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Rama09 [41]
3 years ago
5

R=8cos(theta)-10sin(theta) to cartesian coordinates

Mathematics
1 answer:
dsp733 years ago
8 0
Convert polar equation (R, Ф):

(1) R= 8cos Ф - 10sin Ф into Cartesian (x , y)
We know that:
x = R.cos Ф  → cos Ф = x/R , and
y = R.sin Ф →  sin Ф = y/R
and that x² +y² = R²

Replace in 
R= 8cos Ф - 10sin Ф , cos Ф and sin Ф by the related x and y:

R = 8(x/R) - 10(y/R)
Multiply both sides by R:

R² = 8R(x/R) - 10R(y/r) ↔ R² = 8x - 10y , but we have also R² = x² + y². hence: 8x -10y = x² + y²
OR x² + y² - 8x + 10y = 0
We can continue in completing th squares of (x² - 8x + ?) and (y² +10y + ?)

(x² - 8x + ?) = (x - 4)² - 16

and  (y² +10y + ?) = (y +5)² - 25
Final Equation:
(x - 4)² - 16 + (y +5)² - 25 →→→(x - 4)² + (y +5)² = 41 
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Four friends were born in consecutive years. The sum of their ages is 94. What is the age of the oldest friend?
Savatey [412]
Hello,

We don't need algebra to solve this.

I suppose the ages are 1,2,3,4
Their sum is 1+2+3+4=10.
To obtain 94 we must add 94-10=84 for 4 persons =>84/4=21 to each

Ages are
1+21=22
2+21=23
3+21=24
4+21=25

But if really want an algebric resolution:

Let's x the age of the youngest
x+1,x+2,x+3 the others.

x+(x+1)+(x+2)+(x+3)=94
==>4x+6=94
==>4x=88
==>x=22
Ages are 22,23,24,25.

The oldest friend is 25 years old.

8 0
3 years ago
Read 2 more answers
Write the ratio of the first measurement to the second measurement. Compare in millimeters. Diameter of ball​ A: 44 mm diameter
Aneli [31]

Answer:

11:18

Step-by-step explanation:

Here, we are interested in calculating the ratio of diameter of ball A to that of ball B

what to do here is to ensure that both diameters have measurements that are same units.

Thus, mathematically;

44 mm to 7.2cm

But, mathematically;

10 mm = 1 cm

Thus 7.2cm = 7.2 * 10 = 72mm

Thus, our ratio becomes;

44:72

divide through be 4, we have

44/4 : 72/4

= 11 : 18

6 0
3 years ago
Please help <br><br><br><br> …………………………
faltersainse [42]

Answer:

u=22

Step-by-step explanation:

Triangel JKI and Triangel HKI are congruent by rule SAS (Side Angel Side)

JI and IH are congruent by rule CPCTC (Coungruent Parts of Cogruent Triangels are Cogruent).

2u=u+22

u=22

6 0
3 years ago
Angle RZT=110<br> Angle RZS=3s<br> Angle TZS=8s<br> What are angles RZS and TZS?
nekit [7.7K]
Angles RZT, RZS, and TZS form triangle RZT, so they sum to 180.  Thus, we have:

110+3s+8s=180

Simplifying, we have:

11s=70

Dividing by 11, we see that:

s=70/11

Therefore, RZS=3s=210/11, and TZS=8s=560/11.
6 0
3 years ago
What is the rule for the sequence with the first four terms below?
inessss [21]

Answer: f (x) = 0.75 minus 0.25x

Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference.

The formula for determining the nth term of an arithmetic sequence is expressed as

an = a1 + (n - 1)d

Where

a1 represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a1 = 0.5

d = 0.25 - 0.5 = - 0.25

n = 25

The rule for the sequence is

an = 0.5 + (n - 1)-0.25

an = 0.5 - 0.25n + 0.25

an = 0.5 + 0.25 - 0.25n

an = 0.75 - 0.25n

Substituting f(x) for an and x for n, it becomes

f(x) = 0.75 - 0.25x

3 0
3 years ago
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