All categories

3 years ago

1+4=5, 2+5=12, 3+6=21, 8+11?

1 answer:

7 0

The answer is 96.
Solution:
1+4(5) = 5
2+5(7) = 12(5+7)
3+6(9) = 21(12+9)
4+7(11) = 32(21+11)
5+8(13) = 45(32+13)
6+9(15) = 60(45+15)
7+10(17) = 77(60+17)
8+11(19) = 96(77+19).

You might be interested in

I need help with part "C" and "D"

dmitriy555 [2]

3x²cos( x³ ) and 3sin²( x ) cos( x ) are the derivatives of the composite functions f(x) = sin(x³) and f(x) = sin³(x) respectively.

<h3>What are the derivative of f(x) = sin(x³) and f(x) = sin³(x)?</h3>

Chain rule simply shows how to find the derivative of a composite function. It states that;

d/dx[f(g(x))] = f'(g(x))g'(x)

Given the data in the question;

f(x) = sin(x³) = ?

f(x) = sin³(x) = ?

First, we find the derivate of the composite function f(x) = sin(x³) using chain rule.

d/dx[f(g(x))] = f'(g(x))g'(x)

f(x) = sin(x)

g(x) = x³

Apply chain rule, set u as x³

d/du[ sin( u )] d/dx[ x³ ]

cos( u ) d/dx[ x³ ]

cos( x³ ) d/dx[ x³ ]

Now, differentiate using power rule.

d/dx[ xⁿ ] is nxⁿ⁻¹

cos( x³ ) d/dx[ x³ ]

In our case, n = 3

cos( x³ ) ( 3x² )

Reorder the factors

3x²cos( x³ )

Next, we find the derivative of f(x) = sin³(x)

d/dx[f(g(x))] = f'(g(x))g'(x)

f( x ) = x³

g( x ) = sin( x )

Apply chain rule, set u as sin( x )

d/du[ u³ ] d/dx[ sin( x )]

Now, differentiate using power rule.

d/dx[ xⁿ ] is nxⁿ⁻¹

d/du[ u³ ] d/dx[ sin( x )]

3u² d/dx[ sin( x )]

Replace the u with sin( x )

3sin²(x) d/dx[ sin( x )]
Derivative of sin x with respect to x is cos (x)

3sin²( x ) cos( x )

Therefore, the derivatives of the functions are 3x²cos( x³ ) and 3sin²( x ) cos( x ).

Learn more about chain rule here: brainly.com/question/2285262

#SPJ1

4 0

1 year ago

The diameter of the base of the cone measures 8 units. The height measure 6 units. What is the volume of the cone?

ivolga24 [154]

Answer:

The volume of the cone is 100.48 units³ approximately

Step-by-step explanation:

To find the volume of a cone with a diameter of 8 unit and height of 6 units, we will follow the steps below;

first, write down the formula for calculating the volume of a cone

v= πr² $\frac{h}{3}$

where v is the volume of the cone

r is the radius and h is the height of the cone

from the question given, diameter d = 8 units but d=2r which implies r=d/2

r=8/2 = 4 units

Hence r= 4 units

height = 6 units

π is a constant and is ≈ 3.14

we can now proceed to insert the values into the formula

v= πr² $\frac{h}{3}$

v ≈ 3.14 × 4² × 6/3

v ≈ 3.14 × 16 × 2

v ≈ 100 .48 units³

Therefore the volume of the cone is 100 .48 units³ approximately

6 0

3 years ago

ASAP ANSWER PLEASE!! Name the relationship between the two angles a and b

Irina-Kira [14]

They’re complimentary angles (add up to 90)

5 0

3 years ago

Find q<br> (7q-46)<br> (3q+6)

kap26 [50]

Answer:

$q = 22$

Step-by-step explanation:

The angle measure of a straight line is (180) degrees As given in the picture, line (AC) is a straight line, thus its angle measure is (180) degrees. Angles (ABD) and (DBC) make up line (AC). Therefore, one can conclude that the sum of angles (ABD) and (DBC) is (180) degrees. Form an equation, simplify and use inverse operations to solve for the unknown parameter (q).

$($