The volume of a cone is 400π cm3. The height of the cone is 12 cm.

What is the length of the radius of the cone?

Answer:

a) exponential growth   b) 8000  c) 1.02  d) f(x) = 8000(1+.05/4)^(4)(5)   e)  $11887.58

Step-by-step explanation:

This situation is exponential growth because the money will be increasing over time.  The initial amount is the amount invested in the beginning so in this case 8000.  The growth factor is found by 1+r/n where r is the rate and n is the number of compounds per year so 1 + .08/4 where the r is expressed as a decimal and compounding quarterly means 4 times per year.  The function is modeled by f(x) = P(1 +r/n)^nt.  Evaluating the function gives f(x) = 8000(1 + .08/4)^(4*5).

[tex]2.5x = 15[/tex]

[tex]x = \frac{15}{2.5} = 6[/tex]

Answer:

or Also

[tex] \frac{5}{2} x = 15 \\ 5x = 15 \times 2 \\ 5x = 30 \\ 5x \div 5 = 30 \div 5 \\ x = 6[/tex]

Answer:

270 sq. m [b]

Step-by-step explanation:

So the area of a triangle is 1/2 bh (1/2 of base x height).

The base of the triangle shown is 20m. The height is 27m.

(1/2) (20)(27) = 270.

The area of this triangle is 270 sq. m (b)

Step-by-step explanation:

2 m corresponds to 0.4 cm on a blueprint.

so,

2 m / 0.4 cm = 200 cm / 0.4 cm

our fun the point of view of the blueprint

0.4 cm / 200 cm

the scale on a map or blueprint is usually normed to one unit on the blueprint :

0.4/200 × f/f = 1/(200×f)

0.4 × f = 1

f = 1/0.4 = 2.5

so, our scale is

(0.4 × 2.5) / (200 × 2.5) = 1 / 500

that means 1 cm on the blueprint corresponds to 500 cm or 5 m in reality.

Answer:

sin M = [tex]\frac{12}{13}[/tex], tan M = [tex]\frac{12}{5}[/tex], cos M = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

The sine of an angle is equal to [tex]\frac{opposite}{hypotenuse}[/tex].  The opposite (opposite from the angle) side is 12 and the hypotenuse is 13.

The tangent of an angle is equal to [tex]\frac{opposite}{adjacent}[/tex].  The opposite side is 12 and the adjacent (next to the angle) side is 5.

The cosine of an angle is equal to [tex]\frac{adjacent}{hypotenuse}[/tex].  The adjacent (next to the angle) side is 5 and the hypotenuse is 13.

Answer:

(b1+b2)h divided by 2 is the formula for a trapezoid

Step-by-step explanation:

ANSWER: 468 ft (squared?)

Answer:

27

Step-by-step explanation:

a + b = 7

a - b = 3

2a = 10

a = 5

b = 7 - 5

b = 2

3⁵ / 3² = 3³ using law of indices

3³ = 27.

Answer:

27

Step-by-step explanation:

a + b = 7

a - b = 3

2a = 10

a = 5

b = 7 - 5

b = 2

3⁵ / 3² = 3³ using law of indices

3³ = 27

Answer:

1. 43.01 mm²

2. 13.82yd

3. 15.71cm

4.18.85m

5. 13.85m²

6. 8.17mm²

Step-by-step explanation:

/ means divided by

* means multiplied by

radius is half of a diameter

circumference of a circle is pi multiplied by diameter

area of a circle is pi multiplied by radius squared

1. radius is 7.4 divided by 2 which is 3.7

radius of 3.7 squared is 13.69

pi multiplied by 13.69 is 43.01

2. diameter is radius times 2

2.2 times 2 is 4.4

ℼ * 4.4 = 13.82

3. pi*5=15.71

4. pi*6=18.85

5. 2.1*2.1 = 4.41 -> pi*4.41 = 13.85

6. 1.3*2= 2.6 -> pi*2.6=8.17

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Answer:

Formula for volume of hemisphere;

V = 2/3 * π * [tex]r^{3}[/tex]

π - pi, which is 3.14 or 22/7

r = radius (half of the diameter/ 1/2 x diameter)

Since we are given the diameter, we find 1/2 of the diameter to find the radius.

1/2 x 8.9(diameter)

8.9/2 = 4.45 is our radi.

So now, we plug in this value into our equation.

V = 2/3 * π * [tex]r^{3}[/tex]

V = 2/3 * 22/7 * 4.45^3

V = 2/3 * 22/7 * 88.12

V = 2/3 * 276.95

V = 184.63 cubic centimetres.

Let the number to be added be A

Now,

[tex]\begin{gathered}\implies\quad \sf −5x^3 + 4x − 3 + A = x^2 − x − 1 \\\end{gathered} [/tex]

Transposing (−5x³+ 4x − 3 ) to other side-

[tex]\begin{gathered}\\\implies\quad \sf A = x^2 − x − 1 -( −5x^3 + 4x − 3) \\\end{gathered} [/tex]

Remember if there is a -ve sign before a bracket the signs of whole of the terms changes on opening bracket

[tex]\begin{gathered}\\\implies\quad \sf A = x^2 − x − 1 + 5x^3 - 4x + 3\\\end{gathered} [/tex]

Putting like terms together -

[tex]\begin{gathered}\\\implies\quad \sf A = 5x^3 +x^2 - x -4x +3 -1 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf A = 5x^3 +x^2 -5x +2 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Therefore, 5x³+x²-5x +2 should be added to −5x³+ 4x − 3 to get x²− x − 1

The function p(t) for the number of visitors over 1-year is an exponential function

The function is given as:

p(t) = 119 + (t-83)e^0.02t

Start by plotting the graph of the function p(t).

From the graph (see attachment), we have the parameters to be:

Hence, the function has no critical point

Read mroe about critical points at:

https://brainly.com/question/7805334

[tex] = (3x + 2)(x + 1) \\ = 3x(x + 1) + 2(x + 1) \\ = {3x}^{2} + 3x + 2x + 2 \\ = {3x}^{2} + 5x + 2[/tex]

Answer:

Step-by-step explanation:

I'll work on the left triangle first:

tan 20 = x /10

x = 10tan 20 = 3.64

cos 20 = 10/y

y = 10/cos20 = 10.64.

tan 70 = 12/x

x = 12/tan 70 = 4.37.

sin 70 = 12/y

y =  12/sin70 = 12.77.

Answer:

∠ SOU = 138°

Step-by-step explanation:

the opposite angles of a tangent kite are supplementary, sum to 180° , so

∠ SOU + ∠ STU = 180° , that is

∠ SOU + 42° = 180° ( subtract 42° from both sides )

∠ SOU = 138°

Answer:

[tex]3.5\times10^-^1^2[/tex]

Step-by-step explanation:

[tex](7 \times 10^-5) \times (5 \times 10^-8)[/tex]

Evaluate

[tex](7 \times 5)\times(10^-^5\times10^-^8)[/tex]

[tex]35\times10^-^5^-^8[/tex]

[tex]35\times10^-^1^3[/tex]

[tex]35\times10^1\times10^-^1^3[/tex]

[tex]3.5\times10^1^-^1^3[/tex]

[tex]3.5\times10^-^1^2[/tex]

Thus, the answer is [tex]3.5\times10^-^1^2[/tex]

~Lenvy~

Answer: -1

Step-by-step explanation:

Total time used= 15+45+30=90 mins

Initial time=7:45

final time will be 1 hr 30 mins more than initial Time

final time= 9:15 am

Answer:

a rhombus would have 2 pairs of parallel sides, or a parallelogram. (First image is parallelogram and second is rhombus)

Answer:

Alright so the answer is B but I'll explain why because im nice ig.

Step-by-step explanation:

So lets do some calcumalations.

We'll use 1 as n and should get an output of 3 to check these formulas. Since 1 is the first term and 3 is the first term value makes sense alright.

So 9^1-1 is 0 and any number to the 0 power is 1 so that wont work.

3(4)^1-1 = 3(1); that's the answer

4^1-1 = 1, + 3 = 4 so that wont work either

I hope this helps ya have a great afternoon

Answer:

Step-by-step explanation:

The volume of a sphere can be found using the formula ...

  V = 4/3πr³ . . . . . where r is the radius

__

The figure points to a diameter line and indicates 2.2 m. The arrowhead is in the middle of a radius line, making it easy to interpret the dimension as the radius of the sphere.

If 2.2 m is used as the radius, the volume is computed to be ...

