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1 year ago

11

tara bakes 225 cookies in 5 hours, and she uses 8 pounds of sugar. she divide 225 by 5 to grt a rate of 45. which of the followi

ng correspond to this rate

1 answer:

Sati [7]1 year ago

6 0

Options :

A cookies per pound

B. O pounds per hour

c. cookies per hour

D. hours per cookie

Answer: C.) Cookies per hour

Step-by-step explanation:

Given the following :

Number of cookies baked = 225 cookies

Total time taken = 5 hours

Amount of sugar used = 8 pounds

Tara divides 225 by 5; 225 / 5 = 45

Rate gives the amount or number of times something occurs within a given period, Hence

The rate obtained by Tara corresponds to the ratio of ; (Total cookies baked / total time taken) = (225 / 5), this translates to the amount or number of cookies baked within an hour.

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1 year ago

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2 years ago

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Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. <u>Normal</u> <u>vector</u> is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = $\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]$ $\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]$

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

$a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0$

Then, replacing with point P and normal vector n:

$36(x-5) + 20(y-0) + 45(z-0) = 0$

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

$z = \frac{180-36x-20y}{45}$

When z = 0:

$y = 9 + \frac{-9x}{5}$

When z=0 and y=0:

x = 5

Then, triple integral is:

$\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx$

Calculating:

$\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx$

$\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx$

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$\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx$

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$\frac{1}{45} [30375-60750+118462.5-39150]$

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<u>The volume of the tetrahedon is 1087.5 cubic units.</u>

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1 year ago