Answer:
Step-by-step explanation:
Let the numbers be x and y.
<u>The equations are:</u>
<u>Add up the equations to eliminate y and solve for x:</u>
- x - y + 2x + y = 2 + 13
- 3x = 15
- x = 15/3
- x = 5
<u>Now find the value of y:</u>
- y = x - 2
- y = 5 - 2
- y = 3
Answer:
90 hours
Step-by-step explanation:
- 67 + 6 + 9 + 8 = 90 hours
<span>Given that Tamara's annual salary is $48,000 means that his monthly salary is $48,000 / 12 = $4,000. For Tamara to make $6,000 this month, she needs to make an additional $2,000 from commissions in addition to her salary. Given that she earns 4% commision on all sales, let the sale she needs to make to get $2,000 be S, then 4 / 100 x S = 2000 this gives 0.04S = 2000 giving that S = 2000 / 0.04 = 50,000. Therefore, Tamara needs to make a sales of $50,000 to be able to earn $6,000 this month.</span>
Answer:
The area is growing at a rate of
Step-by-step explanation:
<em>Notice that this problem requires the use of implicit differentiation in related rates (some some calculus concepts to be understood), and not all middle school students cover such.</em>
We identify that the info given on the increasing rate of the circle's radius is 3 and we identify such as the following differential rate:
Our unknown is the rate at which the area (A) of the circle is growing under these circumstances,that is, we need to find .
So we look into a formula for the area (A) of a circle in terms of its radius (r), so as to have a way of connecting both quantities (A and r):
We now apply the derivative operator with respect to time () to this equation, and use chain rule as we find the quadratic form of the radius:
Now we replace the known values of the rate at which the radius is growing ( ), and also the value of the radius (r = 12 cm) at which we need to find he specific rate of change for the area :
which we can round to one decimal place as: