What are the coordinates of the vertex of the parabola described by the
equation below?
y = 4(x + 7)2 - 2

The area of one petal of the polar curve r = 5 sin 2θ would be 25π/4.

Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.

Then summing all those pieces' area gives us the area of the main big region.

The polar curve r = 5sin 2θ

When r = 0, θ = 0, π/2 which corresponds to one loop.

We need the limits to provide r=0 or cos(5x) =0 so:

Therefore the area of the region enclosed by this curve is

[tex]A = \dfrac{1}{2} \int\limits^a_b {r^{2} } \, d\theta \\\\\\A = \dfrac{1}{2} \int\limits^{\pi /2}_0 {25sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 {sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 \dfrac {1-cos^{2}4\theta } {2}\, d\theta\\ \\\\A = \dfrac{25}{2}( \theta - \dfrac {sin4\theta} {2})\, d\theta |^{\pi /2}_0\\\\\\A = \dfrac{25}{2} \times \dfrac{\pi }{2} \\\\\\A = \dfrac{25\pi }{4}[/tex]

Thus, the area of one petal of the polar curve r = 5sin 2θ would be 25π/4.

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#1

Area

#2

Area

#3

Area

#4

Area

Answer:

Formula:    Area of a rectangle = width × length

Substitution:    Area = 2.5 mi × 5 mi

Answer:    Area = 12.5 mi²

Formula:   Area of a triangle = 1/2 × base × height

Substitution:   Area = 1/2 × (12 ft + 4 ft) × 5 ft

Answer:   Area = 40 ft²

Formula:  Area of a parallelogram = base × height

Substitution:   Area = 24 cm × 6 cm

Answer:   Area = 144 cm²

Formula:   Area of a parallelogram = base × height

Substitution:   Area = 7 m × 4 m

Answer:   Area = 28 m²

what is the question tho?

Answer:

sin Ф.

Step-by-step explanation:

Cos (-270) = cos 90 = 0 and sin(-270) = sin 90 = 1.

So cos ( Ф - 270) =   cos Ф cos (-270) + sin Ф sin(-270)

=  cos Ф * 0 + sin Ф * 1

= sin Ф.

Answer:

5.5 km/h

Step-by-step explanation:

→ 5% of 110

→ (5/100) × 110

→ 0.05 × 110

→ 5.5 km/h

Answer:

13%

Step-by-step explanation:

Total is 100 tickets sold as 13+87=100, 13/100 is 13%

The absolute maximum of the function is 184 and the minimum value of the function is -72.

If the graph of an absolute value function opens downward, the y-value of the vertex is the maximum value of the function.

Given the function f(x) = x⁴-18x²+9 at the interval [-5, 5], the absolute maximum and minimum values at this endpoints are as calculated;

At end point x = -5

f(-5) = (-5)⁴-18(-5)²+9

f(-5) = 625-450+9

f(-5) = 184

At end point x = 5

f(5) = (5)⁴-18(5)²+9

f(5) = 625-450+9

f(5) = 184

To get the critical point, this point occurs at the turning point i.e at

dy/dx = 0

if y = x⁴-18x²+9

dy/dx = 4x³-36x = 0

4x³-36x = 0

4x (x²-9) = 0

4x = 0

x = 0

x²-9 = 0

x² = 9

x = ±3

Using the critical points [0, ±3]

when x = 0, f(0) =  0⁴-18(0)+9

f(0) = 9

Similarly when x = 3, f(±3)=  (±3)⁴-18(±3)²+9

f(±3) = 81-162+9

f(±3) = -72

It can be seen that the absolute minimum occurs at x= ±5 and the absolute minimum occurs at x =±3

absolute maximum = 184

absolute minimum = -72

Hence, the absolute maximum of the function is 184 and the minimum value of the function is -72.

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Answer:

∠A≅∠X          AB≅XZ

∠B≅∠Z          AC≅XY

∠C≅∠Y          BC≅ZY

ΔABC≅ΔZXY

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

Answer: Explanation:The slope-intercept form of a linear equation is: y=mx+bWhere m is the slope and b is the y-intercept value.We can subtract 5x from each side of the equation to put the equation in slope intercept form while keeping the equation balanced:−5x+5x+y=−5x+40+y=−5x+4y=−5x+4Therefore:The slope is: m=−5The y-intercept is: b=4 or (0,4)

Step-by-step explanation:

Answer:

Slope m=-5  Y intercept=4 (-5,4)

Step-by-step explanation:

To get the slope you will need Rise over Run. 5/1 which is slope

which will make x=0 and y=4  which is y intercept.

Answer:

271 to 133

Step-by-step explanation:

Answer:

a = 9

Step-by-step explanation:

45 = 4(a + 3) – 3

Add 3 to both sides.

48 = 4(a + 3)

Divide both sides by 4.

12 = a + 3

Subtract 3 from both sides.

