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blondinia [14]
3 years ago
13

Find the total lateral area of the following

Mathematics
1 answer:
maxonik [38]3 years ago
7 0

Answer:

15π cm²

Step-by-step explanation:

The total lateral area of a cone

= πr√h² + r²

= √h² + r² = l

h = Height = 4cm

r = radius = 3cm

Hence:

= π × 3 √4² + 3²

= 3π × √16 + 9

= 3π × √25

= 3π × 5

= 15π cm²

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Two complex numbers have a sum of 14 and a product of 74. Write either of the two numbers.
IrinaVladis [17]

Answer:

Hello,

Step-by-step explanation:

The 2 numbers are roots of the equation:

U²-14U+74=0

Discriminant=14²-4*74=-100

<u>U=7-5i or U=7+5i</u>

3 0
2 years ago
Read 2 more answers
Divide 21 by g. Then, subtract 6.
IrinaVladis [17]
21/g - 6 = (21-6g)/g. G
8 0
3 years ago
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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 73 and 9
Naddika [18.5K]

Answer: After about 9.03 hours the temperature first reach 82 degrees.

Step-by-step explanation:

The sinusoidal function is given by :

y=A\sin[\omega(x-\alpha)]+C

where, A =  amplitude; \omega=\dfrac{2\pi}{period} ,  α= phase shift on the Y-axis and C = midline.

As per given,

Average daily temperature= C=\dfrac{73+97}{2}=85   [midline is average of upper and lower limit.]

A=  97-85 = 12

Phase shift: \alpha=10

Period = 24 hours;

\omega=\dfrac{2\pi}{24}=\dfrac{\pi}{12}

Substitute all values in sinusoidal function, we get

y=12\sin[\dfrac{\pi}{12}(x-10)]+85

Put y= 82, we get

82=12\sin[\dfrac{\pi}{12}(x-10)]+85\\\\\Rightarrow\ -3= 12\sin[\dfrac{\pi}{12}(x-10)]\\\\=\dfrac{-1}{4}= \sin[\dfrac{\pi}{12}(x-10)]\\\\\Rightarrow\ \dfrac{\pi}{12}(x-10)=\sin^{-1}(\dfrac{-1}{4})\\\\\Rightarrow\ x-10=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))\\\\\Rightarrow\ x=\dfrac{12}{\pi}(\sin^{-1}(\dfrac{-1}{4}))+10\\\Rightarrow\ x\approx9.03

Hence, After about 9.03 hours the temperature first reach 82 degrees.

3 0
3 years ago
What is the range of function y=√(-2cos^2x+3cosx-1)
Ugo [173]
Hello Friend,here is the solution for your question


<span>so the given function is </span>
y= √(-2cos²x+3cosx-1)
 i.e = √[-2(cos²x-3/2+1/2)]
i.e = √[-2(cosx-3/4)²-9/16+1/2]
i.e. = √[-2(cos-3/4)²-1/16]
i.e. = √[1/8-3(cosx=3/4)²]-----------(1)

Now here  in this equation is this quantity :-
<span>(cosx=3/4)²----------------(2)   is to it's minimum value then the whole equation </span>
<span>i.e. = √[1/8-3(cosx=3/4)²] will be maximum and vice versa </span>


And we know that cosx-3/4 will be minimum if cosx=3/4
<span>therefore put this in (1) we get </span>
(cosx=3/4)²=0    [ cosx=3/4]
<span>hence the minimum value of the quantity (cosx=3/4)² is 0 </span>

<span>put this in equation (1) </span>
we get ,
i.e. = √[1/8-3(cosx=3/4)²]
   =√[1/8-3(0)]        [ because minimum value of of the quantity (cosx=3/4)² is 0 ]
     =√1/8
      =1/(2√2)

<span>this is the maximum value now to find the minimum value </span>

<span>since this is function of root so the value of y will always be ≥0 </span>

<span>hence the minimum value of the function y is 0 </span>


<span>Therefore, the range of function </span>y is [0,1/(2√2)]


__Well,I have explained explained each and every step,do tell me if you don't understand any step._

8 0
3 years ago
Simplity:<br> 17 (-12 + 3)
Schach [20]

Answer:

\Huge\boxed{\mathsf{-153}}}

Step-by-step explanation:

\Large\boxed{\mathsf{LESSON: ORDER \quad OF \quad OPERATIONS}}}

\Large\boxed{\mathsf{SUBJECT: MATH}}}

To use the order of operations stands for (Parenthesis, Exponents, Multiply, Divide, Add, and Subtract) from left to right.

First, do parenthesis.

17(-12+3)

(-12+3)=-9

17(-9)

Then, multiply.

17*9=153

17(-9)=-153

-153

\Large\boxed{\mathsf{\Rightarrow -153}}

The correct answer is -153.

3 0
3 years ago
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