Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.
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• (1) x= sqrt t, y=4t+3; 0 ≤ t ≤ 4

A) y = - 3x ^ 2 + 19; 0 ≤ x ≤ 2
B ) y = - 3x + 19; 0 ≤ x ≤ 2
C) y=4x^ 2 +3; 0 ≤ x ≤ 2
D ) y=3x^ 2 +4; -1 ≤ x ≤ 2

• (2) x=2t, y=t+2; -2 ≤ t ≤ 3

A ) y=x ^2 + 1; - 2 ≤ x ≤ 2
B) y= 1/2x -2; -∞ C) y= 1/2x +2; -4 ≤ x ≤ 6
D ) y=-2x+2; -∞

Answer:

We know the volume formula of rectangular prism is:

Volume = Length × Width × Height

We are given:

Volume = 1428 in³

Height = 6 in

Length = 17 in

Width = p

Apply the formula!

1428 = 6 × 17 × p

1428 = 102p

Divide by 102 on either side to isolate p

p = 14  

The width is 14 inches

Step-by-step explanation:

Answer: -5x+2y

Step-by-step explanation: Have a brilliant day! - Lily ^_^

Answer:

105

Step-by-step explanation:

Given the sequence of numbers

5,15,35,65

First lets get the common difference

d1 = 15-5 = 10

d2 = 35 - 15 = 20

d3 = 65-35 = 30

We can see that the differences form an arithmetic sequence

10, 20, 30..

Let's get the next term fist

Tn = a + (n-1)d

T4 = 10+(4-1)(10)

T4 = 10 + 3(10)

T4 = 10+30

T4 = 40

This means that the next term of the original sequence will be gotten by adding 40 to the preceding value

Next term = 65 + 40

Next term = 105

Hence the next term is 105

Answer:

The formula for slope is sometimes referred to as "rise over run", because the fraction onsists of the "rise" (being the change in y, going up or down) divided by the "run" (being the change in x, going from left to the right).

Step-by-step explanation:

Answer:

What?

Step-by-step explanation:

what looks right?

Answer:

what ???¿???????

?????

Answer:

31.4 in

Step-by-step explanation:

This is a tricky question,

if you observe the shape carefully, you will notice that if you mirror (flip outward) each curve surface of each quardrant, what you will end up with is a complete circle with a radius of 5 inches.

Hence the combined length of all the curved surfaces is simply the circumference of the circle, given by:

Circumference = 2πr

= 2 x 3.14 x 5

= 31.4 in

Answer:

(3.5, 5) is my answer

Answer:

x = 59

Step-by-step explanation:

since the quadrilateral add up to 360 degrees,

X + X + (2x + 3 ) + (2x + 3) would equal 360 degrees

x + x + (2x + 3) + (2x + 3) = 360

6x + 6 = 360, addtion

6x = 354, subtraction

x = 59, division

Answer:

160

I hope it is helpful to you

Answer:

[tex]\frac{1-\tan x }{1+\cot x}[/tex]

Step-by-step explanation:

Let [tex]\frac{\sin 2x+\cos 2x-1}{\sin 2x+\cos 2x + 1}[/tex], we proceed to prove the given identity by trigonometric and algebraic means:

1) [tex]\frac{\sin 2x+\cos 2x-1}{\sin 2x+\cos 2x + 1}[/tex] Given

2) [tex]\frac{2\cdot \sin x \cdot \cos x +\cos ^{2}x - \sin^{2}x-1}{2\cdot \sin x \cdot \cos x +\cos ^{2}x - \sin^{2}x+1}[/tex] [tex]\sin 2x = 2\cdot \sin x \cdot \cos x[/tex]/[tex]\cos 2x = \cos^{2}x - \sin^{2}x[/tex]

3) [tex]\frac{2\cdot \sin x \cdot \cos x -\sin^{2}x-(1-\cos^{2}x)}{2\cdot \sin x\cdot \cos x +\cos^{2}x+(1-\sin^{2}x)}[/tex] Commutative, associative and distributive properties/[tex]-a = (-1)\cdot a[/tex]

4) [tex]\frac{2\cdot \sin x \cdot \cos x -2\cdot \sin^{2}x}{2\cdot \sin x \cdot \cos x +2\cdot \cos^{2}x}[/tex] [tex]\sin^{2}x + \cos^{2}x = 1[/tex]

5) [tex]\frac{(2\cdot \sin x)\cdot (\cos x-\sin x)}{(2\cdot \cos x)\cdot (\sin x +\cos x)}[/tex] Distributive and associative properties.

6) [tex]\frac{\sin x\cdot (\cos x-\sin x)}{\cos x\cdot (\sin x +\cos x)}[/tex] Existence of multiplicative inverse/Commutative and modulative properties.

