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Marina CMI [18]
1 year ago
10

The size, S, of a tumor (in cubic millimeters) is given by S=2^t, where t is the number of months since the tumor was discovered

. Give units with your answers.
(a) What is the total change in the size of the tumor during the first 9 months?

Answer: The total change is
and its units = .

(b) What is the average rate of change in the size of the tumor during the first 9 months?

Answer: The average rate of change is

,
and its units = .

(c) Use an interval of 0.001 to approximate the rate of change at which the tumor is growing at t=9.

Answer: The rate is

,
Mathematics
1 answer:
nordsb [41]1 year ago
4 0
A) you just do 2^9 which is 512 cubic millimeters
b) using the average rate of change formula you get 56.78 cubic millimeters per month
c) I do not understand at all I am stuck on the same one<span />
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What is the slope intercept form of (3,3) (7,-1)
kow [346]
Slope intercept form follows this general equation...
y=mx+b
With this information you have posted, all you can do is find slope, your m. To calculate for slope, you need to use this following equation...
m= \frac{y_2-y_1}{x_2-x_1}
Then, you pick one of your coordinate pairs to be 1 and the other to be 2. I will choose the first coordinate pair as 1, so...
m=\frac{-1-3}{7-3} =-1
You plug in -1 into your slope formula...
y=-1x+b
Now, to find your y-intercept, or b, you must plug in one of your coordinate pairs. In that equation, you may plug in the values (3,3), so you'll have...
3=-1(3)+b
Just solve for b and you will be done
5 0
1 year ago
Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy c
enyata [817]

Answer:

0.95

Step-by-step explanation:

The computation of the probability that a customer neither buys beer nor buys cigars is given below;

Given that, the probabilities are

The customers who purchased cigars be 0.02

The customers who purchased cigars + beer 0.50

And, the customers who purchased beer + cigars be 0.25

Now the probabilities where the customer purchased both

= 0.05 × 0.02

= 0.10

The probability where the customer purchased beer is

= 0.01 ÷ 0.25

= 0.04

Now the probability where a customer neither buys beer nor buys cigars is

= 1 - 0.02 + 0.04 - 0.01

= 0.95

4 0
1 year ago
5. Anthony has 80 pine tree seedlings to plant in his meadow. He first plants one row of 12
inna [77]
D. 16 clusters
Hope it helps
7 0
1 year ago
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).
Elan Coil [88]

Answer: \int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV = 1087.5

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

\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}}  \, dy } \, dx

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

\frac{1}{45} \int\limits^5_0  {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4}  } \, dx

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

\int\limits^5_0 {\int\limits {\int\ {xyz}  \, dy } \, dx = 1087.5

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

3 0
1 year ago
The cost of an item is 100% of its price. What number goes in place of ? in the addition problem?
Dmitry_Shevchenko [17]
I believe this is the complete problem. 

<span>Anton bought a picnic cooler. His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without the tax? The cost of an item is 100% of its price. What number goes in place of ? in the addition problem?
</span>
The answer is the below:

<span>He paid $7.473 without tax because $7.95 x 96% or (0.96) =$7.473</span>
8 0
1 year ago
Read 2 more answers
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