2

(EH)^2 = (QH)^2 + (QE)^2

(EH)^2 = (sqrt(80))^2 + (4)^2

(EH)^2 = 80 + 16

(EH)^2 = 96

EH = sqrt(96)

EH = sqrt(16*6)

EH = sqrt(16)*sqrt(6)

EH = 4*sqrt(6), showing the answer is choice C

-------------------------

A shortcut is to use the space diagonal formula. As the name suggests, a space diagonal is one that goes through the solid space (rather than stay entirely on a single face; which you could possibly refer to as a planar diagonal or face diagonal).

The space diagonal formula is

d = sqrt(a^2+b^2+c^2)

which is effectively the 3D version of the pythagorean theorem, or a variant of such.

We have a = HP = 8, b = PQ = 4, and c = QE = 4 which leads to...

d = sqrt(a^2+b^2+c^2)

d = sqrt(8^2+4^2+4^2)

d = sqrt(96)

d = sqrt(16*6)

d = sqrt(16)*sqrt(6)

d = 4*sqrt(6), we get the same answer as before

The space diagonal formula being "pythagorean" in nature isn't a coincidence. Repeated uses of the pythagorean theorem is exactly why this is.

4 0

3 years ago

What is the y-intercept of a line that passes through the points (5, -6.5) and (-12, 2)?

n200080 [17]

Answer:

y-intercept = -4

Step-by-step explanation:

equation of a line: y=mx+b

two points given are (5, -6.5) and (-12, 2)

first we can easily find value of m or the slope, by using the slope formula. the value of m=-0.5.

formua to find m: $\frac{2-(-6.5)}{-12-5}$ = -0.5

to find the value of b (the y-intercept), we need to plug in a y and x value, we are given 2 ordered pairs, you can use either one and plug x-value in for x and the y-value in for y.

if i plug in (5, -6.5), my equation looks like this: -6.5=5(-0.5)+b

then you just solve for b and it turns out to be -4.

4 0

3 years ago

You currently earn $11,50 per hour. Assuming that you work 40-hour weeks with no raises, what total gross salary will

RUDIKE [14]

Answer: $119,600

Step-by-step explanation:

8 0

3 years ago