To solve the question we proceed as follows:
length=width=x ; g=height=h
thus
V=x*x*h
v=x^2h
dv/dt=2xh dx/dt+x^2 dh/dt
but
dx/dt=2 ft/sec
dh/dt=-2 ft/sec
thus plugging the values in the equation we get:
dv/dt=2×10×12+10²(-2)
dv/dt=240-200
dv/dt=40 ft³/sec
Answer:
x = 15.2
Step-by-step explanation:
you can use the Pythagorean Theorem on either half of the large triangle because you know one leg is 29/2 and the hypotenuse is 21
(29/2)² + x² = 21²
210.25 + x² = 441
x² = 230.75
x = 
x = 15.2
Answer:
200 students must agree to attend in order for the school to have the festival.
Step-by-step explanation:
200 is 40% of 500. We can also use fractions to figure this out.
For 100 to become 500 it must be multiplied by 5. And whatever we do to the denominator we have to do to the numerator. So we multiply 40 × 5 = <em>x</em>
<em>x</em> = 200
Remember that multiplication is <em>commutative</em>, which means the order in which we multiply things doesn't matter.
The order of u × q × v × p (which we can abbreviate uqvp) isn't as important as the fact that <em>we're multiplying all four values together</em>. We could just as easily rewrite the expression as pquv, and it'd represent the same value.
To find this value then, we can simply multiply pq and uv - the values we already know - together.
If we start with the expression pq = 23, we can multiply either side by uv (taking advantage of the <em>multiplication property of equality) </em>to get
pquv = 23uv
And since we know that uv = 1/23, we can use the <em>substitution property of equality</em> to replace the uv on the right side with 1/23:
pquv = 23(1/23)
The <em>inverse property of multiplication </em>states that any number multiplied by its inverse (its reciprocal) gives us 1. 23 and 1/23 are reciprocals of each other, so 23(1/23) = 1, which means
pquv = 1
Finally, going back to the second paragraph, we can use the <em>commutative property of multiplication </em>to rearrange the left side of the equation, giving us the solution
uqvp = 1
Answer:
x = 8, y = -5
Step-by-step explanation:
Multiplying the 2nd equation by 3, we get -3x-9y = 21. Then eliminating with the first equation we get -5y = 25. y = -5. Substituting this into the original equation, we get x = 8.