  V = 4/3π(2.2 m)³ ≈ 44.58 m³

This agrees with your friend's volume, suggesting the diameter was used in place of the radius in the computation.

__

The correct volume, using 2.2 m as the diameter, is ...

  V = 4/3π(1.1 m)³ ≈ 5.57 m³

Answer:

diameter is half the value of circumference 15/2 =7.5 diameter

[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]

Let's solve ~ ☂

[tex]\qquad \sf  \dashrightarrow \: - 0.6(m + 1) = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: - (m + 1) = 3 \div 0.6[/tex]

[tex]\qquad \sf  \dashrightarrow \: - (m + 1) = 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: - m - 1= 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: - m = 5 + 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: - m = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: m = - 6[/tex]

I hope it helps ~

Answer:

1. -39/50

2. -0.77777

3. square root of 92

4. 9.73

Answer:

one gadget costs $15.80

Step-by-step explanation:

Let w = cost of one widget

Let g = cost of one gadget

Given:

⇒ 5w + 3g = 109.9

Given:

⇒ w + 4g = 75.7

Rewrite  w + 4g = 75.7  to make w the subject:

⇒ w = 75.7 - 4g

Substitute into  5w + 3g = 109.9  and solve for g:

⇒ 5(75.7 - 4g) + 3g = 109.9

⇒ 378.5 - 20g + 3g = 109.9

⇒ 378.5 - 109.9 = 20g - 3g

⇒ 268.6 = 17g

⇒ g = 15.8

Therefore, one gadget costs $15.80

To find the cost of one widget, substitute the found value for g into
w = 75.7 - 4g and solve for w:

⇒ w = 75.7 - 4(15.8)

⇒ w = 75.7 - 63.2

⇒ w = 12.5

Therefore, one widget costs $12.50

Answer:

0864

Step-by-step explanation:

The answer is 0864.

Hope it helps!

Study well!

Answer:

TRUE

Step-by-step explanation:

A:

16a^2-24a+9

16a^2-12a-12a+9

4a(4a-3)-3(4a-3)

(4a-3)(4a-3)

(4a-3)^2

(4a-3)^2

B: Use difference of squares method

(3a+5b)(3a−5b)

Part A: The length of each side of the square is (4a - 3) units.

Part B: The dimensions of the rectangle are (3a + 5b) units (length) and (3a - 5b) units (width).

Part A:

The area of a square is given by the formula A = s^2, where "s" is the length of each side of the square. In this case, the area is (16a² - 24a + 9) square units.

To determine the length of each side of the square, we need to factor the area expression completely and set it equal to (s^2).

The area expression is a quadratic trinomial: 16a² - 24a + 9.

To factor the trinomial, we look for two binomials that, when multiplied together, give us the original trinomial. The binomials will have the form: (ma ± b)(na ± c).

To factor 16a² - 24a + 9, we look for two numbers whose product is 16 * 9 = 144, and whose sum is -24 (the middle coefficient).

The two numbers are -12 and -12 because (-12) * (-12) = 144 and (-12) + (-12) = -24.

Now, rewrite the middle term (-24a) using -12a - 12a:

16a² - 12a - 12a + 9

Group the terms and factor by grouping:

(16a² - 12a) - (12a - 9)

Now, factor out the greatest common factor (GCF) from each group:

4a(4a - 3) - 3(4a - 3)

Now, notice that we have a common binomial factor of (4a - 3):

(4a - 3)(4a - 3)

Since both binomials are the same, we can rewrite it as (4a - 3)^2.

Now, set (4a - 3)^2 equal to (s^2):

(4a - 3)^2 = s^2

To find the length of each side (s), take the square root of both sides:

√((4a - 3)^2) = √(s^2)

4a - 3 = s

Therefore, the length of each side of the square is (4a - 3) units.

Part B:

The area of a rectangle is given by the formula A = length * width. In this case, the area is (9a² - 25b²) square units.

To determine the dimensions of the rectangle, we need to factor the area expression completely and identify the length and width.

The area expression is a difference of squares: 9a² - 25b².

To factor a difference of squares, we use the formula: a² - b² = (a + b)(a - b).

In this case, a = 3a and b = 5b:

9a² - 25b² = (3a + 5b)(3a - 5b)

Therefore, the dimensions of the rectangle are (3a + 5b) units (length) and (3a - 5b) units (width).

To know more about  square:

https://brainly.com/question/14790824

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