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2 years ago

Can someone help me on this?

Mathematics

1 answer:

Dima020 [189]2 years ago

6 0

Step-by-step explanation: We are given to find the value of x from the following trigonometric equation:

sin55=cosx

We know that the sine of any acute angle is equal to the cosine of its complement and cosine of any acute angle is equal to the sine of its complement.So, from equation (i), we get

sin55 ∘ =cosx

⇒sin55 ∘ =sin(90 ∘−x)

⇒55 ∘ =90 ∘ −x

⇒x=90 ∘ −55 ∘

⇒x=35 ∘

Thus, the required value of x is 35°.

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A scientist builds a Mars rover that can travel 4.9 centimeters per second on flat ground.

tatyana61 [14]

Answer:

75.95cm

Step-by-step explanation:

4.9 multiplied by 15 will represent the 15 seconds

4.9 • 15 = 73.5

4.9 divided by 2 will equal the 1/2 seconds

4.9 ÷ 2 = 2.45

add them all together

73.5 + 2.45 = 75.95 cm

7 0

3 years ago

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: Sam is 12 years older than John. For the last four years, Sam and John have been friends. Five years ago, Sam was 5 times as o

Firlakuza [10]

Answer:

The present age of Sam is 20 years .

Step-by-step explanation:

Given as :

Let The age of John = J years

Let The age of Sam = S years

∵ Sam is 12 years older than John

so, The age of Sam = 12 + The age of John

i.e S = 12 + J .....1

Again

Before 5 years ago

The age of Sam = 5 times age of John

So, (S - 5) = 5 × (J - 5)

Or, S - 5 = 5 J - 25

Or, 5 J - S = 25 - 5

Or, 5 J - S = 20 .........2

Solving eq 1 and eq 2

[5 J - (12 + J)] = 20

Or, 5 J - 12 - J = 20

Or, 4 J = 20 + 12

Or, 4 J = 32

∴ J = $\frac{32}{4}$

i.e J = 8 years

So, The age of John = J = 8 years

Put The value of J into eq 1

∵ S = 12 + J

So, S = 12 + 8

i.e S = 20 years

So, The present age of Sam = S = 20 years .

Hence, The present age of Sam is 20 years . Answer

7 0

4 years ago

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4) A safe contains 120 coins, the value of which is $10. If the coins consist of nickels and dimes, how many of each kind are in

alexandr1967 [171]

There are 40 nickels and 80 dimes

8 0

3 years ago

HELP!! Algebra help!! Will give stars thank u so much <333

Anna35 [415]

Answers:

Part a) $\bf{\sqrt{x^2+(x^2-3)^2}$
Part b) 3
Part c) 2.24
Part d) 1.58

============================================================

Work Shown:

Part (a)

The origin is the point (0,0) which we'll make the first point, so let (x1,y1) = (0,0)

The other point is of the form (x,y) where y = x^2-3. So the point can be stated as (x2,y2) = (x,y). We'll replace y with x^2-3

We apply the distance formula to say...

$d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(0-x)^2+(0-y)^2}\\\\d = \sqrt{(0-x)^2+(-y)^2}\\\\d = \sqrt{x^2 + y^2}\\\\d = \sqrt{x^2 + (x^2-3)^2}\\\\$

We could expand things out and combine like terms, but that's just extra unneeded work in my opinion.

Saying $d = \sqrt{x^2 + (x^2-3)^2}$ is the same as writing d = sqrt(x^2-(x^2-3)^2)

-------------------------------------------

Part (b)

Plug in x = 0 and you should find the following

$d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(0) = \sqrt{0^2 + (0^2-3)^2}\\\\d(0) = \sqrt{(-3)^2}\\\\d(0) = \sqrt{9}\\\\d(0) = 3\\\\$

This says that the point (x,y) = (0,3) is 3 units away from the origin (0,0).

-------------------------------------------

Part (c)

Repeat for x = 1

$d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(1) = \sqrt{1^2 + (1^2-3)^2}\\\\d(1) = \sqrt{1 + (1-3)^2}\\\\d(1) = \sqrt{1 + (-2)^2}\\\\d(1) = \sqrt{1 + 4}\\\\d(1) = \sqrt{5}\\\\d(1) \approx 2.23606797749979\\\\d(1) \approx 2.24\\\\$

-------------------------------------------

Part (d)

Graph the d(x) function found back in part (a)

Use the minimum function on your graphing calculator to find the lowest point such that x > 0.

See the diagram below. I used GeoGebra to make the graph. Desmos probably has a similar feature (but I'm not entirely sure). If you have a TI83 or TI84, then your calculator has the minimum function feature.

The red point of this diagram is what we're after. That point is approximately (1.58, 1.66)

This means the smallest d can get is d = 1.66 and it happens when x = 1.58 approximately.

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3 years ago

What is the solution set of the equation x^2 - 7x - 18 = 0

photoshop1234 [79]

(x-9)(x+2)=0
x=9 or x=-2

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3 years ago

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