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postnew [5]
2 years ago
9

A rhombus has a perimeter of 52 inches. It’s shorter diagonal is 10 inches in length. which of the following is the length of it

s longer diagonal?
Mathematics
1 answer:
Korolek [52]2 years ago
4 0

Answer:

ok it's a good question... so answer to that is... I also don't know..

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Help me please so I can turn this in
Ber [7]

Answer:

10y-12

Step-by-step explanation:

3 0
2 years ago
In a G.P the difference between the 1st and 5th term is 150, and the difference between the
liubo4ka [24]

Answer:

Either \displaystyle \frac{-1522}{\sqrt{41}} (approximately -238) or \displaystyle \frac{1522}{\sqrt{41}} (approximately 238.)

Step-by-step explanation:

Let a denote the first term of this geometric series, and let r denote the common ratio of this geometric series.

The first five terms of this series would be:

  • a,
  • a\cdot r,
  • a \cdot r^2,
  • a \cdot r^3,
  • a \cdot r^4.

First equation:

a\, r^4 - a = 150.

Second equation:

a\, r^3 - a\, r = 48.

Rewrite and simplify the first equation.

\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}.

Therefore, the first equation becomes:

a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150..

Similarly, rewrite and simplify the second equation:

\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}.

Therefore, the second equation becomes:

a\, r\, \left(r^2 - 1\right) = 48.

Take the quotient between these two equations:

\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}.

Simplify and solve for r:

\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}.

8\, r^2 - 25\, r + 8 = 0.

Either \displaystyle r = \frac{25 - 3\, \sqrt{41}}{16} or \displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}.

Assume that \displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}. Substitute back to either of the two original equations to show that \displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75.

Calculate the sum of the first five terms:

\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}.

Similarly, assume that \displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}. Substitute back to either of the two original equations to show that \displaystyle a = \frac{497\, \sqrt{41}}{41} - 75.

Calculate the sum of the first five terms:

\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}.

4 0
3 years ago
Determine the range of the following graph:
Allushta [10]

Answer:

Determine the range of the following graph:

12

11

O

10

9

8

7

6

5

NA

Step-by-step explanation:

(f+g)(x)

f(x)= x-3, g(x)= 2x+8

8 0
2 years ago
The sphere below has a radius of 2.5 inches and an approximate volume of 65.42 cubic inches.
Stells [14]

Part a: The radius of the second sphere is 5 inches.

Part b: The volume of the second sphere is 523.33 in³

Part c; The radius of the third sphere is 1.875 inches.

Part d: The volume of the third sphere is 27.59 in³

Explanation:

Given that the radius of the sphere is 2.5 inches.

Part a: We need to determine the radius of the second sphere.

Given that the second sphere has twice the radius of the given sphere.

Radius of the second sphere = 2 × 2.5 = 5 inches

Thus, the radius of the second sphere is 5 inches.

Part b: we need to determine the volume of the second sphere.

The formula to find the volume of the sphere is given by

V=\frac{4}{3}  \pi r^3

Substituting \pi=3.14 and r=5 , we get,

V=\frac{4}{3} (3.14)(125)

V=\frac{1580}{3}

V=523.3333 \ in^3

Rounding off to two decimal places, we have,

V=523.33 \ in^3

Thus, the volume of the second sphere is 523.33 in³

Part c: We need to determine the radius of the third sphere

Given that the third sphere has a diameter that is three-fourths of the diameter of the given sphere.

Hence, we have,

Diameter of the third sphere = \frac{3}{4} (5)=3.75

Radius of the third sphere = \frac{3.75}{2} =1.875

Thus, the radius of the third sphere is 1.875 inches

Part d: We need to determine the volume of the third sphere

The formula to find the volume of the sphere is given by

V=\frac{4}{3}  \pi r^3

Substituting \pi=3.14 and r=1.875 , we get,

V=\frac{4}{3} (3.14)(1.875)^3

V=\frac{4}{3} (3.14)(6.59)

V=27.5901 \ in^3

Rounding off to two decimal places, we have,

V=27.59 \ in^3

Thus, the volume of the third sphere is 27.59 in³

4 0
3 years ago
Find the value of x.
faust18 [17]

Answer:

          7 sqrt(3) =x

Step-by-step explanation:

We know that sin 60 = opposite / hypotenuse

                       sin 60 = x/14

Multiply both sides by 14

                          14 sin 60 = x

                        14 * (sqrt(3)/2) =x

                      7 sqrt(3) =x

8 0
3 years ago
Read 2 more answers
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