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2 years ago

Please help with this question if possible.

Mathematics

1 answer:

alexandr1967 [171]2 years ago

3 0

Volume of the large pyramid = 1/3*(10)² *30= 1000 cm³
Height of the small pyramid that was cut = 30-15=15 cm
Volume of the small pyramid = 1/3*(5)²*15=125 cm³

Volume of the frustum = Volume large pyramid - volume small pyramid=
=1000-125=875 cm³
Answer is 875 cm³.

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At noon, ship A is 130 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast is

Hitman42 [59]

Answer:

answer = 12.87 km/h

Step-by-step explanation:

Given

Ship A is sailing east at 25 km/h = $\frac{dx}{dt}$

ship B is sailing north at 20 km/h = $\frac{dy}{dt}$

here x and y are the sailing at t = 4 : 00 pm for ship A and B respectively

so we get x = 4 ×25 =100 km/h

y = 4× 20 = 80 km/h

let z is the distance between the ships, we need to find $\frac{dz}{dt}$ at t = 4 hr

At noon, ship A is 130 km west of ship B (12:00 pm)

so equation will be

$z^2 = (130-x)^2 + y^2......................(i)\\put x = 100 and y = 80 \\\\we | | get \\$

$z^2 = 30^2 + 80^2\\z =\sqrt{7300} km/h$

derivative first equation w . r. to t we get

$2z\frac{dz}{dt} =$ $-2(130-x)\frac{dx}{dt}$ $+2y\frac{dy}{dt}$

$\frac{dz}{dt} =\frac{1}{z}[(x -130)\frac{dx}{dt} +y\frac{dy}{dt}]$

$\frac{dz}{dt} = \frac{( -20\times25 + 80\times20)}{\sqrt{7300} }$

$= \frac{1100}{85.44}\\ = 12.87km/h$

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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The School has budgeted $3,500 for an end- of -year party in the local park. The cost to rent the park shelter is $250. How much

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Answer:

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Step-by-step explanation:

1) Ask yourself: How much money is left to spend?

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3,500 - 250 = 3,250

- Find the total amount of money spent on gifts for students:

300 * 5.50 = 1,650

- Subtract the total money spent on gifts for students:

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2 years ago

What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9

skelet666 [1.2K]

Answer:

Step-by-step explanation:

Let $u^2=x^4\\u = x^2$

Subbing in:

$9u^2-2u-7=0$

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:

$9u^2-9u+7u-7=0$

Group together in groups of 2:

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Now factor out what's common within each set of parenthesis:

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We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:

$(u-1)(9u+7)=0$

Remember that $u=x^2$

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$(x^2-1)(9x^2+7)=0$

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring $(x^2-1)$ gives us that x = 1 and -1. The other set is a bit more tricky. If

$9x^2+7=0$ then

$9x^2=-7$ and

$x^2=-\frac{7}{9}$

You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:

$x=$ ± $\sqrt{-\frac{7}{9} }$

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Answer:

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