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3 years ago

Geometry. helppp!!! please explain this

Mathematics

1 answer:

Yuri [45]3 years ago

6 0

Answer: 10

----------------------------------------------

Explanation:

Segment TU must be congruent (equal in length) to segment UV in order for the angle TSV to be bisected by segment SU

Bisected = cut in half

So because TU = UV, we can say,

TU = UV
3x+18 = 4x+8
3x+18-3x = 4x+8-3x
18 = x+8
18-8 = x+8-8
x = 10

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7.29 divided by 90 is ?

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Step-by-step explanation:

7.29 divided by 90 = <u>0.081</u>

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2 years ago

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and t

WINSTONCH [101]

Answer:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.

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Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

$\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}$

Seperate the differential equation and solve for the constant C.

$\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}$

You have 100 rodents when:

$100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months$

You have 1000 rodents when:

$1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months$

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2 years ago

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Step-by-step explanation:

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2 years ago

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2 years ago

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Lera25 [3.4K]

Answer:

40 minutes

Step-by-step explanation:

Let c represent the number of minutes it would take colleen to finish the job when he is working alone. Hence, it can be represented by the equation:

$\frac{1}{c}+\frac{1}{c+20} =\frac{1}{24} \\\\Finding\ the\ L.C.M\ of\ the\ fraction\ to\ get\ 24c(c+20)\ as\ the\ L.C.M.\\Multiply\ the\ whole\ equation\ by\ 24c(c+20):\\\\\frac{1}{c}(24c(c+20))+\frac{1}{c+20}(24c(c+20)) =\frac{1}{24}(24c(c+20)) \\\\24c+480+24c=c^2+20c\\\\48c+480=c^2+20c\\\\c^2+20c-48c-480=0\\\\c^2-28c-480=0$

Solving the quadratic equation to get c gives:

c = -12 and c = 40

Since the time cannot be negative, hence c = 40 minutes.

It would take colleen 40 minutes to clear the yard of leaves alone

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3 years ago