3. Error Analysis Isabel says that the equation x - 2 = -(x - 2) has no
1 answer:
Given:
The equation is
Isabel says that the given equation has no solution because a number can never be equal to its opposite.
To find:
Isabel's mistake.
Solution:
Her reason "a number can never be equal to its opposite" is not correct.
Zero is a number that can be equal to its opposite.
So, the given equation has solution for which LHS=RHS=0.
We have,
Add x and 2 on both sides.
Divide both sides by 2.
So, the given equation has a solution x=2.
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The product of the lengths of the parts of the chord is equal to the product of the lengths of the parts of the chord that divides it.
(7 cm)*(8 cm) = n*(4 cm)
(7*8 cm²)/(4 cm) = n
14 cm = n
(7 cm)*(8 cm) = n*(4 cm)
(7*8 cm²)/(4 cm) = n
14 cm = n
The matrix equation that represents this situation is
![\left[\begin{array}{ccc}3&2&0\\1&0&4\\3&1&1\end{array}\right]*\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}13.50\\16.50\\14.00\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%262%260%5C%5C1%260%264%5C%5C3%261%261%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D13.50%5C%5C16.50%5C%5C14.00%5Cend%7Barray%7D%5Cright%5D%20)
Use technology to find the inverse of matrix A:
![A^{-1}= \left[\begin{array}{ccc}-\frac{2}{5}&-\frac{1}{5}&\frac{4}{5}\\ \frac{11}{10}&\frac{3}{10}&-\frac{6}{5}\\\frac{1}{10}&\frac{3}{10}&-\frac{1}{5}\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B2%7D%7B5%7D%26-%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B4%7D%7B5%7D%5C%5C%0A%5Cfrac%7B11%7D%7B10%7D%26%5Cfrac%7B3%7D%7B10%7D%26-%5Cfrac%7B6%7D%7B5%7D%5C%5C%5Cfrac%7B1%7D%7B10%7D%26%5Cfrac%7B3%7D%7B10%7D%26-%5Cfrac%7B1%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D%20)
Multiplying A inverse by B, we get the solution matrix
[tex]\left[\begin{array}{ccc}2.50\\3\\3.50\end{array}\right][\tex]
Use technology to find the inverse of matrix A:
Multiplying A inverse by B, we get the solution matrix
[tex]\left[\begin{array}{ccc}2.50\\3\\3.50\end{array}\right][\tex]
radius of bottle is 7 cm. height is 28 cm
so total milk in bottle is equal to total volum of bottle.
so volume of cylinder is = pi × r^2 × h
V = (22/7 )× 7×7×28 = 22×7×28
= 4312 cm^3
so volume of the milk before used to make tea is 4312 cm^3
now milk taken to make tea make height reduced to 20 cm.
so volume of the left milk in bottole is
= (22/7) × 7×7×20 = 22×7×20
= 3080 cm^3
so milk used for making tea = total milk before making the tea - total milk left in bottle after making the tea
= 4312 - 3080 = 1232 cm ^3
so volume of milk used
