2x(z+4)+1-z+xy; x=4, y=2, z=-3

Mathematics

2 answers:

Marina CMI [18]2 years ago

6 0

Answer:

=20

Step-by-step explanation:

in pic

(hope this helps can I pls have brainlist (crown) ☺️)

Arte-miy333 [17]2 years ago

5 0

$\huge\text{Hey there!}$

<h2> $\large\textsf{2x(z + 4) + 1 - z + xy}$ </h2><h2> $\large\text{= 2(4)(-3 + 4) + 1 - (-3) + 4(2)}$ </h2><h2> $\large\text{= 8(1) + 1 - (-3) + 4(2)}$ </h2><h2> $\large\text{= 8 + 1 - (-3) + 4(2)}$ </h2><h2> $\large\text{= 9 - (-3) + 4(2)}$ </h2><h2> $\large\text{= 12 + 4(2)}$ </h2><h2> $\large\text{= 12 + 8}$ </h2><h2> $\large\text{= 20}$ </h2><h2 /><h3> $\large\boxed{\textsf{Therefore, your answer is: \rm{20}}}\huge\checkmark$ </h3><h3> $\mathsf{Good \ luck \ on \ your \ assignment \ and \ enjoy \ your \ day!}$ </h3><h3 /><h3> $\frak{Amphitrite1040:)}$ </h3>

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Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$