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3 years ago

Find the exact value: tan40/cot50 sec55/csc35 SHOW ALL WORK!

1 answer:

5 0

These are the important trigonometric relations to base on:

cot (x) = 1/tan(x)
sec(x) = 1/cos(x)
csc(x) = 1/sin(x)

Following these properties, we could simplify the equation and input into the calculator to determine the exact value.

<span>tan40/cot50 = tan40/(1/tan50) = tan40tan50 = 1

</span><span>sec55/csc35 = (1/cos 55)/(1/sin 35) = sin35/cos55 = 1</span>

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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.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

5 0

3 years ago

Function g can be thought of as a translation (shifted) version of f(x)=x^2

dimaraw [331]

Answer:

(x+5)²

Step-by-step explanation:

To solve this we just need to shift the graph 5 spots to the left

to do this we need to add 5 to the x

(x+5)²

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3 years ago

Please help me with this question

sergejj [24]

Answer:

49π

Step-by-step explanation:

Circle area: πr^2

Since A to C is 14, and they're both in the center, A to B and B to C will both be 7 as a radius.

Since we know the radius, we can put it in the formula, πr^2.

We only need to solve for one circle, since both circles are the same. By solving the circle, we will put in 7 for the radius, giving us π7^2, which is 49π.

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3 years ago

What value in Vertex Form moves the graph up?

Leno4ka [110]

Changing from negative to positive

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3 years ago

Venetta buys 2 pounds of pistachios and 3 pounds of almonds. The pistachios cost $4 more per pound than the almonds. She pays a

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Answer: the answer is 2 and 5

Step-by-step explanation:

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3 years ago