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Sholpan [36]
3 years ago
14

A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obt

ained only by surgery. Suppose that a CAT scan of a human liver shows cross-sections spaced 1.5 cm apart. The liver is 15 cm long and the cross-sectional areas, in square centimeters, are 0, 18, 59, 78, 93, 105, 118, 128, 63, 38, and 0. Use the Midpoint Rule with n = 5 to estimate the volume V of the liver.

Mathematics
1 answer:
Semmy [17]3 years ago
6 0

Answer:

V=1101cm^3

Step-by-step explanation:

You are given this data:

\left[\begin{array}{cccccccccccc}long&0&1.5&3&4.5&6&7.5&9&10.5&12&13.5&15&&\\Area&0&18&59&78&93&105&118&128&63&38&0\end{array}\right]

First, calculate the x points by dividing the total length in 5:

\Delta{x}=\frac{l_f-l_0}{5}= \frac{15-0}{5}= 3

x=3,6,9,12,15

Now you calculate the half point of the x axis intervals you just calculated:

x_h=1.5,4.5,7.5,10.5,13.5

and find the function values of each of them (the Area for each cut):

A(1.5) = 18

A(4.5)=78

A(7.5)=105

A(10.5)=128

A(13.5)=38

Now you have formed the rectangles (see diagram below).

To calculate the volume, just use the next equation given by the midpoint rule:

V=\Delta{x}\sum_1^5{h_{rectangle}}\\V=3\sum(18, 78, 105, 128, 38)\\V=3(367)\\V=1101cm^3

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Which statements are true about ΔJKL and ΔLMN? Select all that apply.
svp [43]

Answer:

A. ΔJKL and ΔLMN have only one pair of angles that are congruent

C. ΔJKL has angles that measure 50^o,60^o,70^o

Step-by-step explanation:

step 1

Find the value of x

we know that

m\angle KLJ=m\angle MLN ----> by vertical angles

substitute the given values

(6x-2)^o=(5x+10)^o

solve for x

6x-5x=10+2\\x=12

step 2

Find the measure of the interior angles of triangle JKL

we have

m\angle KLJ=(6(12)-2)=70^o

m\angle KJL=(5(12))=60^o

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

m\angle JKL=180^o-130^o=50^o

therefore

Triangle JKL has angles that measure 50^o,60^o,70^o

step 3

Find the measure of the interior angles of triangle LMN

we have

m\angle MLN=(5(12)+10)=70^o

m\angle LMN=(6(12)-7)=65^o

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

m\angle LNM=180^o-135^o=45^o

Triangle LMN has angles that measure 45^o,65^o,70^o

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding angles of triangle JKL and LMN are not congruent

therefore

The triangles are not similar

<u><em>Verify each statement</em></u>

Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent

The statement is true (see the explanation)

Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent

The statement is false

Because have only one pair of angles that are congruent

Part c) ΔJKL has angles that measure 50^o,60^o,70^o

The statement is true  (see the explanation)

Part d) ΔLMN has angles that measure 50^o,60^o,70^o

The statement is false

Because, Triangle LMN has angles that measure 45^o,65^o,70^o

Part e) ΔJKL and ΔLMN are similar

The statement is false

Because, the corresponding angles are not congruent

6 0
3 years ago
1.7.3 Quiz: Intersecting Lines and Proofs
faltersainse [42]

Answer:

Perpendicular lines.

Perpendicular lines are lines that intersect at a right (90 degrees) angle.

7 0
2 years ago
Read 2 more answers
It took a sports store 9 weeks to sell 90 soccer<br> balls. How many are sold per week?
Anton [14]

Answer:

it would be 10 soccer balls

Step-by-step explanation:

10 every week if it was constant (because they could've sold more one week then less the next) but the genuine answer is 10 soccer balls :)

5 0
3 years ago
Which inequality models this problem?
IgorC [24]

The correct answer would be  

D) 25s>2500+4.5s

Hope this helps and have a great day!        


because $2500 spent + $4.50 supplies on each T shirt

so selling each shirt $25, if you want to make profit...total selling t shirt has to be greater than the total spent

4 0
3 years ago
I don't understand how to set up this problem.
Stells [14]
So its in the pic i hope it helps it is correct because i am in highschool i like to help people

7 0
3 years ago
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