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Given:

An angle θ on the unit circle has a sine of [tex]\dfrac{1}{4}[/tex].

To find:

The value of cosθ.

Solution:

We have,

[tex]\sin \theta=\dfrac{1}{4}[/tex]

Since sinθ is positive, therefore, θ lies in first or second quadrant.

We know that,

[tex]\sin^2 \theta +\cos^2 \theta =1[/tex]

[tex](\dfrac{1}{4})^2+\cos^2 \theta =1[/tex]

[tex]\dfrac{1}{16}+\cos^2 \theta =1[/tex]

[tex]\cos^2 \theta =1-\dfrac{1}{16}[/tex]

Taking square root on both sides.

[tex]\cos \theta =\pm \sqrt{\dfrac{16-1}{16}}[/tex]

[tex]\cos \theta =\pm \dfrac{\sqrt{15}}{4}[/tex]

Therefore, the value of cosθ is either [tex]\dfrac{\sqrt{15}}{4}[/tex] or [tex]-\dfrac{\sqrt{15}}{4}[/tex].

Step-by-step explanation:

D (-2,2)

:) good day

good day

Answer:

because of vertical angles, 108

Step-by-step explanation:

Answer:

108 degrees

Step-by-step explanation:

Opposite angles are equal.

Thus, x = 108 degrees.

Answer:

linear

non-linear

Step-by-step explanation:

Answer:

Ax + By = C the answer is C 1/2x+2y=7

Step-by-step explanation:

Answer:

nope

Step-by-step explanation:

sorry about not knowing how to

Answer:

08

16

24

32

40

48

56

64

72

80

Step-by-step explanation:

From 1-10 You can see the numbers going from 0-8 on the left side except you repeat the number 4 twice then proceed. Then on the right side you do it backwards but instead you use the 2 times tables and you’re going to want to work your way from bottom to top and then when you reach to 0 which is the number 10 you repeat the 2 times tables again.

Answer:

sorry homie im bad at math but download conects

Step-by-step explanation:

i just cheat my way through life

Answer:

plz give me BRAINLIEST

Step-by-step explanation:

c. p >-13

Answer:

They will have the same population after 6 hours

Step-by-step explanation:

The general exponential equation format for this is;

P = P_o(e^(kt))

For Culture A, we are told that it had an initial population of 200 and doubles every hour.

Thus;

After 1 hour, P = 400

After 2 hours, P = 800

After 3 hours, P = 1600

Thus;

At t = 1, we have;

400 = 200(e^(k × 1))

400/200 = e^(k)

e^(k) = 2 - - - (eq 1)

At t = 2, we have;

800 = 200(e^(k × 2))

800/200 = e^(2k)

e^(2k) = 4 - - - (eq 2)

To find k, let's divide eq 1 by eq 2.

(e^(2k))/e^(k) = 4/2

e^(2k - k) = 2

e^(k) = 2

k = In 2

k = 0.6931

Thus;

P = 200e^(0.6931t)

For Culture B, we are told that it had an initial population of 819200 but has been contaminated. Its population is now decreasing by half every hour.

Thus;

After 1 hour, P = 409600

After 2 hours, P = 204800

After 3 hours, P = 102400

Thus;

At t = 1, we have;

409600 = 819200(e^(k × 1))

409600/819200 = e^(k)

e^(k) = 0.5 - - - (eq 1)

At t = 2, we have;

204800 = 819200(e^(k × 2))

204800/819200 = e^(2k)

e^(2k) = 0.25 - - - (eq 2)

To find k, let's divide eq 1 by eq 2.

(e^(2k))/e^(k) = 0.25/0.5

e^(k) = 0.5

k = In 0.5

k = -0.6931

Thus;

P = 819200(e^(-0.6931t))

We want to find the time when the 2 cultures will have the same population. Thus;

200e^(0.6931t) = 819200(e^(-0.6931t))

Arranging, we have;

(e^(0.6931t))/(e^(-0.6931t)) = 819200/200

e^(0.6931t - (-0.6931t) = 4096

e^(1.3862t) = 4096

1.3862t = In 4096

1.3862t = 8.3178

t = 8.3178/1.3862

t ≈ 6 hours

Answer:

the 2 one is better because you get more pens

Step-by-step explanation:

you get more pens

Answer:

c

Step-by-step explanation:

but if C is incorrect i believe your second choice should be D

Answer:

D: 15

Step-by-step explanation:

Ok, by looking at the first equation, you know that one triangle equals 10. By looking at the second one, you see that two circles equal 10, since 20- triangle(10) equals 10. This means a circle has to equal 5. looking at the third one, the answer is 13, and a circle is 5, so 13-5=8. Two squares equal 8. the last one shows one triangle, one circle, and a half square. From the third one, you know that one square equals 4, so a half square equals two. I do not know why this logic doesn't match with the answers, since 10(triangle) plus 5(circle) and 2(half square) is 17, but in terms of what makes sense and just matching it with the answers provided, I say go with the third option.  

