<span>Surface Area <span>= [Base Area] + 12 × Perimeter × [Slant Length]
</span></span><span>
Ryan square pyramid
</span>[Base Area]=10*10=100 feet²
<span>Perimeter=10+10+10+10=40 feet
</span>[Slant Length]=12 feet
Surface Area=100+12*40*12=5860 feet²
Scott square pyramid
[Base Area]=12*12=144 feet²
Perimeter=12+12+12+12=48 feet
[Slant Length]=10 feet
Surface Area=144+12*48*10=5904 feet²
the answer is <span>D.Scott’s pyramid has a greater surface area.</span>
<span>We want to optimize f(x,y,z)=x^2 y^2 z^2, subject to g(x,y,z) = x^2 + y^2 + z^2 = 289.
Then, ∇f = λ∇g ==> <2xy^2 z^2, 2x^2 yz^2, 2x^2 y^2 z> = λ<2x, 2y, 2z>.
Equating like entries:
xy^2 z^2 = λx
x^2 yz^2 = λy
x^2 y^2 z = λz.
Hence, x^2 y^2 z^2 = λx^2 = λy^2 = λz^2.
(i) If λ = 0, then at least one of x, y, z is 0, and thus f(x,y,z) = 0 <---Minimum
(Note that there are infinitely many such points.)
(f being a perfect square implies that this has to be the minimum.)
(ii) Otherwise, we have x^2 = y^2 = z^2.
Substituting this into g yields 3x^2 = 289 ==> x = ±17/√3.
This yields eight critical points (all signage possibilities)
(x, y, z) = (±17/√3, ±17/√3, ±17/√3), and
f(±17/√3, ±17/√3, ±17/√3) = (289/3)^3 <----Maximum
I hope this helps! </span><span>
</span>
Answer:
The last answer choice: Phillip will lose (1/2) of his points in his next crash.
Step-by-step explanation:
For every crash, Phillips points will continue to reduce by (1/2) the amount that he currently has. That means after 1 crash, he will 5,000 points left. After 2 crashes, he will have 2,500 points left. After 3 crashes, he will have 1250 points left. After 4 crashes, he will have 625 points left, and so on like that.
The measure of angle PQR when Zubin drew a circle with right triangle will be 65°.
<h3>How to find the measure of the angle?</h3>
From the information given, when Zubin drew a circle with right triangle, arc QR measures 50 degrees.
Therefore, the measure of angle PQR will be:
= 180° - 90° - (1/2 × 50°)
= 180° - 90° - 25°
= 65°
In conclusion, the angle is 65°.
Learn more about circle on:
brainly.com/question/24375372
Answer:
The characteristic of a logarithm is the number to the left of the decimal.
(The characteristic is like an exponent).
We are working with base 3 logs.
So if we are increasing a number by multiplying it by the base of the logarithm, (in this case 3 times 3) then we increase the characteristic by two.
Since 2 is the exponent of 3^2 then to get the log 3 of 72, we get the log3 (8) and increase it by 2.
1.8928 +2 = 3.8928
Had we been working with base 10 logs and we were multiplying a number by 100, We would increase the characteristic by 2 because 100 = 10^2.
Step-by-step explanation:
