Please help on questions 8&9!!!!(higher maths vectors)

Mathematics

1 answer:

alekssr [168]3 years ago

4 0

How are we supposed to draw a diagram for you? do you want me to explain to you how to answer the question?

You might be interested in

The volume V of an ice cream cone is given by V = 2 3 πR3 + 1 3 πR2h where R is the common radius of the spherical cap and the c

Nuetrik [128]

Answer:

The change in volume is estimated to be 17.20 $\rm{in^3}$

Step-by-step explanation:

The linearization or linear approximation of a function $f(x)$ is given by:

$f(x_0+dx) \approx f(x_0) + df(x)|_{x_0}$ where $df$ is the total differential of the function evaluated in the given point.

For the given function, the linearization is:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh$

Taking $R_0=1.5$ inches and $h=3$ inches and evaluating the partial derivatives we obtain:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh\\V(R, h) = V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh$

substituting the values and taking $dx=0.1$ and $dh=0.3$ inches we have:

$V(R_0+dR, h_0+dh) =V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh\\V(1.5+0.1, 3+0.3) =V(1.5, 3) + (\frac{2 \cdot 3 \pi \cdot 1.5}{3} + 2 \pi 1.5^2)\cdot 0.1 + (\frac{\pi 1.5^2}{3} )\cdot 0.3\\V(1.5+0.1, 3+0.3) = 17.2002\\\boxed{V(1.5+0.1, 3+0.3) \approx 17.20}$

Therefore the change in volume is estimated to be 17.20 $\rm{in^3}$

4 0

3 years ago

Katie draws two chords in a circle in a certain way. She then draws in four segments between adjacent endpoints of the chords to

FromTheMoon [43]

Answer: The answer that is not true is choice D.

If Katie drew those chords and those line segments to form a square, then the diagonals would have to be congruent. The only way to have them would be through the center, therefore they must be diameters.

And if it is a square, then the diagonals are perpendicular bisectors meaning the angles would be right angles not acute or obtuse as in Choice D. <span />

7 0

3 years ago

-3x+4y=-4 -2x+5y=9<br>solve the following system of equations

Vesnalui [34]

the answer is x= 8, and y=5

3 0

3 years ago

Read 2 more answers

GREATEST COMMON FACTOR OF 8 OF 36

Mekhanik [1.2K]

Answer:

Step-by-step explanation: