Answer:
true
Step-by-step explanation:
Pam saved 40
her bro saves 100
let us take this as ration 40 is to 100 which can also be written in fractional for like 40/100 now we simplify it how by dividing both by 20 so (40/20)/(100/20) which will give 2/5 which can be written as 2 is to 5 so this is true
Answer:
Time taken to reach maximum height=4.69 seconds
Maximum Height=371.56feet
Step-by-step explanation:
Given the height function of the pumpkin:
![h = -16t^2 + 150t + 20](https://tex.z-dn.net/?f=h%20%3D%20-16t%5E2%20%2B%20150t%20%2B%2020)
The pumpkin reaches it's maximum height at its axis of symmetry.
Therefore, we determine its equation of symmetry.
The equation of symmetry:
![t=-\frac{b}{2a}](https://tex.z-dn.net/?f=t%3D-%5Cfrac%7Bb%7D%7B2a%7D)
a=-16, b=150.
Therefore:
![t=-\frac{150}{2*-16}=4.6875](https://tex.z-dn.net/?f=t%3D-%5Cfrac%7B150%7D%7B2%2A-16%7D%3D4.6875)
The pumpkin reaches maximum height after 4.6875 seconds.
At t=4.6875
![h = -16(4.6875)^2 + 150(4.6875)+ 20\\=371.5625\approx 371.56 \:feet](https://tex.z-dn.net/?f=h%20%3D%20-16%284.6875%29%5E2%20%2B%20150%284.6875%29%2B%2020%5C%5C%3D371.5625%5Capprox%20371.56%20%5C%3Afeet)
The pumpkin's maximum height is 371.56 feet.
Answer:
Therefore surface integral is
.
Step-by-step explanation:
Given function is,
![\vec{F}=\frac{bx}{a}\uvec{i}+\frac{ay}{b}\uvec{j}](https://tex.z-dn.net/?f=%5Cvec%7BF%7D%3D%5Cfrac%7Bbx%7D%7Ba%7D%5Cuvec%7Bi%7D%2B%5Cfrac%7Bay%7D%7Bb%7D%5Cuvec%7Bj%7D)
To find,
where S=A=surfece of elliptic cylinder we have to apply Divergence theorem so that,
![\int\int_{S}\vec{F}dS](https://tex.z-dn.net/?f=%5Cint%5Cint_%7BS%7D%5Cvec%7BF%7DdS)
![=\int\int\int_V\nabla.\vec{F}dV](https://tex.z-dn.net/?f=%3D%5Cint%5Cint%5Cint_V%5Cnabla.%5Cvec%7BF%7DdV)
![=\frac{a^2+b^2}{ab}\int\int\int_VdV](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%5E2%2Bb%5E2%7D%7Bab%7D%5Cint%5Cint%5Cint_VdV)
![=\frac{a^2+b^2}{ab}\times \textit{Volume of the elliptic cylinder}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%5E2%2Bb%5E2%7D%7Bab%7D%5Ctimes%20%5Ctextit%7BVolume%20of%20the%20elliptic%20cylinder%7D)
![=\frac{a^2+b^2}{ab}\times \pi ab\times 2c=\pi (a^2+b^2)c](https://tex.z-dn.net/?f=%3D%5Cfrac%7Ba%5E2%2Bb%5E2%7D%7Bab%7D%5Ctimes%20%5Cpi%20ab%5Ctimes%202c%3D%5Cpi%20%28a%5E2%2Bb%5E2%29c)
- If unit vector
directed in positive (outward) direction then z=c and,
![=\int\int_{S_1}.dA=0](https://tex.z-dn.net/?f=%3D%5Cint%5Cint_%7BS_1%7D%3C%5Cfrac%7Bbx%7D%7Ba%7D%2C%5Cfrac%7Bay%7D%7Bb%7D%2C%200%3E.%3C0%2C0%2C1%3EdA%3D0)
- If unit vector
directed in negative (inward) direction then z=-c and,
![=\int\int_{S_2}. -dA=0](https://tex.z-dn.net/?f=%3D%5Cint%5Cint_%7BS_2%7D%3C%5Cfrac%7Bbx%7D%7Ba%7D%2C%5Cfrac%7Bay%7D%7Bb%7D%2C%200%3E.%20-%3C0%2C0%2C1%3EdA%3D0)
Therefore surface integral without unit vector of the surface is,
![\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c](https://tex.z-dn.net/?f=%5Cpi%28a%5E2%2Bb%5E2%29c-0-0%3D%5Cpi%28a%5E2%2Bb%5E2%29c)
Answer:
Because you didn't give the line, it is impossible to write it completely. However, the line would be y - 1 = m(x + 3), in which m is the slope in the line.
Step-by-step explanation:
We know this firstly because parallel lines have the same slope. So whatever the slope is to the given line, it must match the point-slope form.
So, we'll call this mystery slope m and then use the point in plug in the point into point-slope form.
y - y1 = m(x - x1)
y - 1 = m(x - -3)
y - 1 = m(x + 3)