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REY [17]
3 years ago
9

D=6, Dx=-6, Dy=-24, Dz=-30 what is the solution set

Mathematics
1 answer:
Elis [28]3 years ago
3 0

Answer:

  (x, y, z) = (-1, -4, -5)

Step-by-step explanation:

(x, y, z) = (Dx, Dy, Dz)/D = (-6, -24, -30)/6

(x, y, z) = (-1, -4, -5)

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A car travels a distance of d km in t hours. The formula that
V125BC [204]

Answer:

Direct Variation

Step-by-step explanation:

Given: A car travels at a distance of d km. The formula that relates d to t is d=kt

To find: kind of variation

Solution:

The formula that relates d to t is d=kt

Here, k is a constant of proportionality.

Constant of proportionality is also called as constant of variation.

d varies directly as t.

Therefore, this is a direct variation.

5 0
3 years ago
in a local coed softball keague, male to female ratio is 6:6. if there is 160 players in the league, how many are female?
Nonamiya [84]
80. Bc a 6:6 ratio is also a 1:1. So half of 160 them would be female.
4 0
3 years ago
For the following telescoping series, find a formula for the nth term of the sequence of partial sums
gtnhenbr [62]

I'm guessing the sum is supposed to be

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}

Split the summand into partial fractions:

\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}

1=a(5k+4)+b(5k-1)

If k=-\frac45, then

1=b(-4-1)\implies b=-\frac15

If k=\frac15, then

1=a(1+4)\implies a=\frac15

This means

\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}

Consider the nth partial sum of the series:

S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)

The sum telescopes so that

S_n=\dfrac2{14}-\dfrac2{5n+4}

and as n\to\infty, the second term vanishes and leaves us with

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17

7 0
3 years ago
A school paid $31.25 for each calculator. If the school bought x calculators, how much did they pay?
Katyanochek1 [597]

Answer:

31.25×

Step-by-step explanation:

suppose that the value of x was 3 . that would mean that they bought 3 calculators .

if one calculator is $31.25 then 3 would be $31.25× 3

the same rule would apply for x

7 0
3 years ago
Q5.Jumbo is standing on top of a cliff looking at a speed boat out at sea.The vertical of the cliff from the base (sea level) to
Leni [432]

Answer:

A) 150 m

B) 180.28 m

Step-by-step explanation:

A) In order to find the horizontal distance from the base of the cliff to the speed boat, use the Pythagorean theorem to calculate the length of the missing side.

We are told that one of the sides is 80 m and the hypotenuse is 170 m. Therefore,

  • a² + b² = c²
  • (80)² + b² = (170)²
  • b² = 170² - 80²
  • b² = 22500
  • b = 150

The horizontal distance between the base of the cliff and the boat is 150 m.

B) Now, the side that was 80 m is now 100 m (includes the height that the helicopter is above Jumbo). The horizontal distance remains the same, 150 m, but the hypotenuse is different. Solving for the hypotenuse will give us the distance between the helicopter and the speed boat.

  • (100)² + (150)² = c²
  • 32500 = c²
  • 180.28 = c

The distance between the helicopter and the speed boat is 180.28 m.

8 0
3 years ago
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