<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
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Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
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See the attached drawing below. The altitude BH forms three similar triangles which makes the proportion below possible
HC/BH = BH/AH
x/y = y/(12-x) ... substitution
x(12-x) = y^2 ... cross multiply
y^2 = -x^2+12x
note how I isolated y^2 instead of y. We will use this equation later.
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Focus on triangle AHB. Use the pythagorean theorem
(BH)^2 + (AH)^2 = (AB)^2
(y)^2 + (12-x)^2 = (9)^2
y^2 + 144-24x+x^2 = 81
-x^2+12x + 144-24x+x^2 = 81 ... replace y^2 with -x^2+12x
-x^2+12x + 144-24x+x^2-81 = 0
-12x + 63 = 0
-12x = -63
x = -63/(-12)
x = 5.25 <<-- answer in decimal form
x = 5 + 0.25
x = 5 + 1/4
x = 20/4 + 1/4
x = 21/4 <<-- answer as a fraction
Answer:
Step-by-step explanation:
You have the following differential equation:
This equation can be written as:
where
If the differential equation is exact, it is necessary the following:
Then, you evaluate the partial derivatives:
The partial derivatives are equal, then, the differential equation is exact.
In order to obtain the solution of the equation you first integrate M or N:
(1)
Next, you derive the last equation respect to t:
however, the last derivative must be equal to M. From there you can calculate g(t):
Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:
where C is the constant of integration
The 8 ounce can of tomatoes that costs $1.14 has the better unit price.
Explanation: It’s $0.14 per oz and the 10-ounce can has the unit price of $0.19. The cheaper unit price is the “better” unit price.
Answer:
1/5
Step-by-step explanation:
Given,
Soccer 7
basketball 9
baseball 4
Tennis 5
So, the total number of students: 7+9+4+5= 25
So the ratio will be 5/25 or 1/5 because 5 students had chosen tennis as their favorite sport.