48/4 = 12 teaspoons per each batch
454/12 = 37.83 batches can be made
3.49/37.83 = 0.092$ per each batch
That is the slope at f(1)
one way is to just take the derivitive
f'(x)=2x+(1/x)
for ti-89, do calc then derivitive then input "x^2+ln(x),x)" and click enter to get the derivitive
you would get f'(x)=2x+(1/x)
an easier way would be to have
click calc then differntiate then type x^2+ln(x),x)|x=1 then click enter
you get f'(1)=3
answer is 3
Answer:
The mentioned number in the exercise is:
Step-by-step explanation:
To obtain the mentioned number in the exercise, first you must write the equations you can obtain with it.
If:
- x = hundredths digit
- y = tens digit
- z = ones digit
We can write:
- x = z + 1 (the hundreds digit is one more than the ones digit).
- y = 2x (the tens digit is twice the hundreds digit).
- x + y + z = 11 (the sum of the digits is 11).
Taking into account these data, we can use the third equation and replace it to obtain the number and the value of each digit:
- x + y + z = 11
- (z + 1) + y + z = 11 (remember x = z + 1)
- z + 1 + y + z = 11
- z + z +y + 1 = 11 (we just ordered the equation)
- 2z + y + 1 = 11 (z + z = 2z)
- 2z + y = 11 - 1 (we passed the +1 to the other side of the equality to subtract)
- 2z + y = 10
- 2z + (2x) = 10 (remember y = 2x)
- 2z + 2x = 10
- 2z + 2(z + 1) = 10 (x = z + 1 again)
- 2z + 2z + 2 = 10
- 4z + 2 = 10
- 4z = 10 - 2
- 4z = 8
- z = 8/4
- <u>z = 2</u>
Now, we know z (the ones digit) is 2, we can use the first equation to obtain the value of x:
- x = z + 1
- x = 2 + 1
- <u>x = 3</u>
And we'll use the second equation to obtain the value of y (the tens digit):
- y = 2x
- y = 2(3)
- <u>y = 6</u>
Organizing the digits, we obtain the number:
- Number = xyz
- <u>Number = 362</u>
As you can see, <em><u>the obtained number is 362</u></em>.
Answer:
Step-by-step explanation:
Here, we need to know about the concept of the alternate interior angle theorem. This says that the alternate interior angle of two parallel lines formed with one transversal is equal. For a more graphical explanation, please refer to the attachment below.
--------------------------------------------------------------------------
Given
∠GBD=4x+84
∠EFC=16x
m∠GBD=m∠EFC
Solve
4x+84=16x ⇔ Given
4x+84-4x=16x-4x ⇔ Subtract 4x on both sides
84=12x ⇔ Simplify
84/12=12x/12 ⇔ Divide 12 on both sides
x=7 ⇔ Simplify
Substitute the x value into each angle expression
∠GBD=4x+84=4(7)+84=28+84=112
∠EFC=16x=16(7)=112
Hope this helps!! :)
Please let me know if you have any questions