7) [tex]\frac{\frac{\cos x -\sin x}{\cos x} }{\frac{\sin x + \cos x}{\sin x} }[/tex] [tex]\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}[/tex]

8) [tex]\frac{\frac{\cos x}{\cos x}-\frac{\sin x}{\cos x} }{\frac{\sin x}{\sin x}+\frac{\cos x}{\sin x} }[/tex] [tex]\frac{x+y}{w} = \frac{x}{w} + \frac{y}{w}[/tex]

9) [tex]\frac{1-\tan x }{1+\cot x}[/tex] Existence of multiplicative inverse/[tex]\tan x = \frac{\sin x}{\cos x}[/tex]/[tex]\cot x = \frac{\cos x}{\sin x}[/tex]/Result

Answer:

x+74=135

x=135-74=61(exterior angle of a triangle is equal to the sum of two opposite interior angle)

Answer:

x^5-25x^3-4x+144/x

Step-by-step explanation:

x^4-25x^2+144 by x-4

Write the division as a fraction

x^4-25x^2+144/x -4

Write all numerators above the common denominator

x^5-25x^3+144-4x/x

Use the commutative property to reorder the terms

x^5-25x^3-4x+144/x

if you can give me brainliest thad be amazing! if not thats fine as well, hope this helps

Answer: 12 kilograms= 12000 grams

Step-by-step explanation:

multiply the mass value by 1000

Answer:

1 Kg = 1000 grams

hence

12Kg = 12000 grams

Answer:

Obtuse

Step-by-step explanation:

Has one obtuse angle, i hope this helps you

Answer:

56

Step-by-step explanation:

(4+7)²-(4²+7²)=121-65

                     =56

Answer:

56

Step-by-step explanation:

(4 + 7)² - (4² + 7²)  =  11² - (16 + 49)  =  121 - 65  =  56

Answer: C

Step-by-step explanation:

hope this helped

Answer:

D and E.

Step-by-step explanation:

Each angle is a different length and no sides can be the same length. If two angles are the same the triangle is considered an isosceles triangle. If all sides are the same it is an equilateral triangle.

Answer:

Answer is 2

Step-by-step explanation:

Answer:

1st do you do 6 × 3 to get 18 and then you add that by 4 because parentheses come 1st. You want to use Pemdas so you do 1/2 times 22 and then you want to subtract 9 from 22 to get 12.

Answer:1.15

Step-by-step explanation:

2/5 =.40

.75+.40=1.15

Answer:

1.05

Step-by-step explanation:

2/5 is equal to .4%.

We can then also interpret the equation as "What number is 1.4% more than .75?".

We need to only multiply 1.4 x .75, to which we will get 1.05.

Answer:

The answer is...... NO

Step-by-step explanation:

Step 1: Plug in your values in the x and y cordinates.

2(5) + 8 > 18

Step 2: Solve

Then you multiply 2 and 5 and get 10.

SO then your equation should look like this:

10 + 8 > 18

The answer to the question is no because in order for this to work it would need to be the greater than or equal to sign, which looks like this ≥.

Hope this helps and have a great day! :)

Answer:

D. 204% increase

Answer:

X=2

Step-by-step explanation:

3x = x + 4

3x - x = 4

2x = 4

x = 4/2

x = 2

Check:

3(2) = 2 + 4

6 = 6

Explanation:

The curve is going downhill as you move from left to right, and as you move from x = -3 to x = -1.

The interval notation of (-3,-1) means -3 < x < -1.

Since the curve is going downhill on this region, this means the function is decreasing on this interval.

Yes, the function is decreasing over the interval (-3,-1).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given interval is (-3, -1).

The curve is going downhill as you move from left to right, and as you move from x = -3 to x = -1.

The interval notation of (-3,-1) means -3 < x < -1.

Since the curve is going downhill on this region, this means the function is decreasing on this interval.

Yes, the function is decreasing over the interval (-3,-1).

To learn more about the function visit:

https://brainly.com/question/28303908.

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Answer:

8/20-5/20

Step-by-step explanation:

Answer:

0.15

Step-by-step explanation:

0.4-0.25

0.15

Answer:

23ft

Step-by-step explanation:

Area of the rectangle = LW

L is the length

W is the width

Given

Area = 414ft²

If the length of this garden is 5 feet longer than its width, then;

L = W+5

Substitute into the formula

414 = (W+5)W

414 = W²+5W

W²+5W-414 = 0

W = -5±√5²-4(-414)/2

W = -5±√25+1656/2

W = -5±√1681/2

W = -5+41/2

W = 36/2

W = 18ft

Since L = W+5

L = 18+5

L = 23ft

Hence the length of the rectangle is 23ft

Answer:

r≈7cm

Step-by-step explanation:

Using the formula

V=4

--------= πr^3

    3

r=(3V

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

4π)⅓=(3·1436

4·π)⅓≈6.99877cm

the answer is 7cm

Answer:

C. 7 cm

Step-by-step explanation:

Took the quiz. Trust

Answer:

Exact Form:

(41036433850368 ^6  x  2419 ^54 )− 328

Decimal Form:

2.48516121  x  10 ^264

Answer:

Heyyy T-T

Step-by-step explanation: