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2 years ago

Will someone help me with problem 21?

Mathematics

1 answer:

Juliette [100K]2 years ago

6 0

Sin^(1/2) x cos x - sin^(5/2) cos x
= sin^(1/2) x cos x - sin(1/2)x sin^2 x cos x
factoring we get:
cos x sin^(1/2) x ( 1 - sin^2 x)
Now 1 - sin^2 x = cos^2 x so we have

cos x sin^(1/2) x * cos^2 x

= cos^3 x sqrt sin x

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In a sample of 77 children , the mean age as at which they first began to combine words was 16.51 months

astraxan [27]

Answer:

Mean age = 1271.27

Step-by-step explanation:

No of children = 77

The age at which children first began to combine words = 16.51 months

Mean age = No of children × age at which children first began to combine words

= 77 × 16.51

= 1271.27

Mean age = 1271.27

7 0

2 years ago

What is the y intercept of the graph y= -2x^2 -4x-3

Kitty [74]

the answer for this question is -3

4 0

2 years ago

four families go to the cinema. the reid family take 2 adults and 2 children for £18 ; the mghee family take 1 senior, 2 adults

RoseWind [281]

Answer:

$\pounds 26.50$

Step-by-step explanation:

Let

x = cost for one adult

y = cost for one child

z = cost for one senior.

The Reid family:

take 2 adults and 2 children and paid $2x+2y$ that is $\pounds 18$ , so

$2x+2y=18$

The Mghee family:

take 1 senior, 2 adults and 1 child and paid $x+2x+y$ that is $\pounds 18.50$ , so

$x+2x+y=18.50$

The Griffiths family:

take 1 senior and 3 adults and paid $z+3x$ that is $\pounds 19.50$ , so

$z+3x=19.50$

You get the system of three equations:

$\left\{\begin{array}{l}2x+2y=18\\ \\z+2x+y=18.50\\ \\z+3x=19.50\end{array}\right.$

From the first equation:

$2y=18-2x\\ \\y=9-x$

From the third equation:

$z=19.50-3x$

Substitute them into the second equation:

$19.50-3x+2x+9-x=18.50\\ \\-3x+2x-x=18.50-19.50-9\\ \\-2x=-10\\ \\2x=10\\ \\x=5$

Then

$y=9-5=4\\ \\z=19.50-3\cdot 5=19.50-15=4.50$

Hence,

the cost for one adult is $\pounds 5$

the cost for one child is $\pounds 4$

the cost for one senior is $\pounds 4.50$

The Linton family takes 1 senior, 2 adults and 3 children and paid

$\pounds 4.50+2\cdot \pounds 5+3\cdot \pounds 4=\pounds 26.50$

3 0

2 years ago

Last one, use trigonometry to help you solve for y given that one side is 4 and there is an angle of 50 degrees.

Ostrovityanka [42]

Answer:

y = 6.22

You can solve this in two ways.

1.) Use SOH CAH TOA:

I typically start off by labeling the sides of the triangle with H (hypotenuse), O (opposite), and A (adjacent). Because I need to figure out what y is when given an angle and 4, I will use CAH, or cosine.

$\cos(angle) = \frac{adjacent}{hypotenuse}$

$\cos(50) = \frac{4}{y}$

$\cos(50) \times y = 4$

$y = \frac{4}{ \cos(50) }$

$y = 6.22$

2.) Use Law of Sines:

Solve for the last angle inside the triangle first.

$180 - (50 + 90) = 40$

Then use the angle you found (40°) in the equation.

$\frac{4}{ \sin(40) } = \frac{y}{ \sin(90) }$

$\frac{4}{ \sin(40) } \times \sin(90) = y$

$y = 6.22$

3 0

2 years ago

jose drives 65 miles per hour when he travels.sherry drive 450 miles in 9 hours. which driver has a faster rate of change

Alona [7]

Josie does bc If ur looking for the unit rate u only need to find it for sherry. you will get 50 miles per hour. if that's how u mean then Josie goes faster. hope this helps
$450 \div 9$

6 0

2 years ago

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