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Monica [59]
2 years ago
9

Complete the recursive formula of the arithmetic sequence 4, 22, 40,58, ....

Mathematics
1 answer:
dlinn [17]2 years ago
5 0

Answer:

b (1)= 4

b (n)= b (n-1)+ 18

Step-by-step explanation:

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A sphere has a decimeter of 12 ft what is the volume of the sphere? Give the exact value in terms of
meriva

Answer: 904.78 cu. ft

Step-by-step explanation:

Volume of sphere = 4/3 pi r^3

Assuming 12 ft. is the diameter of the sphere.

6 0
3 years ago
Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less
Sergio039 [100]

Answer:

The shortest side of the triangle is 18

Step-by-step explanation:

Let the sides the triangle be x, y and z.

From the question, the perimeter of the rectangle is 64, that is

x + y + z = 64 ...... (1)

Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)

The third side, z, is 20 less than the sum of the other two, that is

z + 20 = x + y ...... (3)

Substitute equation (3) into (1)

Then,

z + 20 + z = 64

2z +20 = 64

2z = 64 - 20

2z = 44

z = 44/2 k

z = 22

From equation (3)

z + 20 = x + y

Then, k

22 + 20 = x +y

42 = x + y

x = 42 - y ...... (4)

Substitute this into equation 2

3x = 4y

3(42-y) = 4y

126 - 3y = 4y

4y + 3y = 126

7y = 126

y = 126/7

y = 18

Substitute this into equation (4)

x = 42 - y

x = 42 - 18

x = 24

∴ x = 24, y = 18 and z = 22

Hence, the shortest side of the triangle is 18.

4 0
2 years ago
0.3(n-5)=0.4-0.2 solve for n!
mariarad [96]

Answer:

n = 5.67

Step-by-step explanation:

0.3(n-5)=0.4-0.2

0.3(n-5) = 0.2

Dividing 0.3 both side

\frac{0.3(n-5) }{0.3}  = \frac{0.2}{0.3}

n-5 = 0.67

n = 0.67+5

n = 5.67

4 0
3 years ago
Consider the logarithms base 5. For each logarithmic expression below, either calculate the value of the expression or explain w
Tom [10]

Answer:

log₅(3125) = 5

Step-by-step explanation:

Given:

log₅(3125)

Now,

using the property of log function that

logₐ(b) = \frac{\log(b)}{\log(a)}

thus,

Therefore, applying the above property, we get

⇒ \frac{\log(3125)}{\log(5)}   (here log = log base 10)

now,

3125 = 5⁵

thus,

⇒  \frac{\log(5^5)}{\log(5)}

Now,

we know from the properties of log function that

log(aᵇ) = b × log(a)

therefore applying the above property we get

⇒ \frac{5\log(5)}{\log(5)}

or

⇒ 5

Hence,

log₅(3125) = 5

8 0
3 years ago
Find the equation of all tangent lines having slope of -1 that are tangent to the curve y=(9)/(x+1)
fredd [130]

Answer:

f(x)=\frac9{x+1}\\ f'(x)=-\frac9{(x+1)^2}\\ f'(x)=-1\ \iff\ -\frac9{(x+1)^2}=-1\ \to \ \frac9{(x+1)^2}=1\ \to \ (x+1)^2=9\\ |x+1|=3\ \to \ x+1=3\ \vee\ x+1=-3\\ x_1=2\ \vee\ x_2=-4\\ f(x_1)=f(2)=\frac9{2+1}=3\\ f(x_2)=f(-4)=\frac9{-4+1}=-3

First tangent line:

y=f'(x_1)\cdot (x-x_1)+f(x_1)\ \to \ y=-1(x-2)+3\ \to \ y=-x+5

Second tangent line:

y=f'(x_2)\cdot (x-x_2)+f(x_2)\ \to \ y=-1(x+4)-3\ \to \ y=-x-7


Notice: slope of -1 means that both f'(x_1), \ f'(x_2) are equal to -1, so f'(x_1)=-1 \ and \ f'(x_2)=-1


6 0
2 years ago
Read 2 more answers
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