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Zolol [24]
3 years ago
11

Karen made 175 quarts of punch for her son and 11.3 quarts for

Mathematics
1 answer:
Alenkinab [10]3 years ago
6 0

Answer:

186.3 quarts of punch

Step-by-step explanation:

175+11.3=186.3

it asks how much did she make in total so you would need to add the 2 together to get the total

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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
pantera1 [17]

Answer:

The height of the pile is increasing at the rate of  \mathbf{ \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

Step-by-step explanation:

Given that :

Gravel is being dumped from a conveyor belt at a rate of 20 ft³ /min

i.e \dfrac{dV}{dt}= 20 \ ft^3/min

we know that radius r is always twice the   diameter d

i.e d = 2r

Given that :

the shape of a cone whose base diameter and height are always equal.

then d = h = 2r

h = 2r

r = h/2

The volume of a cone can be given by the formula:

V = \dfrac{\pi r^2 h}{3}

V = \dfrac{\pi (h/2)^2 h}{3}

V = \dfrac{1}{12} \pi h^3

V = \dfrac{ \pi h^3}{12}

Taking the differentiation of volume V with respect to time t; we have:

\dfrac{dV}{dt }= (\dfrac{d}{dh}(\dfrac{\pi h^3}{12})) \times \dfrac{dh}{dt}

\dfrac{dV}{dt }= (\dfrac{\pi h^2}{4} ) \times \dfrac{dh}{dt}

we know that:

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

So;we have:

20= (\dfrac{\pi (15)^2}{4} ) \times \dfrac{dh}{dt}

20= 56.25 \pi \times \dfrac{dh}{dt}

\mathbf{\dfrac{dh}{dt}= \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

The height of the pile is increasing at the rate of  \mathbf{ \dfrac{20}{56.25 \pi}   \ \ \ \ \  ft/min}

8 0
3 years ago
PLEASE PLEASE HELP
noname [10]

Answer:

8.51x10^{-3}cm

Step-by-step explanation:

In order to add or subtract numbers in scientific notation, the powers of ten must have the same exponent.  In this caes the diameter of an average human body cell is a power of -4 and the diameter of a plant cell is a power of -3.  In order to add them, we can move the decimal over for the body cell diameter:

5.1x10^{-4}=0.51x10^{-3}

Add the two values: 0.51x10^{-3}+8x10^{-3}=8.51x10^{-3}cm

7 0
3 years ago
Read 2 more answers
HELP ASAP!!!!!!!
Musya8 [376]

I believe the correct option is C.

8 0
3 years ago
What’s the answer to this ?
Juli2301 [7.4K]

Answer:

the second one because 3 divided by 1.5 is 2 then it's right

7 0
3 years ago
Need answer quickly! thank you in advance!
anyanavicka [17]

Answer:

b)(b²-a²)

Step-by-step explanation:

a cotθ + b cosecθ =p

b cotθ + a cosecθ =q

Now,

p²- q²

=(a cotθ + b cosecθ)² - (b cotθ + a cosecθ)²     [a²-b²=(a+b)(a-b)]

=(acotθ+bcosecθ + bcotθ+ acosecθ) (a cotθ + bcosecθ -bcotθ-acosecθ)

={a(cotθ+cosecθ)+b(cotθ+cosecθ)} {a (cotθ-cosecθ)+b (cosecθ-cotθ)}

={a(cotθ+cosecθ)+b(cotθ+cosecθ)} [a (cotθ-cosecθ) + {- b (cotθ-cosecθ)} ]

={a(cotθ+cosecθ)+b(cotθ+cosecθ)} {a (cotθ-cosecθ) - b (cotθ-cosecθ)}

={(cotθ+cosecθ)(a+b)} {(cotθ-cosecθ) (a-b)}

=(cotθ+cosecθ) (a+b) (cotθ-cosecθ) (a-b)

=(cotθ+cosecθ) (cotθ-cosecθ) (a+b) (a-b)        

= (cot²θ-cosec²θ) (a²-b²)                                 [(a+b) (a-b)= (a²-b²)]

= -1 . (a²-b²)                               [ 1+cot²θ=cosec²θ ; ∴cot²θ-cosec²θ=-1]

=(b²-a²)

6 0
3 years ago
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