Answer:
156.5
Step-by-step explanation:
Thinking process:
The area can be calculated using the formula:
We let the substitution take place.
Therefore, we let
Thus,
So,
Also, the interval of the integration changes to [ 37, 65]
Thus,
=
= 156.5 units²
Answer:
Rosaria purchased 50 bracelets and 70 necklaces
Step-by-step explanation:
Let the number of bracelets be b and the number of necklaces be n
b + n = 120 •••••(i)
Secondly;
10b + 11n = 1270 ••••(ii)
Total cost of b bracelets at 10 per 1 is 10b
Total cost of n bracelets at 11 per 1 is 11n
Adding both gives 1270
From i, b = 120-n
Substitute this into ii
10(120-n) + 11n = 1270
1200 - 10n + 11n = 1270
n = 1270-1200
n = 70
b = 120-n
b = 120-70
b = 50
6 strawberries.
one plum= 32 calories
one strawberry=4 calories
total calories=56
56-32=24
24 calories come from the strawberries
24÷4=6
Therefor 6 strawberries
Answer:
108 cm²
Step-by-step explanation:
A = πr²
A = 3 * 6²
A = 3 * 36
A = 108
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Answer:
increasing 7/24 ft per week
Step-by-step explanation:
An expression for the length of the base can be written from the Pythagorean theorem relation between the sides of the triangle.
If the height is 7-x, where x is the number of weeks after the height is 7 feet, then the base length is ...
b = √(25^2 -(7-x)^2) = √(625 -(49 -14x +x^2)) = √(-x^2 +14x +576)
Then the rate of change of b with respect to x is ...
b' = (-2x +14)/(2√(-x^2 +14x +576))
When x=0, the rate of change of the base is ...
b' = 14/(2√576) = 7/24
The base is increasing 7/24 ft per week when the height is 7 ft.