Answer:

X=1/5

Step-by-step explanation:

7×-2×-10=-9

5×=-9 +10

5×/5=1/5

×=1/5

Answer:

cool, but what is the question?

Answer:

78

Step-by-step explanation:

102+x=180

x=180-102

x=78

Answer:

25 ft

Step-by-step explanation:

Got it right on EDG2020

The ball will reach the maximum height in a second. Then the maximum height the ball reaches will be 25 ft.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

Lori tosses a ball into the air. The equation models the height, y, in feet, of the ball after x seconds.

[tex]\rm y = -16(x - 1)^2 + 25[/tex]

Differentiate the equation with respect to x, then we have

[tex]\begin{aligned} y' &= 0\\\\\dfrac{d}{dx}[-16(x - 1)^2 + 25] &= 0\\\\ -32(x-1) &= 0\\\\x &= 1 \end{aligned}[/tex]

Then the maximum height the ball reaches will be

[tex]\rm y = -16(1 - 1)^2 + 25\\\\y = -16*0^2 + 25\\\\y = 25[/tex]

Then the maximum height the ball reaches will be 25 ft.

More about the differentiation link is given below.

https://brainly.com/question/24062595

#SPJ2

Answer:

y = -3/5x + 1.3

Step-by-step explanation:

y = mx + b

m: slope

b: y-intercept

First, let's substitute in the values.

Point: (2, 1)

Slope: -3/5

y = mx + b

(1) = (-3/5)(2) + b

1 = -0.3 + b

1 + 0.3 = -0.3 + b + 0.3

b = 1.3

Now, let's add the slope and y-intercept to the equation.

y = mx + b

m = -3/5

b = 1.3

y = -3/5x + 1.3

Hope this helped! <3

Answer:

34+15y

Step-by-step explanation:

Let x players want a sweatshirt and y players want sweatpants.

Each sweatshirt costs ​$34 and each pair of sweatpants costs ​$15.

Cost of sweatshirt = 34x

Cost of sweatpants = 15y

Total cost = cost of sweatshirt + cost of sweatpants

= 34x+15y

Hence, the total cost is "34x+15y".

Answer:

Was number 11

Step-by-step explanation:

50 - 6 = 44

44 dividid 4 is 11

Answer:

x = 0

Step-by-step explanation:

Let's divid both sides of the equation by 2 first, so we don't have as much work to do in the next step:

[tex]4x-2y=6\\2x-y=3[/tex]

Substituting -3 for y:

[tex]2x-(-3)=3\\2x+3=3\\2x=0\\x=0[/tex]

Answer:

-9

Step-by-step explanation:

Can I have brainliest?

Also can you please thank me, it'll be gratefully appreciative.

:)

Answer: 78 degrees

Step-by-step explanation:

well u can transfer the -5 in denominator to the right hand side

so x=1.2*(-5)

x=-6.0

Answer:

Yes, Simon is correct.

Step-by-step explanation:

A trapezoid refers to a quadrilateral that is convex in shape; as such it has no equal sides and no parallel sides.

Let the height of a trapezoid be h.

Let the top base of a trapezoid be b1.

Let the bottom base of a trapezoid be b2.

[tex] Area \; of \; trapezoid = \frac {1}{2} * (Sum \; of \; nonparallel \; sides) * height [/tex]

Therefore, [tex] Area \; of \; trapezoid = \frac {1}{2} * (b_{1} + b_{2}) * h [/tex]

[tex] Area \; of \; trapezoid = \frac {1}{2} * (b_{1}h + b_{2}h) [/tex]

[tex] Area \; of \; trapezoid = \frac {b_{1}h + b_{2}h}{2} [/tex]

Hence, to find the area of a trapezoid, you will multiply the height by the top base and the height by the bottom base. Then you add the two products together and divide the sum by 2.

9514 1404 393

Answer:

  325 cm³

Step-by-step explanation:

The volume is the product of the dimensions shown.

  V = LWH

  V = (13 cm)(5 cm)(5 cm) = 325 cm³

Answer:

9360 square inches

Step-by-step explanation: