Hi there!

We are given:
cos(7x)cos(4x) = -1 - sin(7x)sin(4x)
Begin by moving all terms with variables to one side:
cos(7x)cos(4x) + sin(7x)sin(4x) = -1
The corresponding trig identity is cos(A - B). Thus:
cos(7x - 4x) = cos(7x)cos(4x) + sin(7x)sin(4x) = -1
cos(3x) = -1
cos = -1 at π, so:
3x = π
x = π/3
We can also find another solution. Let 3π = -1:
3x = 3π
x = π
Thus, solutions on [0, 2π) are π/3 and π.
Answer:
17
Step-by-step explanation:
7h+3
7(2)+3
14+3
=17
Answer:
M(t) = 64 Kgs
Step-by-step explanation:
To find the total mass of the rod, we have to integrate the expression
M(x) = ∫₀⁴ rho(x)*dx
Where rho (x) = 6 + 5*x in Kgs /m
M(x) = ∫₀⁴ ( 6 + 5*x ) dx ⇒ M(x) = ∫₀⁴ 6 dx + ∫₀⁴ 5*x dx
M(x) = 6x |₀⁴ + 5* x²/2 |₀⁴
M(x) = 6( 4 - 0 ) + 5/2 ( 16 - 0 )
M(x) = 24 + 40 Kgs
M(t) = 64 Kgs
The following triangle is classified as: Scalene acute.
<h3>Why is the triangle classified as scalene?</h3>
The triangle is classified as scalene because all side lengths are different. If there were 2 equal side lengths, the triangle would be isosceles, and if all three were equal, equilateral.
<h3>Why is the triangle classified as acute?</h3>
The triangle is classified as acute because all angles are less than 90º. If there was one angle with measure greater than 90º, the triangle would be classified as obtuse.
More can be learned about classification of triangles at brainly.com/question/1058720
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Answer:
a
The 95% confidence interval is 
b
The sample proportion is 
c
The critical value is 
d
The standard error is 
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is 
The alternative hypothesis is 
Generally the sample proportion is mathematically evaluated as

Given that the confidence level is 95% then the level of significance is mathematically evaluated as



Next we obtain the critical value of
from the normal distribution table, the value is

Generally the standard of error is mathematically represented as

substituting values


The margin of error is

=> 
=> 
The 95% confidence interval is mathematically represented as

=> 
=> 