Answer:
Around 100,i.e. 105
Step-by-step explanation:
In the given cube
Length of the cube = 7 unit cells
Breadth of the cube = 3 unit cells
Height of the cube = 5 unit cells
Therefore the number of unit cubes required to make such big cube is nothing but the volume of the big cube = length*breadth*height
⇒Number of cubes used to make that big cube= 7*5*3
= 105
Hence, option D (around 100) is the correct answer
Answer:
C
Step-by-step explanation:
In general for arithmetic sequences, recursive formulas are of the form
aₙ = aₙ₋₁ + d,
and the explicit formula (like tₙ in your problem), are of the form
aₙ = a₁ + (n - 1)d,
where d is the common difference. So converting between the two of these isn't so bad. In this case, your problem wants you to have an idea of what t₁ is (well, every answer says it's -5, so there you are) and what tₙ₊₁ is. Using the formulas above and your given tₙ = -5 + (n - 1)78, we can see that the common difference is 78, so no matter what we get ourselves into, the constant being added on at the end should be 78. That automatically throws out answer choice D.
But to narrow it down between the rest of them, you want to use the general form for the recursive formula and substitute (n + 1) for every instance of n. This will let you find tₙ₊₁ to match the requirements of your answer choices. So
tₙ₊₁ = t₍ₙ₊₁₎₋₁ + d ... Simplify the subscript
tₙ₊₁ = tₙ + d
Therefore, your formula for tₙ₊₁ = tₙ + 78, which is answer choice C.
For this case, the first thing we must do is define a variable.
We have then:
x: unknown number
We now write the expression that models the problem:
From here, we clear the value of x.
We have then:
Answer:
4/9 divided by 1/27 equals 12
Answer:
Step-by-step explanation:
Let's re-write the equations in order to get the variables as separated in independent terms as possible \:
First equation:
Second equation:
Third equation:
Now let's subtract term by term the reduced equation 3 from the reduced equation 1 in order to eliminate the term that contains "y":
Combine this last expression term by term with the reduced equation 2, and solve for "x" :
Now we use this value for "x" back in equation 1 to solve for "y":
And finally we solve for the third unknown "z":
Answer: infinite
Step-by-step explanation:
the lines go on forever