9 = a

a = 9

Answer: a = 9

Answer:

Possible base lengths are 1, 2, 3, 4, 5

Step-by-step explanation:

Area = base x height / 2

Let base be b

b x 8 / 2 < 24 (Area < 24)

4b < 24

b < 6

Answer:

A and C

Step-by-step explanation:

Because the numbers are smaller so you need to look for a bigger number than what the number you have is.

Answer:

looks like a triangle to me

Step-by-step explanation:

Answer:

A: 12

Step-by-step explanation:

Using the pythagoreom theorem, a^2+b^2=c^2. We can plug in the lengths of 5 and 13 which is 5^2+b^2=13^2. Now we can square the numbers to get 25+b^2=169. Subtract 25 from 169 to get 144. Now find the square root of 144 which is 12.

Answer:

Simplify????

1. 24x + 348

2. 4005p

3. 432

Step-by-step explanation:

Step-by-step explanation:

first one- 24x + 348

second one- 4005p

third one- 432

Answer:

12

Step-by-step explanation:

If there are 5 orange beads, and 3 purple beads, that means there is 8 beads that aren't pink in the bag.

If the rest are pink, and it's 3/5, that means 8 is 2/5. Divide by 2, and 4 is 1/5.

We can conclude that there are 12 pink beads, which is 3/5 of the total beads, by adding 2/5 and 1/5 (8 and 4)

The remaining 2/5 are the orange and purple beads.

Answer:

(A) ✔ 0.45

(B) ✔ 0.06

(C) ✔ 0.39

(D) ✔ 7.77

Step-by-step explanation:

Got it right, hope this helps!

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-5)]^2 + [-7 - (-4)]^2}\implies d=\sqrt{(3+5)^2 + (-7+4)^2} \\\\\\ d=\sqrt{8^2 + (-3)^2}\implies d=\sqrt{64+9}\implies d=\sqrt{73}[/tex]

Answer:

Step-by-step explanation:

ΔBOC is isosceles and M is the midpoint of BC

then

∠MOC = ∠BOM = 30°

then

∠BOC = 60°

……………………

OC // AB

then

∠ABO = ∠BOC = 60° (alternate-interior angles)

……………………………………………

In ΔOAB ,we have :

OA = OB and ∠ABO = 60°

Then ,

ΔOAB is an equilateral triangle.

then

∠AOB = 60°

……………………………

We get :

∠AOC = ∠AOB + ∠BOC = 60° + 60° = 120°

……………………………………………………

∠ADC = ∠AOC/2 = 120/2 = 60°

Answer:

The second and fourth choices.

Step-by-step explanation:

Probability of getting a blue marble = 0.25 = 1/4.

Therefore the number of blue bags will be 1/4 of the total of marbles.

The second choice has 10 blue marbles out of a total of 40, so this is one.

The 4th bag has 12 marbles of which 3 are blue. 3/12 = 1/4 so this is another answer which is correct.

Answer:

option 2 and 4

Step-by-step explanation:

add up all the values given then divide the number of blue given.

Answer:

3/8 gallons

Step-by-step explanation:

Let T be the total amount of water which can fill the bin.

The equation formed will be :

Now, multiply each side by 3 :

Divide each side by 2 :

Let the total gallons be x

Multiply 3 to complete whole bin

Step-by-step explanation:

The option "StartFraction 1 Over 3 Superscript 8" is correct

That is 138 is correct answer

Therefore [(2−2)(34)]−3×[(2−3)(32)]2=138

Step-by-step explanation:

Given expression is ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline)

Answer:

[tex]\frac{1}{81}[/tex]

Step-by-step explanation:

[tex](\frac{1}{3} )^{4}[/tex]

We know this is written as

[tex]\frac{1}{3}*\frac{1}{3}*\frac{1}{3}*\frac{1}{3}[/tex]

Let's solve:

[tex]\frac{1}{3} * \frac{1}{3} = \frac{1}{9}\\ \frac{1}{9} *\frac{1}{3} = \frac{1}{27} \\\frac{1}{27} * \frac{1}{3} = \frac{1}{81}[/tex]

Answer:

1. 20.724 or 6.6π

2.3.14 or π

3. 15.7 or 5π

4. 9.42 or 3π

5. 25.12 or 8π

6. 18.84 or 6π

Step-by-step explanation:

just ask :)

Answer:

2hours 20minutes

Step-by-step explanation:

hope this helps

Answer:

[tex]196 m^{2}[/tex]

Step-by-step explanation:

A square is a  shape that which all sides are equal

14 is one side of the square and to find the area of a square/rectangle, you do  length*width

14*14=196

Answer:

50

Step-by-step explanation:

100% - 8% = 92%

Proportions:

46 ⇒ 92%

A ⇒ 100%

A = 46*100/92

A = 4600/92

A = 50