Hello from MrBillDoesMath!
Discussion:
The slope of the tangent to the curve y = 4x^3 is given by the first derivative.
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y' = 4 (3x^2) = 12x^2
At (-3,-108), the slope is 12x^2 = 12(-3)^2 = 12*9 = 108
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y = mx + b
From the first part, m = 108 so y = 108x + b.
Substituting y = -108 when x = -3 gives
-108 = 108(-3) + b => add 3* 108 to both sides
-108 + 108(3) = b => as 3 -1 = 2
108*2 = b = 216
y = 108x + 216
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Thank you,
MrB
Answer:
7.9 X 10^3
standard form means it has to between 1 and 10
Answer:
The price for a small glass of milk is $0.95, and the price for a breakfast taco is $1.15.
Step-by-step explanation:
Let the price of a taco be x and the price for a small glass of milk be y.
Multiply the first equation by 2:
Subtract the new third equation from the second equation:
Hence, the price for a small glass of milk is $0.95.
Substitute y into the first equation.
Therefore, the price for a breakfast taco is $1.15.
Hope this helped!
Answer:
3 large doors
Step-by-step explanation:
Given
Represent small door with S and large with L
From the question, we understand that;
So, we have that
Required
Determine the number of Large doors that can be cut from the board
To do this, we simply divide the size of the board by the size of the large cabinet
i.e.
Convert feet to inches
Get the integer part of the decimal
Hence:
3 large doors can be gotten from the board
Answer:
Elena invested $ 1,700 at 5%, $ 700 at 4%, and $ 600 at 3%.
Step-by-step explanation:
Given that Elena receives $ 131 per year in simple interest from three investments totaling $ 3000, and part is invested at 3%, part at 4% and part at 5%, and there is $ 1000 more invested at 5% than at 4%, to find the amount invested at each rate, the following calculations must be performed:
1500 x 0.05 + 500 x 0.04 + 1000 x 0.03 = 75 + 20 + 30 = 125
1600 x 0.05 + 600 x 0.04 + 800 x 0.03 = 80 + 24 + 24 = 128
1700 x 0.05 + 700 x 0.04 + 600 x 0.03 = 85 + 28 + 18 = 131
Therefore, Elena invested $ 1,700 at 5%, $ 700 at 4%, and $ 600 at 3%
