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neonofarm [45]
3 years ago
5

Given that is directly proportional to (p-1)2 and p is always positive, find the

Mathematics
1 answer:
Arturiano [62]3 years ago
4 0

Answer:

p = 10.8

Step-by-step explanation:

Given that p is directly proportional to (p-1)² and p is always positive, then;

q = k (p-1)²

If q = 30 and p = 7

30 = k(7-1)²

30 = 6²k

30 = 36k

5 = 6k

k = 5/6

To get p when q = 80

q =k (p-1)²

80 = 5/6((p-1)²

480 = 5(p-1)²

480/5 = (p-1)²

(p-1)² = 96

p-1 = √96

p-1 = 9.8

p = 9.8 + 1

p = 10.8

B) 6

Ch 10.82

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Lisa wants to use her calculator to square a two-digit positive integer, but she accidentally enters the tens digit incorrectly.
Svetradugi [14.3K]

Answer: Correct two digit number= 24

Step-by-step explanation:

Let

x= tens digit (wrong one)

and y= zeroes digit

and z= tens digit (right one)

Now according to the statement,

(10x+y)² -  (10z+y)² = 2340

Simplifying this we get

(x-z)(5x+y+5z)= 117= 1 * 3 * 3 * 13

So it could either be

x-z=1 or x-z=3

If we take the x-z=1

then 5x+y+5z=117

which is not possible as maximum value we can get from this is 99.

This leaves us with x-z=3

so 5x+y+5z= 39

Put x=3+z

We get,

y+10z= 24

Now as y and z both are single digits so the only possible numbers to fit these are y=4 and z=2.

Put z=2 in x=3+z , we get x=5

So the numbers become 10x+y= 54

and 10z+y= 24

Their sum is 54+24=78

Check

54²-24²= 2340 so it is correct.

7 0
3 years ago
(7 + 7i)(2 − 2i)
Ostrovityanka [42]

The complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)

\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)

\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

=21-21i

After converting into the exponential form:

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

From part (b) and part (c) both results are the same.

Thus, the complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

3 0
2 years ago
What is 159as a percent
11Alexandr11 [23.1K]

Answer:

159 as a percent = 15900%

Brainiest if helpful!

Step-by-step explanation:

To convert 159 to percent multiply 159 by 100. The result is 15900 percent, or, using the percent sign, 15900 %. Put simply, to change 159 to % move the ″.″ two places to the right.

5 0
3 years ago
Read 2 more answers
What is the slope of the line given by the equation y=4x?
umka2103 [35]

Answer:

the slope is 1 over 4, or up 1 right 4.

Step-by-step explanation:

4 0
3 years ago
A shop advertises a 24% off sale. The coat sold for $258 fins the decrease in price and the sale price
damaskus [11]

Answer:

339.47

Step-by-step explanation:

100 - 24 = 76

258 = 76 percent

3.39473684211 = 1 percent

339.47 = 100 percent

6 0
2 years ago
Read 2 more answers
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