Answer:
24 hours
Step-by-step explanation:
Kristen = 8 hours
Kristen and Courtney = 6 hours
Courtney = x hours
in six hours kirsten can do 6/8 of the job
6/8 = 3/4
So kirsten is going to be doing 3/4 of the job
Courtney is only going to do 1/4 of the job
Number of hours it takes Courtney to do the job
6/x = 1/4
Cross product
6 * 4 = x * 1
24 = x
x = 24 hours
It will take Courtney 24 hours to type a 50-page paper on her own
Answer: yes
Step-by-step explanation: because that how many times it could go in too it
Answer:
B.) 54π units²
Step-by-step explanation:
First, we need to find the height of the cone. We can do this using the Pythagreom Theorem.
a² + b² = c² <----- Pythagreom Theorem
3² + b² = 15² <----- Insert side lengths
9 + b² = 225 <----- Solve 3² and 15²
b² = 216 <----- Subtract 9 from both sides
b = 14.7 units <---- Take square root of 216
Now, we can use the surface area of a right cone equation to find the final answer.
r = 3 units
h = 14.7 units
SA = πr(r + √(h² + r²)) <----- Surface Area equation
SA = π(3)(3 + √(14.7² + 3²)) <----- Insert values
SA = π(3)(3 + √(216 + 9)) <----- Solve 14.7² and 3²
SA = π(3)(3 + √225) <----- Add 216 and 9
SA = π(3)(3 + 15) <----- Take square root of 225
SA = π(3)(18) <----- Add 3 and 15
SA = 54π units² <----- Multiply 3 and 18
Answer:
4x³
Step-by-step explanation:
d/dx ln(x⁴ + 7) = 1/(x⁴ + 7) × _?
To obtain the missing expression, let us simplify d/dx ln(x⁴ + 7). This can be obtained as follow:
Let y = ln (x⁴ + 7)
Let u = (x⁴ + 7)
Therefore,
ln(x⁴ + 7) = ln u
Thus,
y = ln u
dy/du = 1/u
Next, we shall determine du/dx. This is illustrated below:
u = (x⁴ + 7)
du/dx = 4x³
Finally, we shall determine dy/dx of ln (x⁴ + 7) as follow:
dy/dx = dy/du × du/dx
dy/du = 1/u
du/dx = 4x³
dy/dx = 1/u × 4x³
But:
u = (x⁴ + 7)
Therefore,
dy/dx = 1/(x⁴ + 7) × 4x³
Thus, the missing expression is 4x³
