In a 4 by 400 metres relay race, athletes A, B, C and D took 42.91 seconds, 42.95 seconds, 43.11 and 43.06…

Question

In a 4 by 400 metres relay race, athletes A, B, C and D took 42.91 seconds, 42.95 seconds, 43.11 and 43.06 seconds respectively to do their race. An average of one second is spent on each button exchange. Calculate the time they started the race if they completed at 8:24:36 p.m.

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4. Katika mbio za kupokezana za mita 4 kwa 400, wanariadha A, B, C na D walitumia sekunde 42.91, sekunde 42.95, sekunde 43.11 na sekunde 43.83 mtawalia kukamilisha mbio zao. Wastani wa sekunde moja hutumika kwa kila mabadilishano ya kijiti. Kokotoa muda walioanza mbio ikiwa walimaliza saa 8:24:36 p.m.

Kokotoa jumla ya muda wa kukimbia wa wanariadha wote.
$\text{Jumla ya muda wa kukimbia} = 42.91 + 42.95 + 43.11 + 43.83 = 172.80 \text{ sekunde}$
Kokotoa jumla ya muda uliotumika kwenye mabadilishano ya vijiti.
Kuna mabadilishano 3 ya vijiti (kutoka A hadi B, B hadi C, na C hadi D). Kila mabadilishano huchukua sekunde 1.
$\text{Muda wa mabadilishano} = 3 \times 1 = 3 \text{ sekunde}$
Kokotoa jumla ya muda wa mbio.
$\text{Jumla ya muda wa mbio} = \text{Jumla ya muda wa kukimbia} + \text{Muda wa mabadilishano}$ $\text{Jumla ya muda wa mbio} = 172.80 + 3 = 175.80 \text{ sekunde}$
Badilisha muda huu kuwa dakika na sekunde:
$175.80 \text{ sekunde} = 2 \text{ dakika na } 55.80 \text{ sekunde}$
Kokotoa muda wa kuanza mbio kwa kutoa jumla ya muda wa mbio kutoka muda wa kumaliza.
Muda wa kumaliza: 8:24:36 p.m.
Muda wa mbio: 2 dakika 55.80 sekunde.
Ili kutoa, tunahitaji kukopa kutoka dakika:
$8:24:36.00 \text{ p.m.}$ $- \quad 0:02:55.80$ $\text{Kukopa 1 dakika (60 sekunde) kutoka 24 dakika:}$ $8:23:(36.00 + 60.00) \text{ p.m.} = 8:23:96.00 \text{ p.m.}$
Sasa toa:
$8:23:96.00 \text{ p.m.}$ $- \quad 0:02:55.80$ $\text{Muda wa kuanza} = 8:21:40.20 \text{ p.m.}$
Muda walioanza mbio ni $\boxed{\text{8:21:40.20 p.m.}}$ .

15. Panua na rahisha: $(3x - 2y)^2 - (2y + 3x)^2$
Tumia fomula ya tofauti ya miraba, $A^2 - B^2 = (A - B)(A + B)$ .
Hapa, $A = (3x - 2y)$ na $B = (2y + 3x)$ .
Kokotoa $(A - B)$ .
$A - B = (3x - 2y) - (2y + 3x)$ $A - B = 3x - 2y - 2y - 3x$ $A - B = (3x - 3x) + (-2y - 2y)$ $A - B = 0 - 4y = -4y$
Kokotoa $(A + B)$ .
$A + B = (3x - 2y) + (2y + 3x)$ $A + B = 3x - 2y + 2y + 3x$ $A + B = (3x + 3x) + (-2y + 2y)$ $A + B = 6x + 0 = 6x$
Zidisha matokeo ya Step 2 na Step 3.
$(A - B)(A + B) = (-4y)(6x)$ $= -24xy$
Kupanua na kurahisisha hutoa $\boxed{-24xy}$ .

In a 4 by 400 metres relay race, athletes A, B, C and D took 42.91 seconds, 42.95 seconds, 43.11 and 43.06 seconds respectively to do their race. An average of one second is spent on each button exchange. Calculate the time they started the race if they completed at 8:24:36 p.m.

Answer

Step-by-step solution

Kokotoa jumla ya muda wa kukimbia wa wanariadha wote.

Kokotoa jumla ya muda uliotumika kwenye mabadilishano ya vijiti.

Kokotoa jumla ya muda wa mbio.

Kokotoa muda wa kuanza mbio kwa kutoa jumla ya muda wa mbio kutoka muda wa kumaliza.

Tumia fomula ya tofauti ya miraba, $A^2 - B^2 = (A - B)(A + B)$ .

Kokotoa $(A - B)$ .

Kokotoa $(A + B)$ .

Zidisha matokeo ya Step 2 na Step 3.

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More Mathematics Questions

In a 4 by 400 metres relay race, athletes A, B, C and D took 42.91 seconds, 42.95 seconds, 43.11 and 43.06 seconds respectively to do their race. An average of one second is spent on each button exchange. Calculate the time they started the race if they completed at 8:24:36 p.m.

Answer

Step-by-step solution

Kokotoa jumla ya muda wa kukimbia wa wanariadha wote.

Kokotoa jumla ya muda uliotumika kwenye mabadilishano ya vijiti.

Kokotoa jumla ya muda wa mbio.

Kokotoa muda wa kuanza mbio kwa kutoa jumla ya muda wa mbio kutoka muda wa kumaliza.

Tumia fomula ya tofauti ya miraba, A2−B2=(A−B)(A+B)A^2 - B^2 = (A - B)(A + B)A2−B2=(A−B)(A+B).

Kokotoa (A−B)(A - B)(A−B).

Kokotoa (A+B)(A + B)(A+B).

Zidisha matokeo ya Step 2 na Step 3.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Tumia fomula ya tofauti ya miraba, $A^2 - B^2 = (A - B)(A + B)$ .

Kokotoa $(A - B)$ .

Kokotoa $(A + B)$ .