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3 years ago

What is the volume of the prism with a base of 6 height of 5 and lenght of 10

1 answer:

8 0

$\sf Hello!$

$\sf Dimensions\: of \:the \:Prism$ :

• $\sf Base,\: b = 6$
• $\sf Height, \:h = 5$
• $\sf Height, \:H = 10$

$\sf Then,$

$\sf Volume \:of \:Prism$ :

= $\dfrac {\sf 1}{\sf 2} × \sf b × \sf h × \sf H$

= $\dfrac {\sf 1}{\sf 2} × \sf 6 × \sf 5 × \sf 10$

= $\sf 6 × 5 × 5$

= $\sf 150$

$\sf Hence,$
$\sf The\: volume\: of \: the\: prism\: is \:150\: cubic\: units.$

~ $\sf iCarl$

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Todd bought a game for $36 with a coupon for 25% off. How much would it have cost without the coupon?

kotykmax [81]

Answer:

Step-by-step explanation:

x*0.75=36

x=36/0.75=48 $

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3 years ago

Read 2 more answers

Mel Needs to park his car for eight hours. Spikes parking place charges five dollars per hour for the first three hours and thre

Dima020 [189]

Answer:

Spike's Parking
$5 less

Step-by-step explanation:

After 3 hours, Spike charges 6 dollars per hour. For 3 hours, the charge is only $5×3 = $15 (which is $3 less than $6×3). So the rate after 3 hours can be modeled by ...

s(h) = 6h -3

For 8 hours, s(8) = 6·8 -3 = 45 . . . . dollars

After 4 hours, Main Deck charges 8 dollars per hour. For 4 hours, the charge is only $18 (which is $14 less than $8×4). So the rate after 4 hours can be modeled by ...

m(h) = 8h -14

For 8 hours, m(8) = 8·8 -14 = 50 . . . . dollars

For 8 hours, the $45 charge at Spike's is $5 less than the $50 charge at Main Deck.

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3 years ago

Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 81 mm, 7 mm, 6 mm B. 81 mm, 7 mm, 72

Lisa [10]

We know that
The triangle inequality states that for any triangle, the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so
case A. 81 mm, 7 mm, 6 mm
6+7 is not > 81

case B. 81 mm, 7 mm, 72 mm
72+7 is not > 81

case C. 81 mm, 7 mm, 88 mm
81+7 is not > 88

case D. 81 mm, 7 mm, 77 mm
81+7 is > 77------> ok
77+7 is > 81-----> ok
81+77 is > 7-----> is ok

the answer is the option
D. 81 mm, 7 mm, 77 mm

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3 years ago

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$ is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4}$

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

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3 years ago

You offer senior citizens a 20% discount on their tune-ups at your gas station. Assuming that an average of 50 senior citizens g

GREYUIT [131]

X over 49.5 and 20 over 100 then you cross multiply and you get 100x is equal to 990 you divide 100x and 990 both by 100 and get x and 9.9 then you have 50 seniors a month that you give the discount to so you multiply 9.9 by 50 and get 495 so the total discount you give on an average monthly basis is $495.00 Hope this helped

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4 years ago