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3 years ago

Can someone help me on B and C

Mathematics

1 answer:

Elis [28]3 years ago

6 0

B. If you look at the graph and go over 5cm and up 3m, you can see that that point is not near the others, so it can't be accurate according to the data on your graph. C. If you go over 3.2 cm on your graph, go up to where the other points are, and you will see that the most likely height would be about 4.7m. Try to imagine a line going through your graph around where the points are, that might help you see where other points would be. I hope that makes sense let me know if you need anything else I'm always happy to help :)

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Solution:

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

3 years ago

In triangle KLM, if K is congruent to L, KL = 9x - 40, LM = 7x - 37, & KM = 3x + 23, find x & the measure of each angle.

Dennis_Churaev [7]

Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°

Step-by-step explanation:

Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL

KM ≅ LM

3x + 23 = 7x - 37

23 = 4x - 37

60 = 4x

15 = x

KM = LM = 3x + 23

= 3(15) + 23

= 45 + 23

= 68

KL = 9x - 40

= 9(15) - 40

= 135 - 40

= 95

Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.

Since N is the midpoint of KL and KL = 95, then NL = 47.5
Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse

Use trig to solve for ∠L (which equals ∠K):

cos ∠L = $\frac{adjacent}{hypotenuse}$

cos ∠L = $\frac{47.5}{68}$

∠L = cos⁻¹ $(\frac{47.5}{68})$

∠L = 45.7

Triangle sum Theorem:

∠K + ∠L + ∠M = 180°

45.7 + 45.7 + ∠M = 180

91.4 + ∠M = 180

∠M = 88.6

7 0

3 years ago

What’s Volume of a cylinder if the height is 10 diameter is 3

Art [367]

Known :

h = 10

d = 3

Asked :

V = ...?

Answer :

V = ¼πd²h

= ¼ × 3.14 × 3² × 10

= ¼ × 3.14 × 9 × 10

= 70.65

Hope it helpful and useful :)

7 0

3 years ago

Trey is putting up a fence around a 750 foot by 540 foot lot. How many feet of fence dose he need?

anygoal [31]

Given:

The length of the lot l= 750ft

The width of the plot w= 540 ft

Required:

Find the required fence.

Explanation:

The perimeter of the rectangle is given by the formula.

$P=2(length+width)$

Thus the required fence for the lot

$\begin{gathered} =2(750+540) \\ =2(1290) \\ =2580\text{ ft} \end{gathered}$

Final answer:

The required fence is 2580 ft.

6 0

1 year ago

Jade says that the absolute value of a number and the opposite of a number is the same thing. Is Jade correct? Use examples to h

avanturin [10]

Answer:

No, the absolute value of a number is different from the opposite.

Step-by-step explanation:

For example, the absolute value of 4 is 4.

l4l = 4

But the opposite of 4 is -4.

Absolute value is ALWAYS positive, but the opposite of a positive number is a negative number.

8 0

3 years ago