Answer:
See below in bold.
Step-by-step explanation:
(1) cosec ( x + 10) = 3
Now cosec x = 1/sin x so
1 / sin (x + 10) = 3
3 sin (x + 10) = 1
sin (x + 10) = 1/3
x + 10 = 19.47 , 160.53 degrees
x = 9.47, 150.53 degrees.
(ii) cot (x - 30) =0.45
cot (x - 30)= 1 /tan (x- 30) so we have
tan (x - 30) = 1 / 0.45 = 2.2222
x - 30 = 65.77 degrees
x = 95.77 degrees.
<h3>Answer:</h3>
Equation of the ellipse = 3x² + 5y² = 32
<h3>Step-by-step explanation:</h3>
<h2>Given:</h2>
- The centre of the ellipse is at the origin and the X axis is the major axis
- It passes through the points (-3, 1) and (2, -2)
<h2>To Find:</h2>
- The equation of the ellipse
<h2>Solution:</h2>
The equation of an ellipse is given by,
Given that the ellipse passes through the point (-3, 1)
Hence,
Cross multiplying we get,
- 9b² + a² = 1 ²× a²b²
- a²b² = 9b² + a²
Multiply by 4 on both sides,
- 4a²b² = 36b² + 4a²------(1)
Also by given the ellipse passes through the point (2, -2)
Substituting this,
Cross multiply,
- 4b² + 4a² = 1 × a²b²
- a²b² = 4b² + 4a²-------(2)
Subtracting equations 2 and 1,
- 3a²b² = 32b²
- 3a² = 32
- a² = 32/3----(3)
Substituting in 2,
- 32/3 × b² = 4b² + 4 × 32/3
- 32/3 b² = 4b² + 128/3
- 32/3 b² = (12b² + 128)/3
- 32b² = 12b² + 128
- 20b² = 128
- b² = 128/20 = 32/5
Substituting the values in the equation for ellipse,
Multiplying whole equation by 32 we get,
3x² + 5y² = 32
<h3>Hence equation of the ellipse is 3x² + 5y² = 32</h3>
Answer:
E(t) = 5t +672 ($)
Step-by-step explanation: INCOMPLETE QUESTION
FROM GOOGLE
she earns 12 $ per hour as tutor and 7 $ per hour as waitress, this month she worked a combined of 96 hours at her two jobs
Let be t the numbers of hours Leila works as tutor this month
Answer:
If Leila worked t hours as tutor then, she worked (96 - t) hours as waitress
E(t) = 12 * t + 7 * (96-t)
E(t) = 12t + 672 - 7t
E(t) = 5t +672 ($)
The roots of the parabola is where the x-intercepts are so the answer is x=-1 and x= 5
Answer:
a. $270
b. $3,278.18
Step-by-step explanation:
Given that
The principal amount is $3,000
Annual rate of interest is 3%
And, the time period is 3 years
We need to find out the simple interest & compound interest
The following formulas should be used
a. For simple interest
= Principal × rate of interest × time period
= $3,000 × 3% × 3 years
= $270
b. For compound interest
= Principal × (1 + rate of interest)^time period
= $3,000 × (1 + 0.03)3
= $3,000 × 1.03^3
= $3,278.18
