Answer:
B. 14 ⁴⁄₁₀
Step-by-step explanation:
I say its b because all u have to do it multiply 6 ⅕ but not the 6, just the 1 and the 5, just multiply by two and both fractions will have the same total amount which is 10 and 6 ⅕ will turn to 6 with 2/10 so all u have to do now is add that fraction to 8 ²⁄₁₀
Answer:
Needed 7 weeks
Step-by-step explanation:
Let x be the number of weeks.
<u>Nick</u>
- weighs 160 pounds;
- is gaining about 3 pounds per week;
- gains 3x pounds in x weeks;
- weighs 160 + 3x pounds after x weeks.
<u>Adam</u>
- weighs 195 pounds;
- is losing about 2 pounds per week;
- loses 2x pounds in x weeks;
- weighs 195 - 2x pounds in x weeks.
The equation that can be used to find the number of weeks that it will take them to weigh the same amount is
Solve this equation:
It if opens up, then the range will extednd to positive infinity.
if it opens down then the range will exted to negative infintiy.
there, 2 complete sentances
so we got range is from 4 to infinty so it opens up
Step-by-step explanation:
the box is
9 in × 3.5 in × 4.5 in = 141.75 in³
each block is
0.5 in × 0.5 in × 0.5 in = 0.125 in³ (1/8 in³)
so, we can fit
141.75 / 0.125 = 1134
blocks into the box.
and they fit neatly, as the dimensions of the box and the cubes allow a tight packing without any empty left over space in the box.
So it tells us that g(3) = -5 and g'(x) = x^2 + 7.
So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))
now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16
Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84
So we have our linear approximation for the two.
If you wanted to, you could check your answer by finding g(x). Since you know g'(x), take the antiderivative and we will get
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35
So just to check our linear approximations use that to find g(2.99) and g(3.01)
g(2.99) = -5.1597
g(3.01) = -4.8397
So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer. Not a bad method if you ever need to use it.
